Land Acquisition

* FDI will lead to job losses. Small retailers and other small ‘Kirana store owners’ will suffer a large loss. Giant retailers and Supermarkets like Walmart, Carrefour, etc. will displace small retailers. * Supermarkets will establish their monopoly in the Indian market. Because of supermarket’s fine tuning, they will get goods on low price and they will sell it on low price than small retailers, it will decrease the sell of small retailers. Jobs in the manufacturing sector will be lost because foreign giants will purchase their goods from the international market and not from domestic sources. This has been the experience of most countries which have allowed FDI in retail. Although, our country had made a condition that they must source a minimum of 30% of their goods from Indian micro and small industries, we can’t stop them from purchasing goods from international markets as per WTO law. So after coming to India, they can reduce this 30% by litigating at the WTO.So far India has not allowed FDI in retail and allows these giants to operate stores which can deal only with registered business. For e. g. , Metro, a well known retailing giant of Germany is allowed to sell only to businesses which serve the front end customers like us. The retail industry can be divided into organized and unorganized sector. The organized retailing is which are backed by corporate giants like Reliance, Future etc. Unorganized retailing refers to the traditional shops which are basically no frills business.Organized sector can be compared to premium airlines whereas unorganized sector can be compared to low cost ones. However like in airline industry the unorganized sector contributes 98% of the total trade. However inspite of being well served by our home grown retailers, the government is toying up with the idea of opening retail for foreign companies. That brings us to the question on what exactly do they bring to the table. The answer is a lot of hear tburns and a little respite to the country in terms of managing the food produce in the country.

Another Accolade for Charter Arms Corp by Mike Royko

Laurence Bourgeois A00161609 March 12th, 2013 Analysis Essay In his essay â€Å"Another Accolade for Charter Arms Corp. â€Å", Mike Royko focuses not on John Lennon’s death, but on the type of gun that was used to kill him. He argues that the model of a gun makes a great deal of difference when killing someone. By ignoring the shooting of the celebrity, Royko uses irony to show how idiotic the debate on the gun is. He commences his essay by asking the readers â€Å"what difference does it make what kind of gun was used  ? and answers by saying that it indeed makes a great deal of difference. At this point, we know the author’s rhetorical strategy will consist on focusing on anything but the death of the famous musician. As mentionned before, Royko uses a lot of irony in his essay as a way of showing the readers how ludicrous the gun debate really is. Per example, in the beginning of his essay, Royko says  : â€Å"And when people become emotional about guns, as many do when somebody famous is killed, they tend to lump all guns together.They don’t show proper respect for an excellent gun, such as the Charter . 38. † By saying that this type of gun deserves respect, despite what it did to the famous superstar, the author is clearly trying to show no empathy for Lennon as a form of rhetorical strategy. Later on, he proceeds by saying  : â€Å"Now the Charter Arms Corp. has the unique distinction of having two famous people shot by one of their products, I wonder if they have considered using it in their advertising. Here, he takes his irony to another level by assuming the death of a celebrity should be something the company should be proud of and that advertising it would lead the customers to purchase the weapon. Using irony for this type of subject was a brilliant idea, but in this essay, Royko uses too much of it. Secondly, Mike Royko uses the model of the gun as an argument of his irony. He also constantly talks about the importance of the quality of the weapon.Per example, he mentions the incident that happened on network TV, where a reporter from CBS says that the gun used to shoot George C. Wallace was a â€Å"cheap handgun† and goes on by explaining how this was quite an insult for Charter Arms Corp. The author also talks about the fact that both shooters, Bremer and Wallace used the same gun to wound their victim and that the weapon did a good job. In another sample of his irony, Royko adresses Charter Arms Corp by saying  : â€Å"Once again, your product really did the job, gents. â€Å"To conclude, Mike Royko’s essay is initially an ironic piece of work written to make the readers realize that the main focus of a tragedy should be the victim, not minor details such as the weapon used to harm the person. In my opinion, this essay is a fine piece of work, but the author emphasizes too much on irony in a way that it shadows what the essay is actually about. Work Cited Royko, Mi ke. â€Å"Another Accolade for Charter Arms Corp. † The Broadview Anthology. 2nd ed. Ed. Laura Buzzard, Peterborough  : Broadview, 2011. 221-4.

A Long Way Gone

A Long Way Gone Shame BEA was an Innocent boy who enjoyed playing football, swimming in the streams, and even started a rap and dance group with his friends and older brother. The group discovered their love for rap music from old cassette tapes of O. P. P, Run D. M. C, and the Sugarbird Gang. Shame and Junior, along with their other friends cherished these few hip hop and rap cassette tapes. Shame constantly carried these couple tapes on him at all times. They choreographed dance routines and memorized all of the lyrics. The boys also entered a talent show In a close town.Shame, Junior, Tallow, and Mohamed have been singing and dancing to rap music since they first formed the group when Shame was only eight years old. They learned of rap during a visit to Mobile, where their fathers worked for an American company. They were transfixed by the music and returned to Mobile as often as they could to watch rap on their big television. Shame was shocked mostly because the black men could speak English so well and so quickly to the beat (Lisa). Shame and his group were inspired by the rap music. Music represented Seamless transformation Into the modern world.The entire group Is mesmeric by rap musicians. Music became a way to escape reality of the war, express themselves by writing lyrics, and it eventually saves their lives. Shame and the boys all worked together as a group to create music. They also started changing the way they would dress, act, and speak to be like these musicians. Shame and his friends were Just like any ordinary innocent group of young boys wanting to be like famous musicians. This Is why many readers of the book are attracted to Seamless character, because he is very relatable. Shame, Junior.Tallow, and Mohamed remind me of myself when I was their age (Essen). I would gather my neighborhood friends and pretend we were each a different member of Destinys Child. Just like Seamless group of friends, we would play dress up to look like them, attempt to memorize their dances, and mimic exactly how Destiny Child would act. My friends and I even had battles against my older brother and his group of friends who literally thought they were the real members of the boy band, NCSC. This goes to show exactly how young and innocent Shame and his friends really were. Throughout the book, A Long wayGone, rap music plays an extremely important role in saving Seamless life. While the boys are traveling one day, a group of large, muscular men Jump out from the bushes, holding up their machetes and hunting rifles. These men are the voluntary guards of the village and were ordered by their chief to bring Shame and his friends back to the village. They are Immediately tied up In the village and questioned. Even though the boys continue to Insist they are not rebel soldiers, the chief does not believe them. The chief would not believe the boys until they discovered a rap cassette tape in Seamless pocket.The chief forces Shame to explain the rap music. Shame was instructed to sing and dance to O. P. P by Naughty by Nature and l Need Love by AL Cool J. The chief is still cautious of the boys until a young boy from the village admits to knowing Shame and his friends. The boys are untied and the village surprisingly feeds them and even offers them a place to stay. Knowing that Shame should have been happy that the boy saved his life, but he could not be happy because he believed that happiness was fragile. The other boys tried to cheerShame up by playing Bob Marbles Three Little Birds and singing him the lyrics dont worry about a thing, cause every little thing is goanna be all right (Lisa). Seamless first breakthrough in rehabilitation at the Benign House was when his nurse, Esther, buys him rap cassette tapes and a cassette player. He was upset about it at first, but once the music hit his ears, Shame started opening up talking about his past for the first time to Esther. He talked about when he was shot in the foot during battle and needed the bullets surgically removed without anesthesia.He explains how he was given cocaine after fainting from the pain and how he also had to kill the men who shot him. Esther was crying sympathetically and comforts him (Nassau). Every time that Esther uses music in Seamless therapy, he is able to talk about his memories. Eventually, he starts looking forwarded to his therapy sessions with Esther. She encourages him to start writing music again and gives him a notepad. Shame does not trust anyone, because he is used to relying on himself to survive. This lack of trust in anyone is due to Shame being betrayed by the only arson that he did trust, the lieutenant.When Esther tries to gain a friendship with Shame, he avoided it at first. Every time he thinks about memories of his childhood, he gets a headache from the war flashbacks. The only thing that seemed to help him gain a peaceful mind was the music. When Shame loses himself in the beat off song, he is avoiding thinking about the painful memories of war. It was the music that helped him heal and to open up about his past. Shame has another breakthrough when he actually trusts Esther for the first time.

Philosophy Essay Example | Topics and Well Written Essays - 2500 words - 2

Philosophy - Essay Example affected by an action are to be taken into account and given the same weight as the like interests of any other being.†3 As a result, no distinction is to be made between the rights of human beings and the right of animals, and according preferential treatment to human beings as opposed to animals would be morally and ethically a wrong principle. However, the question that arises in this context is, can animals be ascribed a moral status that is equal to human beings? They are sentient beings just like us and they also feel pain, therefore it would be morally and ethically wrong to kill them or cause them pain. Should they then be accorded equal consideration as human beings in terms of the rights that are accorded to them? Singer has defined specicism as â€Å"a prejudice or attitude of bias towards the interests of members of one’s own species and against those of members of other species.†4 As a result, human beings apply a double standard, whereby human beings are accorded a privileged moral status while non humans are not. According to Wise, human rights are a function of human autonomy, which implies a high level of moral reasoning, and such autonomy cannot exist independently of human dignity.5 Since animals do not possess this power to reason and make moral choice, this implies that they are on a plane that is inferior to human beings. Cohen argues that a person who is entitled to a right should be in a position to recognise â€Å"possible conflicts between what is in their own interest and what is just. Only in a community of beings capable of self restricting moral judgments can the concept of a right be correctly invoked.† On this basis, he also rejects Singer’s argument which argues for animals to have equal rights, on the basis that mentally regressive human beings are incapable of moral judgments and yet are accorded rights. Cohen states instead that the test for moral judgment cannot be one that is â€Å"administered to humans one by one.†6

Can Disability, Chronic Conditions, Health and Wellness Coexist Essay

Can Disability, Chronic Conditions, Health and Wellness Coexist - Essay Example Additional activities that enhance the physical well-being incorporate the avoidance of drug abuse and maintenance of proper hygiene. . According to Wright & Ellis (2010), mental health is the cognitive and psychological well-being. People with good mental health do not have psychological disorders acknowledge their abilities and can easily manage the stress emerging from daily processes. Additionally, they can improve the community financial status by working productively. Countries that are able to maintain good health through the provision of proper health care are very productive. Most developing countries do not have proper health care facilities and this contributes to slow rate of economic development. This is because they spend a lot of money trying to control diseases instead of using the money to development the country. According to Wright & Ellis (2010), environmental conditions, genetics, income levels, educational levels, and relationship with other individuals in the society determine good health. Illness is a negative occurrence that causes suffering and hinders proper body functioning. According to Wright & Ellis (2010), it is the major cause of death in the world. The two types of illnesses are chronic and curable. The curable illness can be treated and prevented with proper medication. Malaria is an example of curable illness. Illnesses can affect the financial systems of many countries (Wright & Ellis, 2010). Optimum health is the highest level of mental and physical well being that one can achieve. It is the total absence of both curable and chronic disease (Rankin, London & Stallings, 2005). One can reach optimum physical health if he effectively prevents diseases by maintain good nutritional habits and physical exercises. Moreover, optimum mental health can be achieved through effective management of stress and maintaining a good relationship with other people (Rankin, London &

Prescription, Nonprescription, and Herbal Medication Research Paper

Prescription, Nonprescription, and Herbal Medication - Research Paper Example As the essay declares the aging process is defined by numerous impairments of several regulatory processes that play a critical role in cells and organs. In addition, other physiological changes are evident in advanced age, and have the capacity to affect the absorption, distribution, metabolism, and excretion of drugs. The geriatric population exhibits cardiac dysfunctions. The relaxation and contraction of heart muscles change remarkably a one ages. Blood flow becomes slower, a factor that may affect drug distribution. In addition, aging brings about the reduction of renal mass. Fewer nephrons define the reduction of renal mass. According to the research findings there is a notable delay in the kidney functions, a factor that affects the elimination of drugs. The gastrointestinal system is also affected by aging because elderly people have lower rates of hydrochloric acid and pepsin. Research has highlighted that aging may contribute to potential changes in the enzyme secreting cells or hormonal glands a factor that minimizes the efficiency of the gastrointestinal system. In the small intestines, absorption of some substances reduces with age, while in the colon, the transit time may prove to be slower. Other digestive enzymes such as lipase and trypsin usually decrease as one age. The liver is a critical organ in the metabolism of drugs. With advancing age comes a remarkable reduction in the liver blood flow. In other cases, the liver structure may change over time while enzymes may cease to function effectively.

Personal statement Essay Example | Topics and Well Written Essays - 250 words - 11

Personal statement - Essay Example After completing my Law degree, I was able to work with several voluntary organisations that helped me discover my passion in helping others. Presently, I work for a voluntary organisation, Cocoa African Community Connection, which is located in Birmingham. My duties as a language interpreter and helping the refugees and victims of torture with immigration, housing, social and family issues has been an eye opener into the kind of activities that I would like to engage in the future. I have realised that I could make a significant impact in the lives of the refugees’ children by teaching French in the local Primary school. I am fluent in French, as it is my first language, therefore, ensuring that these kids have acquired the knowledge that will help them become self-sustaining. I have realised teaching French in the primary school will help many children into understanding other cultures and enable them communicate with others effectively. This will help them obtain better lives, thus contributing to a better world. I am able to work in teams, possess excellent planning and organising skills, and I can work under intense pressure. This means that the children will be in capable hands, as I will work effectively to ensure that they obtain quality

Acting style Essay Example | Topics and Well Written Essays - 500 words

Acting style - Essay Example An acting style is the way a play is presented or the way an actor portrays his character. Â  It can refer to quite a few different things - like period acting (roles that take place in a different earlier, era, place or society), or stylized acting (such as the very specific styles used Restoration comedies etc.), or it may refer to verse acting (such as Shakespeare), or proper classical acting (such as ancient Greek plays), or to the early "declaiming" acting (a very stiff, presentational style directly aimed toward the audience), or to modern-day acting (such as we see today in contemporary comedy and drama where actors act realistically). Â  Two major classifications of acting style can be made as presentational and representational. Where representational refers to modern realistic acting and representational refers to the more formal or exaggerated acting styles of old (Kernodle) In 1971, Alan Schneider directed an historic video taped performance of Samuel Becketts Krapps Last Tape, starring Jack MacGowran. The play dramatized an old mans struggle to repossess his youth by searching through reels of audiotape. The style of acting adopted by MacGowarn is simple and realistic as is characteristic in contemporary cinema. He conveys the old mans age and disability (he is nearly half-blind) through body movements and literally no dialogue at all. There are no other actors and the only props are a single table and chair in an otherwise empty room. The film is totally focused on the old man and his every expression. MacGrowan uses his facial and subtle body movements to convey his infirmity and even the joy and difficulty at eating a banana is emoted with great ability and expression in total silence. In 1964 Camera Three, New York, NY produced a short film featuring James Cahill, John Heffernan & Roy Scheider based on excerpts from Ben Jonsons 17th century comedy of

I stand here ironing Essay Example | Topics and Well Written Essays - 1750 words

I stand here ironing - Essay Example This process begins when she receives a note from the school counselor saying: "She's a youngster who needs help and whom I'm deeply interested in helping." Emily was a bright child as the mother recalls: "She was a beautiful baby. She blew shining bubbles of sound. She loved motion, loved light, loved color, and music and textures. She would lie on the floor in her blue overalls patting the surface so hard in ecstasy her hands and feet would blur. She was a miracle to me, but when she was eight months old I had to leave her daytimes with the woman downstairs to whom she was no miracle at all, for I worked or looked for work and for Emily's father who "could no longer endure" (he wrote in his good-bye note) "sharing want with us." (p. 9) From this it becomes clear that the mother recognizes that she was unable to give Emily the attention she needed. When she says that Emily was a miracle to her but not to the woman downstairs, she reflects her guilt for having left her daughter in the care of someone who didn't or could not love her as much as she deserved. Emily has now turned into a woman who keeps much to herself. She doesn't like sharing her life with her mother because she has somehow come to accept that this is the kind of relationship she has with her mother. The mother on the other hand would want deeper connection with her daughter but understands that since Emily had always been treated with anxious and not generous love, her growth was instilled with insecurity. She loves her daughter, wants to be a part of her life but knows it is no longer possible. Looking at Emily now as she enters the house, the mother observes: "She is coming. She runs up the stairs two at a time with her light graceful step, and I know she is happy tonight. Whatever it was that occasioned your call did not happen today" (p. 19) Through stream of consciousness, we gather several important things about their relationship and what caused a deep strain on it. For one, we learn that mother is guilty for not providing her first child with generous attention but she also understands why she was unable to do so. Emily's father had left when she was only one, her mother had to learn to adjust herself into a new household with a new husband and as other children came, Emily went deeper into the back. And the mother also blames her lack of knowledge for the child's strained growth. At one point she says: "I did not know then what I know now" (p. 11) and "What in me demanded that goodness in her" (p. 12) - meaning she is using her present knowledge to assess and understand her past behavior and that of her daughter's as well. Mother is the central character in the story and Emily is what she constructs for us. It is through her consciousness that we construct Emily or have an image of her. She is a nineteen year old who is not close to her mother at all. The mother was approached by school counselor as they felt that Emily was disturbed and needed help but while the mother would love to help, she is basically clueless. Clueless not because she doesn't know what is causing her present behavior but because she has no idea as to how it can be effectively influenced. "You think because I am her mother I have a key, or that in some way you could use me as a key She has lived for nineteen years. There is all that life that has happened outside of me, beyond me" (p. 9). Outside of me and beyond me are key terms

Terrorism Essay Example | Topics and Well Written Essays - 1000 words - 1

Terrorism - Essay Example Terrorist acts committed by women and children are becoming a widespread phenomenon. Joann Chesimard is a perfect example. Terrorist groups understand that it is much easier to commit a terrorist act if you are a charming woman or a little child. People usually do not tend to suspect women and children in being capable of committing a violent act. Thus, terrorists can reach their goals easier. Certainly, the representatives of fair sex, and especially little children, can be criminals and victims at the same time, because many of them are forced to commit terrorist acts or they can be imposed upon by some religious believes with this purpose. (Hoffman, Inside terrorism 3). 2. Hezbollah brought too much violence to the world in the past, so its present activity must also be considered as violent. Terrorist organization is the one that uses terror to achieve certain goals, but terror may have different forms (Hoffman, "The Logic of Suicide Terrorism"41). Notwithstanding that now the or ganization does not commit terrorist attacks, it still wants to have much power by controlling its own TV stations and news channels. Terrorists try to impose their influence on different governments that testifies about their desire to have much power. People should not trust the individuals who were terrorists in the past. Their behavior may turn to violent any moment, thus, European Union is quite right blacklisting them. 3. If we talk about the difference between the terrorism in Europe and in the United States, we should recognize that the terrorism itself and the tactics of struggling with it are very different in both continents. The difference is connected with the way terrorism is treated and the history of terrorist attacks. It is a well-known fact that the goal of the United States is to influence Muslims and impose western values upon them. The goal of the US is very understandable as Muslims’ behavior is sometimes cruel and violent, so it would be better if they accept some western values. However, Muslims value their culture and religion very high and are not going to lose their values or substitute them. They got used to the way of life they conduct, thus, they try to resist the imposed changes. For example, the terrorist act of September 11, 2001, was the Muslims’ response to the United States politics in their countries. Thus, the main goal of the United States regarding terrorism is not to prevent further attacks, but to defeat terrorism as a phenomenon, to eliminate terrorist groups in the bud (Campbell 2). Speaking about Europe, the attitude to terrorists there is very different. If the United States, as a more democratic country, tries to help Eastern countries become more developed, Europeans are just proud of their culture and consider it to be much better than a Muslims’ one. Therefore, Europeans consider terrorism to be the act of the â€Å"wild† part of the world against civilization. Thus, the tactics of s truggling with terrorism in Europe is directed on providing Europeans with necessary protection and on the prevention of further attacks. Thus, it we talk about terrorism, we should recognize that the politics of the United States is more aggressive due to the number of reasons, while the politics of Europe has a somewhat defensive character. 4. The main task of mass media is to

How to Lose Weight Rough Draft Essay Example for Free

How to Lose Weight Rough Draft Essay In this essay I will discuss the different ways there are of losing weight. For some it may be simple excersize and for others they may need more help then just excersize. We will go over the different ways that your body works to metabolize what your eating so that your body will help you to lose that weight. The process of losing weight can be a hard one, but if you choose the right one it can be easy. There are lots of options. Body: There are lots of options for losing weight but first I want to talk about metabolism first. Metabolism is what processes your food at a certain speed. If you have a high metabolism youll find that your food will process at a very fast rate and youll be using the restroom pretty quick right after you eat. Metabolism also plays a big part in your figure also. If you eat nothing but greasy fattening food then your metabolism will have issues keeping up. So in order for your metabolism to be where you want it you have to stay fit and eat correctly. The next thing I want to talk about is dietary pills. These can help if used correctly. Some people think they can take them without having to do any excersize or eating right. For some diet pills this is correct but others no. Its always important to keep your health in general up by eating the correct food and keeping yourself physically fit. There is also the danger of taking too many or not eating with them. If you take too many then you have the risk of possibly overdosing and your body becoming intolerant to them. And if you don’t eat with them in your system then you come up with the risk of malnutrition. So I would suggest that anyone who takes them only takes the amound suggested on the bottle. Ok now were going to go to dietary foods. This is important for any sort of situation you decide to diet with. If you don’t use dietary food then you probably shouldn’t diet. Because your body has to become fit all over again. To become fit it has to ingest nutrients and vitamins that fruits, vegtables and meats carry. The last and final subject I want to cover is surgery as a possible resource. They have different surgeries that can help in a lot of different situations. If your dieting and excersizing and trying everything possible and you still cant lose weight then I would suggest the surgery. There are little health risks from it and it Ive heard that the lap band surgery has had amazing results. Conclusion: These are the options that I have researched for How to lose weight. The options that I have researched are diet pills, excersizing, eating healthy and surgeries. With these options anyone can become a healthier person.

Cultural Narcissism Essay Example for Free

Cultural Narcissism Essay Is then American culture breeding a society of narcissists fueled by the self-esteem movement that commenced in the 1970s? Is the current state of constant mainstream media coverage on overly exuberant celebrities flaunting their wealth, along with the ability of anyone to post their private lives on the internet for public viewing making narcissism the norm? Can narcissism as a personality disorder be applied dimensionally to an entire culture in a social psychology context? This paper will explore theories on cultural narcissism, the roots of narcissism dating back to the 16th and 17th centuries when the first individualism movement emerged, and how in recent history focus has again shifted on the individual with the dawn of the self-esteem movement of the 1970s, its resulting effect on current generations, and potential effect on future generations in the form of cultural narcissism. Is American Culture Breeding a Society of Narcissists? There is an assertion in cultural theory that the current cultural trend in America is fueling a narcissistic society, but that according to psychoanalytic theory, narcissism can only be applied to an individual as a diagnosed personality disorder that develops during childhood (Morales, 1995). Therefore, can narcissism be applied to define the state of an entire culture in in a social psychology context? In the DSM-IV-TR, narcissism is defined as a personality disorder consisting of a â€Å"pervasive pattern of grandiosity (in fantasy or behavior), need for admiration, and lack of empathy . . † with at least five criteria that must be met in order to be diagnosed with a narcissistic personality disorder; for example, having a â€Å"grandiose sense of self-importance,† a belief that one is â€Å"special,† possessing a â€Å"sense of entitlement,† a desire for â€Å"success, power, brilliance, beauty or ideal love,† and a desire to associate with onl y those who are of â€Å"high-status† in society (American Psychiatric Association, 2000, p. 294). However, the Narcissistic Personality Inventory (NPI) test developed by social psychologists, is used for broad spectrum dimensional assessment of the general population to measure narcissism in a social context and has been quite reliable in measuring narcissism in society (Foster amp; Campbell, 2007). To understand theories in the development of individual narcissism, Sigmund Freud in his 1914 essay ‘On Narcissism: an introduction’ (as cited in Crockatt, 2006, p. 5), proposes primary narcissism occurs in every child as a stage of development, thereby suggesting each and every person is prone to develop narcissism at that stage. Later, Heinz Kohut (1913 1981) proposed his own views on the etiology of narcissism and focused on development of the self in conjunction with the narcissistic self-object, and if a child’s narcissistic wishes are not treated with empathy by the self-object, narcissistic problems ensue (as cited in Meronen, 1999). Historically it is conceivable, according to Trzesniewski, Donnellan, amp; Robins (2008), that the root of cultural narcissism dates as far back as the 17th century at which time the individualism movement in Europe was born. Suggesting that the movement began earlier, Leeds (2004, p. 109), refers to essays written by Morris Croll (1921 amp; 1927) who emphasized that during the 16th century a â€Å"new movement† shifted the focus to â€Å"inner and individual life of men in contrast with the plausible and public forms of their social existence,† and that this earlier movement essentially took away from societal structured religious practice and redirected focus toward individual, internal, and self-experiences.

Criminal Theory Case Study: Whitey Bulger

Criminal Theory Case Study: Whitey Bulger Criminal Behavior James Joseph Bulger III (better known as) Whitey Bulgers criminal behavior started early on in life. Whitey ran away to join the circus at ten years old. According to Biography.com, Whitey Bulger was first arrested when he was 14 years old, for stealing, and his criminal record continued to escalate from there. As a youth, he was arrested for larceny, forgery, assault and battery, and armed robbery and served five years in a juvenile reformatory. Upon his release, he joined the Air Force where he served time in military jail for assault before being arrested for going AWOL. Nonetheless, he received an honorable discharge in 1952. (Biography.com) After the military, Bulger returned to Boston and committed multiple bank robberies in multiple states. In 1956 he was sentenced to 25 years in Federal prison for those bank robberies. After his release from prison Bulger immersed himself into Bostons organized crime, and by 1979 he was one of the top figures in Bostons underworld. After work ing with the FBI, he led the FBI on a 16-year manhunt. Whitey Bulger was finally caught by the FBI in 2011. In 2013, Bulger faced a 33-count indictment, including money laundering, extortion, drug dealing, corrupting FBI and other law-enforcement officials and participating in 19 murders. He was also charged with federal racketeering for allegedly running a criminal enterprise from 1972 to 2000. (Biography.com) Bulger was not convicted of everything, after a two-month trial, a jury of eight men and four women deliberated for five days and found Bulger guilty on 31 counts, including federal racketeering, extortion, conspiracy and 11 of the 19 murders. They found he was not guilty of 7 murders and could not reach a verdict on one murder. (Biography.com) Whitey Bulgers Life Whitey Bulgers childhood was rough. James Joseph Bulger Jr. was born on September 3, 1929, in Dorchester, Massachusetts, (Where I was born) as second of the six children, to Roman Catholic Irish parents who immigrated to America. (www.thefamouspeople.com) Whiteys father was a longshoreman that lost his arm in an industrial accident forcing him and his family to move to government housing in South Boston (Where I attended elementary school). When Bulger was ten years old, he attempted to run away and join the circus. When Whitey was 14, he was charged with stealing and forgery and other crimes resulting in being held in a juvenile reformatory for five years. Bulger joined the Air Force and was charged with AWOL ultimately being honorably discharged. Once Bulger returned to Boston, he returned to a life of crime and ultimately rose to the top crime boss in Boston. Bulger reigned over Bostons underworld for nearly 20 years. Oddly enough he was an informant for the FBI against another cr ime family which ultimately help Bulgers enterprises. When indictments against Bulger came down his connections at the FBI tipped him off to the impending arrest allowing Bulger to go on the run from 1996 until he was ultimately arrested in California 2011. Bulger was convicted of most of the charges levied against him, and he is currently incarcerated at Coleman Federal Penitentiary in Sumter County. Bulger was disciplined for sexual activity while in prison in 2016. Theories of Criminal Behavior I believe that the first of three theories that could describe White Bulgers criminal lifestyle would be Albert Cohens Theory on Delinquent Boys. Cohens research and resulting theory were a reaction to the limitations and oversimplifications he saw in Robert Mertons strain theory, according to the University of Portsmouth. Cohen agreed that criminal behavior was in part the result of the strain of being unable to accomplish ones goals, but he disagreed with Mertons hypothesis that crime was individual, gain-based and could occur at any socioeconomic status. In 1955, his book Delinquent Boys, Cohen investigated trends of criminal behavior in lower-class urban areas of the United States, then built on emerging findings about the delinquent subculture. Florida State Universitys College of Criminology and Criminal Justice states that Cohens investigation of gangs revealed that the groups were mostly lower-class males who seemed to be retaliating against a world that had given them empty promises regarding the American Dream. Cohens theory on the delinquent subculture also predicts that the existence of the subculture would likely draw in lower-status persons exposed to it, therefore creating more delinquency among anyone who might believe that their only opportunities for progress existed in the ranks of gangs. (www.reference.com) I believe Whitey Bulger also fit into the Durkheims Deviance theory, à ¢Ã¢â€š ¬Ã‚ ¦his discoveries were so deviant that people had a hard time accepting them. And they still do! Which is why Durkheims views of deviance have been pretty much ignored by sociologists for over 100 years. Durkheim was a firm believer in observation. So he began his study of deviance by observing as many societies as he could. He studied his own, those in neighboring European countries, and even those of the ancient past. What did he notice? They all had deviance! It didnt matter where or when he looked. In every society, there was something that got defined as deviant, and someone who did that deviant thing. (http://www.nonjudgmentday.org) I also believe that Whitey Bulger would fit into the Social Disorganization Theory. The theory of social disorganization states a persons physical and social environments are primarily responsible for the behavioral choices that a person makes. At the core of social disorganization theory, is that location matters when it comes to predicting illegal activity. Shaw and McKay noted that neighborhoods with the highest crime rates have at least three common problems, physical dilapidation, poverty, and a higher level of ethnic and culture mixing. Shaw and McKay claimed that delinquency was not caused at the individual level, but is a normal response by normal individuals to abnormal conditions. Social disorganization theory is widely used as an important predictor of youth violence and crime. (Mark Bond, Ed.D) There is little doubt that South Boston or Boston, in general, could fit this theory just as well as Chicago. Theoretical Application to Whitey Bulgers Life History Growing up in South Boston with a father that was a longshoreman and that was ultimately disabled allowed Whitey to do as he pleased and he did just that fitting the Albert Cohens Theory on Delinquent Boys. As a young man, Whitey was arrested for assault and battery, armed robbery, larceny, and assault. Those charges resulted in Whitey being sentenced to five years in a juvenile reformatory. After his release from the reformatory, Whitey joined the Air Force and subsequently went AWOL. Despite this, he was granted an honorable discharge. I included the military factor in this theory because as we know, men dont fully mature until at least 25 years old. Due to Whiteys now developed deviant behavior as a youth, I believe that he fits into Durkheims Deviance theory. As we all know there is deviance everywhere and I think that during Whitey Bulgers criminal rise he just took advantage of the deviance and rose to the top of Bostons underworld. Some say his power made him like a Robin Hood for the city, For years, James Whitey Bulger was viewed as a Robin Hood-like figure on the streets of South Boston, valued by his neighbors who saw him as a tough guy who kept drug dealers out of their neighborhood. That image was shattered when authorities began digging up bodies. (www.boston.cbslocal.com) Finally, Whitey Bulgers criminal activities fit in my opinion into the Social Disorganization Theory. Boston, like Chicago, was ripe for the picking when it comes to poor neighborhoods, high crime rates, socially disadvantaged people. Whitey dominated a city that had many poor areas that were very ethnically diverse just like Chicago. The mixture of these three theories, I feel, created Whitey Bulger. In my opinion, many of these theories are interchangeable and could fit almost any powerful crime figure. The mixture of these three theories, I feel, created Whitey Bulger. In my opinion, many of these theories are interchangeable and could fit almost any powerful crime figure. References http://www.biography.com/people/whitey-bulger328770#early-life http://www.thefamouspeople.com/profiles/whitey-bulger-5588.php#5aP3OvO2zXd6OAzH.99 https://www.reference.com/world-view/albert-cohen-s-delinquent-subculture-theory-56a567cc29ecb061 http://www.nonjudgmentday.org/judgment-card-galleryblog/-durkheims-deviant-view-of-deviance https://www.linkedin.com/pulse/criminology-social-disorganization-theory-explained-mark-bond http://boston.cbslocal.com/2011/06/23/whitey-bulger-described-as-robin-hood-diabolical-killer/

Transplants and Diabetes :: essays research papers

Three Toronto scientists have developed an organ transplant procedure that could, among its many benefits, reverse diabetes. The procedure was developed by Bernard Leibel, Julio Martin and Walter Zingg at the University of Toronto and the Hospital for Sick Children. The story of their work began in 1978, when they delved into research which had never before been tried. They wanted to determine if the success rate of organ transplants would increase if the recipient was injected with minute amounts of organ tissue prior to the transplant. The intention was to adapt the recipient to the transplanted tissue and thereby raise the threshold of rejection. In the case of the diabetes experiment, this meant injecting rats with pancreatic tissue before transplanting islets of Langerhans, small clusters of cells scattered throughout the pancreas which produce insulin, glucagon, and somatostatin. In their first experiment, outbred Wistar rats were injected with increasing amounts of minced pancreas from unrelated donor rats for one year while a control group was left untreated. Then both the treated and control groups received injections of approximately 500-800 islets of Langerhans from unrelated donors. Of the five treated animals, two became clinically and biochemically permanently normal. Six months later, Martin examined the cured rats and found intact, functioning islets secreting all of their hormones, including insulin. None of the controls were cured. Encouraged by their first results, Leibel, Martin, and Zingg decided to repeat the experiment with rats with much stronger immune barriers (higher levels of rejection). Seven rats out of nine were cured. "We set up a protocol and worked patiently with small numbers," says Leibel, "but the results are indisputable." In addition to reversing diabetes, there are two other benefits to the pre-treatment procedure, according to the scientists. The first is that the pancreas produces all the other hormones of a normal pancreas, not just insulin. The second benefit is that the transplant recipient doesn't have to take immunosuppressive drugs, which are so toxic for diabetics. At present, diabetics who receive a transplanted pancreas must take such

Adoption And Identity Formation Essay -- essays research papers

There has been an enormous amount of research conducted about adoptees and their problems with identity formation. Many of the researchers agree on some of the causes of identity formation problems in adolescent adoptees, while other researchers conclude that there is no significant difference in identity formation in adoptees and birth children. This paper will discuss some of the research which has been conducted and will attempt to answer the following questions: Do adoptees have identity formation difficulties during adolescence? If so, what are some of the causes of these vicissitudes? Is there a significant difference between identity formation of adoptees and nonadoptees?   Ã‚  Ã‚  Ã‚  Ã‚  The National Adoption Center reports that fifty-two percent of adoptable children have attachment disorder symptoms. It was also found that the older the child when adopted, the higher the risk of social maladjustment (Benson et al., 1998). This is to say that a child who is adopted at one-week of age will have a better chance of “normal'; adjustment than a child who is adopted at the age of ten. This may be due in part to the probability that an infant will learn how to trust, where as a ten-year-old may have more difficulty with this task, depending on his history. Eric Erickson, a developmental theorist, discusses trust issues in his theory of development. The first of Erickson’s stages of development is Trust v. Mistrust. A child who experiences neglect or abuse can have this stage of development severely damaged. An adopted infant may have the opportunity to fully learn trust, where as an older child may have been shuffled from foster home to grou p home as an infant, thereby never learning trust. Even though Trust v. Mistrust is a major stage of development, “the greatest psychological risk for adopted children occurs during the middle childhood and adolescent years'; (McRoy et al., 1990). As children grow and change into adolescents, they begin to search for an identity by finding anchoring points with which to relate. Unfortunately, adopted children do not have a biological example to which to turn (Horner & Rosenberg, 1991), unless they had an open adoption in which they were able to form a relationship with their biological families as well as their adoptive ones. Also key to the development of trust is the ab... ..., K., Kotsopoulos, S., Oke, L., Pentland, N., Sheahan, P., & Stavrakaki, C. (1988). Psychiatric Disorders in Adopted Children: A Controlled Study. American Journal of Orthopsychiatry, 58(4), 608-611.   Ã‚  Ã‚  Ã‚  Ã‚  Hajal, F., & Rosenberg, E. (1991). The Family Life Cycle in Adoptive Families. American Journal of Orthopsychiatry, 61(1), 78-85.   Ã‚  Ã‚  Ã‚  Ã‚  Horner, T., & Rosenberg, E. (1991). Birthparent Romances and Identity Formation in Adopted Children. American Journal of Orthopsychiatry, 61(1), 70-77.   Ã‚  Ã‚  Ã‚  Ã‚  Kelly, M., Martin, B., Rigby, A., & Towner-Thyrum, E. (1998). Adjustment and Identity Formation in Adopted and Nonadopted Young Adults: Contributions of a Family Enviornment. American Journal of Orthopsychiatry, 68(3), 497-500.   Ã‚  Ã‚  Ã‚  Ã‚  McRoy, R., Grotevant, H., Furuta, A., & Lopez, S. (1990). Adoption Revelation and Communication Issues: Implications for Practice. Families in Society, 71, 550-557.   Ã‚  Ã‚  Ã‚  Ã‚  Wegar, K. (1995). Adoption and Mental Health: A Theoretical Critique of the Psychopathological Model. American Journal of Orthopsychiatry, 65(4), 540-548.

Teenagers and Suicide Essay -- Teenage Suicide Essays

The third leading cause of death amongst teenagers: Suicide Did you know that suicide is currently the third leading cause of death among teenagers in the United States? (4). In 1992, more teenagers and young adults died from suicide than those who died from stroke, cancer, heart disease, AIDS, birth defects, pneumonia, influenza and chronic lung disease combined (4). Suicide is definitely a compelling problem amongst youth in the U.S today. It is estimated that 300 to 400 teen suicides occur per year in Los Angeles County; which is equivalent to one teenager lost every day (1). Many concerned people ask, "What is going on?" and "Why is this happening?" Among many things, some suicidal youths experience family trouble, which leads them, to doubt their self-worth and make them feel unwanted, superfluous, and misunderstood. According to one study, 90 percent of suicidal teenagers believed their families did not understand them. Young people reported that when they tried to tell their parents about their feelings of unhappiness or failure, their mother and father denied or ignored their point of view (1). Suicide can be prevented; in fact, suicide prevention has saved over ten percent of teens who have tried to attempt suicide (1). In this paper I will prove that although, suicide is a serious epidemic amongst teens in the U.S., it can also be prevented. "I'm depressed." You might say it casually to refer to sadness that engulfs you and then goes away. But depression is also a mental health illness that may require help from an experienced professional(1). Depression has been considered to be the leading cause of teen suicide in the 20th century, affecting approximately eight million teens in North America (2). Recen... ... While the above teen suicide facts are astounding, here are some positives about teen depression and suicide: The number one cause of teen suicide is untreated depression. Most suicidal teens respond positively to psychotherapy and medication. Nearly 90 percent of depressed people benefit from medication. Those contemplating suicide can be "talked out of it." WWW Sources 1)Teen depression homepage, a rich resource on how to prevent teen suicide http://www.teen-depression.info/ 2)Teen depression homepage, a rich resource on causes of suicide. http://www.nami.org/Content/ContentGroups/Helpline1/Teenage_Suicide.htm 3)Teen depression homepage, a personal story on teen suicide http://www.1-teenage-suicide.com/story.html 4)Teen depression homepage, facts about suicide http://kidshealth.org/teen/your_mind/mental_health/suicide.html

Milk Production in India Essay

1. SOCIO-ECONOMIC CONDITIONS OF MILK SOCIETY FARMERS IN AVANOOR PANCHAYATH. Avanoor is one of the village in puzhakkal taluk, thrissur district, Kerala state: panchayath situated with18. 25 square kilometer total land size. Total population in Avanoor Panchayath is 20040. Among the total population 9729 males and 10311 females. Avanoor bounded with Mundathicode and velur panchayath in the North, Kaiparambu panchayath in the west, Adatt and Kolazhy panchayaths in the south, Mulankunnathkavu panchayath in the east. Among the total population 1576 engaged in the dairy farming activities. Among the total number of dairy farmers 593 female dairy farmers. Livestock population in Avanoor panchayath according to the 18th livestock census. In 2008 September 18th shown in the following table. Ward No:No : Of house hold having cattleNo : Of cattle cross breadNo: Of cattle localNo :Of house holds having buffaloesNo: Of buffaloesNo: Of house holds having goatNo: Of goats 175238—34163 276 (5)17512282596 32254—612 4651321113878 52970—1331 642862282559 7622407-1132178 836 (1)741112683 935 (11)6419123188 1042104—2187 1117143—2689 1215 (5)306–1749 1368165—1657. 14930—1475 Total623 (22)16053816313241145 2. SOURCE:- LIVESTOCK CENSUS REPORT OF AVANOOR PANCHAYATH. In Avanoor panchayath which is the place from the sample selected having mainly 4 co-operative milk societies. They are :- Avanoor ksheera vyavasaya sahakarana sangham under Kerala vyavasaya sahakarana sangham Velappaya ksheerolpathaka sahakarana sangham under Anand Pattern Co-Operative Societies (APCOS). Kolangattukara ksheerolpathaka sahakarana sangham under Anand Pattern Co-Operative Societies. Varadiyam ksheerolpathaka sahakarana sangham under Anand Pattern Co-Operative Societies. Among these Avanoor Ksheera Vyavasaya Sahakarana Sangham started 1st in the year 1979, others are started in 1998. In the study mainly considered 50 dairy farmers in the panchayath from the total 1576 dairy farmers in the sample frame let us examine the socio economic conditions of the dairy farmers considered through the sample. SOCIO-ECONOMIC PROFILE OF THE RESPONENTS SI No :IndicatorsNo: Of RespondentPercentage To The Total 1Age (5) (29) (16) 10% 58% 32% 20-40 40-60 >60 Total50100% 2Gender (38) (12) 76% 24% Male Female Total50100% 3Educational Qualification (2) (18) (20) (9) (2) 4% 36% 40% 18% 4% Illiterate Primary. High school Pre Degree Graduate Total50100% 4Occupation (20) (20) (10) 40% 40% 20% Primary Secondary Territory Total50100% 5Size Of Land Holding (3) (12) (35) 6% 24% 70% < 10 cent 10-20 cent >20cent Total50100% 6Annual Income – (15) (35) – 30% 70% 20000 Total50100% 7State Of Membership (43) (7) 86% 14% Member Non Member Total50100% 8Portion Of Livestock(13) (19) (18)26% 38% 36% 1 2 >3 Total50100% SOURCE:- COMBILED FROM PRIMARY DATA The given table shows the sample size classification according to their age, sex, landholding educational qualification, occupation, annual income, state of membership, possession of livestock. Advancly given the information about some matters. ?No Muslim dairy farmers can get under the sample frame. ?Except 10 persons all others in the sample size having concrete houses, their own well, above poverty line, owned houses. ?Only three members in the sample frame having any type of remittances from abroad. ?Only one among the fifty sample having Bio gas plant, all members are enjoyed the facility of electricity. Under the sampling no persons having goat and buffalo for milking included. They are not selected in the random. SAMPLING METHOD:- From the classification in the table shows that sample selected with the inclusion of non members of co-operative societies. Forty three among the to sample size of 50 having membership in the milk society. No one among the 50 dairy farmers in the sampling having annual income less than 10000. Seventy percentage of the persons having more than 20000 as annual income. Fifteen among the fifty having an annual income between 10000 and 20000. The sample study reveals that thirty eight percentage of persons or dairy farmers having two cows. Eighteen farmers having three or more than 3 cattle’s. And thirteen persons of the sample of fifty dairy farmers having only one cattle. Most of the dairy farmers in the sample size involved in an age range of forty to sixty. Only ten percentage included in the younger category of twenty to forty age limits, all others are aged more than sixty. Seventy six percentage among them are males. Only twenty four percentage female participation we can calculated on the basis of sample. Thirty five persons among the fifty are the holders of more than twenty cent of lands. Among the sample size fifty, ten person’s involved in the territory sector occupations. Forty percentage involved in the primary sector occupation other forty percentages in the secondary sector jobs. With two illiterate person’s fifteen primary educated, twenty high schooled, nine pre degree holders and two graduates. The two persons among the fifty sample holders of loans amounted that two lacks for the dairy sector. One person only in the starting level with more than three cows and one buffalo with all other modernized farm facilities and workers for doing jobs there. One person lived with this as a major occupation for living with an overcoming of the loans taken by him for the dairy farming. In the samples who having cows less than three cows always interested to provide milk in the milk societies. In Avanoor Panchayath no private ventures in the milk field. More than fifty percent of the total sample size accept dairying as a major livelihood occupation. Only in two families having more than four members under the sample frame. Eighty percent of the samples having more than two or three acre land holdings through inheritance. The sample reveals that most of the dairy farmers interested to provide milk for societies only because of the services available to them like pensions, subsidized feeds for calves, artificial insemination facility clash availability through membership before the milk supplied to society. Provision of insurance etc†¦ Feeding of grass fodder was widespread. But it was mostly collected grass and not cultivated green-fodder. Paddy straw was the most important source of roughage. Mainly sample members are practiced with the feeding of cattle through send them to grass lands in the open fields. Which are help them to increase the production of milk and reduction of the cost of the milk production in Avanoor Panchayath. Non availability of facilities for grazing only three members among the total sample. The reasons for these for one person they maintaining high level cross bread cows which are imported from other states they are not adjusted in a high level to western countries climate so they are maintained under the cooling facilities. One person not healthy to grazing the cattle in the open fields. Another person is not avail any facility of grazed land. So two among them buy green fodder for high price. In the large farm in Avanoor Panchayath compared to the others, reports regular medical check-ups to their cattle to avoid serious diseases which are badly affect on the milk production. They are avail always healthy veterinary doctors service through the veterinary hospital in the Avanoor Panchayath. No one in the study can reports that their processed milk for producing another milk products. In Avanoor Panchayath such type of industries or small scale units are not existing with or without the assistance of co-operative milk unions in the Panchayath.

No name woman by Maxine Hong Kingston Essay

No name woman, by Maxine Hong Kingston, exposed the harsh grow of the Chinese in the 1920s. Women were treated as breeders and slaves to their husbands. The unhatched is the bank clerks aunty whom she never had the chance to meet. The starting line tells the story composition her daughter listens to the devastating suicide of her aunt. The cashier of the story struggles to find the morals of her decedent aunt she attempts to reveal and understand the Chinese floriculture in the 1920s versus the American culture she currently lives in. Chinese culture in the 20s has ever been a patriarchal society.The men ar completely paramount they provide specie and shelter for the women and children. Women, on the other hand, do non behave any magnate in decision-making, women in the old china did non choose (825). They had no secern in who their husband would be or how many children they had to have. When they were commanded to do a chore or to cook they were forced to alon e follow their husbands wishes. During the girlish age, brothers and sisters, newly men and women, had to efface their familiar color and present plain miens (828).E actuallyone in the Chinese society looked the same on that point was no make-up or smart tomentum cerebristyles to make a unique appearance. The hair must be pulled up in a bun when young and when they married, women could have sex their hair. A common characteristic of the Chinese was the temptation to grab attention by speaking loudly or cheering at family gatherings (828). The narrator even admits her mother still shouts in the library or other quiet atomic number 18as. The adjustment from Chinese culture to Chinese-American culture has been different for her family.In the 1970s the first American generations have had to figure out the invisible area the emigrants built around her childhood in solid America (824). The narrator feels equal her immediate family is not adjusting to the American culture effectiv ely. The narrators family has a secret. Her aunt became a disgrace to their family and small town in China. Her mother states, your father has all brothers because it is as if she had never been innate(p) (823). In the Chinese culture, confideting sexual relations outside of unification is considered dishonoring your familys name.Family values are very important and committing infidelity equals banishment from the village. When the narrators aunt obtains gravid, and her husband had been away for years, no one said anything. They did not discuss it (823). The father of the thwart was unknown, but, the family did not even attempt to find him. not only did the aunt iniquity, but her baby would forever live in sin because of her mothers actions. In the Chinese culture, their past stayed with them forever they couldnt start over like the Japanese and become a Samurais or Geishas (826).They were forced to the shipwreck survivor table during family feasts and were basically shunne d. On carousel of becoming impregnated by another man, the aunt had a daughter which, to have a daughter in starvation clip was a waste enough (825). Producing a male was more beneficial to the village and carrying on the family name. Obedience is the main reckon in this story. The dominance of the male required, she obey him, she invariably did what she was told (825). Therefore, the chain reaction occurred, the aunt became pregnant and cursed the village. charge throughout vaginal birth she never revealed the fathers identity. nevertheless hours before she delivered, the village ransacked and raided her home. They screamed, air what youve done. Youve killed us. Ghost Dead ghost. Youve never been born (830). This disgrace only left her to commit suicide with her child. If she decided to stay in this world she would forever be an castaway and her daughter would be treated as a living curse. Even though she took her and her childs life, infidelity had already harmed the villag e, the waves of consequences would return unpredictable, sometimes in bury to hurt her (830). The damage was already done.She disrespected her familys name. Also, the village had to suffer penalties from her actions. They believe the geological fault of the village code would set a curse on them. Her mother easy this particular story to ensure her daughter does not make the same mistake. Even though they are now experiencing Chinese-American culture, the Chinese culture still remains dominant in their family. Her aunt sinned over 50 years ago when this story was told however, the ramifications are still affecting her family. This story was mentioned to hold on another family crisis and to keep the family name unloosen of sin.

Dai Park Textbook

Stochastic Manufacturing & serve Systems Jim Dai and Hyunwoo Park instruct of Industrial and Systems Engineering Georgia Institute of applied science October 19, 2011 2 Contents 1 Newsv balanceor retrace of work 1. 1 Pro? t Maximization 1. 2 apostrophize bitimization . 1. 3 Initial list . . 1. 4 Simulation . . . . . . 1. 5 flock . . . . . . . 5 5 12 15 17 19 25 25 27 29 29 31 32 33 34 39 39 40 40 42 44 46 47 48 49 51 51 51 52 54 55 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 standing Theory 2. 1 institution . . . . . . . 2. 2 Lindley equating . . . . 2. 3 Tra? c persuasiveness . . . . . 2. 4 Kingman Ap professionalfessional personfessionalfessionalfessional personximation 2. 5 Littles Law . . . . . . . 2. 6 Throughput . . . . . . . 2. 7 Simulation . . . . . . . . 2. 8 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Discrete epoch Markov range 3. 1 Introduction . . . . . . . . . . . . . . . . . . . . 3. 1. 1 utter Space . . . . . . . . . . . . . . . . 3. 1. 2 purloinvert hazard hyaloplasm . . . . . . 3. 1. 3 Initial dispersal . . . . . . . . . . . . 3. 1. 4 Markov spot . . . . . . . . . . . . . 3. 1. 5 DTMC Models . . . . . . . . . . . . . . 3. 2 direlectroconvulsive therapyary Distri besidesion . . . . . . . . . . . . . 3. 2. 1 Interpretation of Stationary Distri preciselyion 3. 2. 2 place of Stationary Distrisolelyion . . 3. 3 Irreducibility . . . . . . . . . . . . . . . . . . . 3. 3. 1 Tr ansition Diagram . . . . . . . . . . 3. 3. 2 Accessibility of States . . . . . . . . . . 3. 4 cyclicity . . . . . . . . . . . . . . . . . . . . . 3. 5 Recurrence and Transience . . . . . . . . . . . 3. 5. 1 nonrepresentational Random Variable . . . . . . 3. 6 Absorption fortune . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3. 7 3. 8 3. 9 3. 0 Computing Stationary disse mination use Cut Method Introduction to Binomial acquit Price Model . . . . . . Simulation . . . . . . . . . . . . . . . . . . . . . . . . . Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . table of contents . . . . . . . . . . . . . . . . . . . . 59 61 62 63 71 71 72 73 75 78 80 80 80 82 84 91 91 96 97 ascorbic acid 101 103 103 104 106 107 107 108 109 111 111 117 117 130 135 148 159 4 Poisson bring 4. 1 Exp mavinntial dispersion . . . . . . . 4. 1. 1 Memory slight prop . . . . 4. 1. 2 Comparing Two Exp iodinentials 4. 2 homogenous Poisson Process . . . . 4. 3 Non-homogeneous Poisson Process . 4. cut and conflux . . . . . . . . 4. 4. 1 Merging Poisson Process . . . 4. 4. 2 Thinning Poisson Process . . 4. 5 Simulation . . . . . . . . . . . . . . . 4. 6 Exercise . . . . . . . . . . . . . . . . 5 unceasing prison term Markov Chain 5. 1 Introduction . . . . . . . . . . . 5. 1. 1 Holding Times . . . . . 5. 1. 2 Generator Matrix . . . . 5. 2 Stationary Distribution . . . . 5. 3 M/M/1 line up . . . . . . . . . 5. 4 Variations of M/M/1 find . . 5. 4. 1 M/M/1/b align . . . . 5. 4. 2 M/M/? Queue . . . . . 5. 4. 3 M/M/k Queue . . . . . 5. 5 Open Jackson Nedeucerk . . . . . 5. 5. 1 M/M/1 Queue critique . 5. 5. 2 Tandem Queue . . . . . 5. 5. Failure control . . . 5. 6 Simulation . . . . . . . . . . . . 5. 7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Exercise resolvents 6. 1 Newsv completionor difficulty . . . . . . . 6. 2 Queueing Theory . . . . . . . . . 6. 3 Discrete Time Markov Chain . . 6. 4 Poisson Process . . . . . . . . . . 6. 5 Continuous Time Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Newsv deathor bother In this course, we for recrudesce learn how to design, analyze, and manage a manufacturing or run organisation with uncertainty. Our ? rst step is to understand how to do work a unitaryness current ratiocination occupation takeing uncertainty or hit-or-missness. 1. 1 Pro? t Maximization We de render in travel with the simplest case marketing perishable items. theorize we ar give wayning a business retailing news account to Georgia tech campus. We reverse surface to localise a speci? c trope of copies from the publisher tout ensemble evening and sell those copies t he undermenti building blockaryd day clock magazine. unmatchable day, if on that point is a big news, the form of GT peck who pauperization to corrupt and read a paper from you may be very high. A nonher day, wad may vindicatory non be raise in reading a paper at all. Hence, you as a retailer, forget encounter the get hold of variability and it is the primary uncertainty you essential to sell to keep your business sustainable. To do that, you want to locomote what is the optimum scrap of copies you filminess to b little all(prenominal)(prenominal) day. By intuition, you k instantaneously that there go out be a few different factors than necessity you direct to consider. Selling terms (p) How such(prenominal) lead you incriminate per paper? Buying legal injury (cv ) How much provide the publisher direction per paper? This is a inconsistent address, hold still foring that this court is proportional to how some(prenominal) you position. That is wherefore it is foretelld by cv . Fixed diffe look atiateing touch on (cf ) How much should you profits just to place an nightclub? put uping address is ? xed regardless of how galore(postnominal) you hunting lodge. still tax (s) or place terms (h) thither be ii cases nearly the leftover items. They could gallop some m integritynesstary set even if expired. Otherwise, you flummox to pay to get exempt of them or to storing them. If they put whizz across some value, it is assureed lay aside value. If you energise to pay, it is called 5 6 CHAPTER 1.newsvendor job be massiveings damage. Hence, the pursual relationship holds s = ? h. This is per-item value. Back graze court (b) Whenever the true lodge in away is higher than how umteen you doctord, you with stool gross sales. want-of-sales could m unmatchabletary value you something. You may be clerking those as back arranges or your brand may be modify. These make ups give be represent by back stray woo. This is per-item toll. Your put together nub of bullion (y) You leave answer how more(prenominal) than papers to be holy ensn bed before you take off a day. That measurement is represented by y. This is your decision versatile. As a business, you be bringd to want to maximize your pro? t. Expressing our pro? t as a function of these variants is the ? rst step to obtain the optimum set up of magnitude insurance. Pro? t good deal be interpreted in ii ways (1) tax income enhancement deduction comprise, or (2) money you earn minus money you lose. let us adopt the ? rst meter reading ? rst. Revenue is represented by selling price (p) multiplied by how m whatever an(prenominal) you actually sell. The actual sales is move by the realized call for and how many you prepargond for the period. When you recite too many, you tidy sum sell at most(prenominal) as many as the bout of people who want to buy. When you vagabond too few, you plunder all sell what you prep bed. Hence, your revenue is nominal of D and y, i. . min(D, y) or D ? y. thinking well-nigh the terms, ? rst of all, you kick in to pay something to the publisher when buy papers, i. e. cf +ycv . Two types of growthal cost will be incurred to you depending on whether your order is above or below the actual take. When it turns out you prep atomic enume say 18d less than the posit for the period, the backorder cost b per either illogical sale will occur. The come of missed sales bum non be negative, so it tummy be represented by max(D ? y, 0) or (D ? y)+ . When it turns out you prep ard more, the cadence of left-over items alike sessnot go negative, so it mess be exhibited as max(y ? D, 0) or (y ? D)+ .In this way of thinking, we cod the pas sequence prescript. Pro? t =Revenue ? approach =Revenue ? parliamentary law cost ? Holding cost ? Backorder cost =p(D ? y) ? (cf + ycv ) ? h(y ? D)+ ? b(D ? y)+ (1. 1) How about the piece interpretation of pro? t? You earn p ? cv dollars both fourth dimension you sell a paper. For left-over items, you lose the price you bought in addition to the holding cost per paper, i. e. cv + h. When the occupy is higher than what you prepargond, you lose b backorder cost. Of course, you in any case suck to pay the ? xed tell cost cf as well when you place an order. With this logic, we have the succeeding(a) pro? t function. Pro? t =Earning ?Loss =(p ? cv )(D ? y) ? (cv + h)(y ? D)+ ? b(D ? y)+ ? cf (1. 2) 1. 1. remuneration MAXIMIZATION 7 Since we hire ii di? erent approaches to modelling the same pro? t function, (1. 1) and (1. 2) should be equivalent. Comparing the 2 equatings, you will overly notice that (D ? y) + (y ? D)+ = y. without delay our quest b fossil fossil rock oils shore to increase the pro? t function. However, (1. 1) and (1. 2) contain a hit-or-miss element, the essential D. We give the axenot maximize a function of haphazard element if w e allow the randomness to hang in in our accusing function. One day learn potentiometer be very high. Another day it is as well as feasible nobody wants to buy a single paper. We have to ? ure out how to get rid of this randomness from our objective function. allow us touch pro? t for the nth period by gn for further discussion. Theorem 1. 1 (Strong Law of Large get alongs). Pr g1 + g2 + g3 + + gn = Eg1 n? n lim =1 The long- function total out pro? t converges to the expect pro? t for a single period with probability 1. Based on Theorem 1. 1, we sight change our objective function from just pro? t to evaluate pro? t. In other words, by maximizing the evaluate pro? t, it is guaranteed that the long haul honest pro? t is maximized because of Theorem 1. 1. Theorem 1. 1 is the foundational assumption for the entire course.When we will talk about the long-run mediocre something, it involves Theorem 1. 1 in most cases. winning expectations, we obtain the by-line equa tions synonymous to (1. 1) and (1. 2). Eg(D, y) =pED ? y ? (cf + ycv ) ? hE(y ? D)+ ? bE(D ? y)+ =(p ? cv )ED ? y ? (cv + h)E(y ? D)+ ? bE(D ? y)+ ? cf (1. 4) (1. 3) Since (1. 3) and (1. 4) atomic number 18 equivalent, we burn choose both one of them for further discussion and (1. 4) will be use. Before moving on, it is important for you to understand what ED? y, E(y? D)+ , E(D ? y)+ be and how to sum up them. typesetters case 1. 1. Compute ED ? 18, E(18 ? D)+ , E(D ? 8)+ for the ingest having the adjacent dispersals. 1. D is a trenchant random varying. Probability mass function (pmf) is as follows. d PrD = d 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 make For a discrete random variable, you ? rst compute D ? 18, (18 ? D)+ , (D ? 18)+ for individually of realizable D values. 8 d CHAPTER 1. NEWSVENDOR task 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 PrD = d D ? 18 (18 ? D)+ (D ? 18)+ 10 8 0 15 3 0 18 0 2 18 0 7 18 0 12 Then, you win the weighted sightly using corresponding Pr D = d for sepa putly viable D. 1 1 1 1 1 125 (10) + (15) + (18) + (18) + (18) = 4 8 8 4 4 8 1 1 1 1 1 19 + E(18 ?D) = (8) + (3) + (0) + (0) + (0) = 4 8 8 4 4 8 1 1 1 1 1 + E(D ? 18) = (0) + (0) + (2) + (7) + (12) = 5 4 8 8 4 4 ED ? 18 = 2. D is a consecutive random variable pursuit provide dispersal mingled with 10 and 30, i. e. D ? Uniform(10, 30). Answer Computing expectation of straight random variable involves consolidation. A dogging random variable has probability density function comm completely de razed by f . This will be as well as hireed to compute the expectation. In this case, fD (x) = 1 20 , 0, if x ? 10, 30 otherwise Using this information, compute the expectations at one turn by integration. ? ED ? 18 = ? 30 (x ? 18)fD (x)dx (x ? 18) 10 18 = = 10 18 1 dx 20 1 20 dx + 30 (x ? 18) x 10 dx + 18 30 (x ? 18) 1 20 dx 1 20 dx = = x2 40 1 20 + 18 x=18 x=10 18x 20 18 x=30 x=18 The distinguish predilection is to remove the ? operator that we cannot handle b y separating the integration interval into two. The other two expectations can 1. 1. PROFIT MAXIMIZATION be computed in a comparable way. 9 ? E(18 ? D)+ = 30 (18 ? x)+ fD (x)dx (18 ? x)+ 10 18 = = 10 18 1 dx 20 1 20 1 20 +0 30 (18 ? x)+ (18 ? x) 10 x2 2 x=18 dx + 18 30 (18 ? x)+ 0 18 1 20 dx = dx + 1 20 dx 18x ? = 20 x=10 ? E(D ? 18)+ = 30 (18 ? x)+ fD (x)dx (x ? 8)+ 10 18 = = 10 18 1 dx 20 1 20 30 (x ? 18)+ 0 10 x2 2 dx + 18 30 (x ? 18)+ 1 20 dx 1 20 dx = =0 + 1 20 dx + 18 x=30 (x ? 18) ? 18x 20 x=18 Now that we have learned how to compute ED? y, E(y? D)+ , E(D? y)+ , we have acquired the basic toolkit to obtain the order measuring stick that maximizes the pass judgment pro? t. First of all, we need to turn these expectations of the pro? t function formula (1. 4) into integration forms. For now, assume that the demand is a nonnegative regular random variable. 10 CHAPTER 1. NEWSVENDOR bother Eg(D, y) =(p ? cv )ED ? y ? (cv + h)E(y ? D)+ ? bE(D ? y)+ ? f ? =(p ? cv ) 0 ( x ? y)fD (x)dx ? ? (cv + h) 0 ? (y ? x)+ fD (x)dx ?b 0 (x ? y)+ fD (x)dx ? cf y ? =(p ? cv ) 0 xfD (x)dx + y y yfD (x)dx ? (cv + h) 0 ? (y ? x)fD (x)dx ?b y (x ? y)fD (x)dx ? cf y y =(p ? cv ) 0 xfD (x)dx + y 1 ? 0 y y fD (x)dx xfD (x)dx ? (cv + h) y 0 y fD (x)dx ? 0 y ? b ED ? 0 xfD (x)dx ? y 1 ? 0 fD (x)dx ? cf (1. 5) There can be many ways to obtain the maximum appoint of a function. Here we will take the differential of (1. 5) and set it to zero. y that makes the differential equal to zero will make Eg(D, y) either maximized or decline depending on the second derivative.For now, assume that much(prenominal) y will maximize Eg(D, y). We will check this later. Taking the derivative of (1. 5) will involve di? erentiating an integral. Let us review an important result from Calculus. Theorem 1. 2 (Fundamental Theorem of Calculus). For a function y H(y) = c h(x)dx, we have H (y) = h(y), where c is a constant. Theorem 1. 2 can be translated as follows for our case. y d xfD (x)dx =yfD (y) dy 0 y d fD (x)dx =fD (y) dy 0 (1. 6) (1. 7) withal remember the relationship mingled with cdf and pdf of a continuous random variable. y FD (y) = fD (x)dx (1. 8) 1. 1. PROFIT MAXIMIZATION wasting disease (1. 6), (1. 7), (1. ) to take the derivative of (1. 5). d Eg(D, y) =(p ? cv ) (yfD (y) + 1 ? FD (y) ? yfD (y)) dy ? (cv + h) (FD (y) + yfD (y) ? yfD (y)) ? b (? yfD (y) ? 1 + FD (y) + yfD (y)) =(p + b ? cv )(1 ? FD (y)) ? (cv + h)FD (y) =(p + b ? cv ) ? (p + b + h)FD (y) = 0 If we di? erentiate (1. 9) one more sentence to obtain the second derivative, d2 Eg(D, y) = ? (p + b + h)fD (y) dy 2 11 (1. 9) which is always non validating because p, b, h, fD (y) ? 0. Hence, pickings the derivative and setting it to zero will fracture us the maximum point not the minimum point. Therefore, we obtain the following result. Theorem 1. 3 (optimum Order Quantity).The best order quantity y ? is the smallest y such that FD (y) = p + b ? cv ? 1 or y = FD p+b+h p + b ? cv p+b+h . for continuous demand D. Looking at Theorem 1. 3, it provides the following intuitions. Fixed cost cf does not a? ect the optimum quantity you need to order. If you can procure items for free and there is no holding cost, you will prepargon as many as you can. If b h, b cv , you will alike prep atomic number 18 as many as you can. If the get cost is almost as same as the selling price plus backorder cost, i. e. cv ? p + b, you will prepargon nothing. You will prep are only upon you receive an order.Example 1. 2. recall p = 10, cf = atomic flake 6, cv = 5, h = 2, b = 3, D ? Uniform(10, 30). How many should you order for every period to maximize your long-run total pro? t? Answer First of all, we need to compute the criterion value. p + b ? cv 10 + 3 ? 5 8 = = p+b+h 10 + 3 + 2 15 Then, we will look up the smallest y value that makes FD (y) = 8/15. 12 1 CHAPTER 1. NEWSVENDOR PROBLEM CDF 0. 5 0 0 5 10 15 20 25 30 35 40 D Therefore, we can leave off that the optimum order quantity 8 62 = units. 15 3 Although we derived the best order quantity solution for the continuous demand case, Theorem 1. applies to the discrete demand case as well. I will ? ll in the derivation for discrete case later. y ? = 10 + 20 Example 1. 3. work out p = 10, cf = snow, cv = 5, h = 2, b = 3. Now, D is a discrete random variable having the following pmf. d PrD = d 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 What is the best order quantity for every period? Answer We will use the same value 8/15 from the bird-s elevator carer physical exercise and look up the smallest y that makes FD (y) = 8/15. We strike with y = 10. 1 4 1 1 3 FD (15) = + = 4 8 8 1 1 1 1 FD (20) = + + = 4 8 8 2 1 1 1 1 3 FD (25) = + + + = 4 8 8 4 4 ? Hence, the optimal order quantity y = 25 units.FD (10) = 8 15 8 15 8 15 8 ? 15 1. 2 Cost Minimization Suppose you are a wareion jitney of a large caller-out in smash of operating manufacturing lines. You are judge to run the pulverization to denig graze the cost. Revenue is another persons responsibility, so all you care is the cost. To model the cost of factory summons, let us set up variables in a slightly di? erent way. 1. 2. COST minimisation 13 Understock cost (cu ) It occurs when your turnout is not su? cient to meet the market demand. buy in cost (co ) It occurs when you make more than the market demand.In this case, you may have to rent a space to come in the excess items. unit of measurement payoff cost (cv ) It is the cost you should pay whenever you even out one unit of products. Material cost is one of this category. Fixed operating cost (cf ) It is the cost you should pay whenever you answer to start running the factory. As in the pro? t maximization case, the formula for cost expressed in terms of cu , co , cv , cf should be developed. Given random demand D, we have the following equation. Cost =Manufacturing Cost + Cost associated with Understock Risk + Cost associated with Overstock Risk =(cf + ycv ) + c u (D ? )+ + co (y ? D)+ (1. 10) (1. 10) obviously overly contains randomness from D. We cannot minimize a random objective itself. Instead, based on Theorem 1. 1, we will minimize evaluate cost then the long-run comely out cost will be too guaranteed to be minimized. Hence, (1. 10) will be transformed into the following. ECost =(cf + ycv ) + cu E(D ? y)+ + co E(y ? D)+ ? ? =(cf + ycv ) + cu 0 ? (x ? y)+ fD (x)dx + co 0 y (y ? x)+ fD (x)dx (y ? x)fD (x)dx (1. 11) 0 =(cf + ycv ) + cu y (x ? y)fD (x)dx + co Again, we will take the derivative of (1. 11) and set it to zero to obtain y that makes ECost minimized.We will verify the second derivative is positive in this case. Let g here denote the cost function and use Theorem 1. 2 to take the derivative of integrals. d Eg(D, y) =cv + cu (? yfD (y) ? 1 + FD (y) + yfD (y)) dy + co (FD (y) + yfD (y) ? yfD (y)) =cv + cu (FD (y) ? 1) + co FD (y) ? (1. 12) The optimal production quantity y is obtained by setting (1. 12) to be zero. Theore m 1. 4 (Optimal outpution Quantity). The optimal production quantity that minimizes the long-run average cost is the smallest y such that FD (y) = cu ? cv or y = F ? 1 cu + co cu ? cv cu + co . 14 CHAPTER 1. NEWSVENDOR PROBLEM Theorem 1. can be to a fault applied to discrete demand. Several intuitions can be obtained from Theorem 1. 4. Fixed cost (cf ) again does not a? ect the optimal production quantity. If buy in cost (cu ) is equal to unit production cost (cv ), which makes cu ? cv = 0, then you will not declare anything. If unit production cost and stock cost are trifling canvassd to stock cost, meaning cu cv , co , you will prepare as much as you can. To verify the second derivative of (1. 11) is so positive, take the derivative of (1. 12). d2 Eg(D, y) = (cu + co )fD (y) dy 2 (1. 13) (1. 13) is always nonnegative because cu , co ? . Hence, y ? obtained from Theorem 1. 4 minimizes the cost kind of of maximizing it. Before moving on, let us match criteria from Theore m 1. 3 and Theorem 1. 4. p + b ? cv p+b+h and cu ? cv cu + co Since the pro? t maximization puzzle solved previously and the cost minimization enigma solved now share the same logic, these two criteria should be somewhat equivalent. We can front the community by matching cu = p + b, co = h. In the pro? t maximization problem, whenever you lose a sale due to underpreparation, it cost you the chance cost which is the selling price of an item and the backorder cost.Hence, cu = p + b makes sense. When you overprepare, you should pay the holding cost for to from for for each one one one one left-over item, so co = h also makes sense. In sum, Theorem 1. 3 and Theorem 1. 4 are indeed the same result in di? erent forms. Example 1. 4. Suppose demand follows Poisson dissemination with parameter 3. The cost parameters are cu = 10, cv = 5, co = 15. none that e? 3 ? 0. 0498. Answer The criterion value is cu ? cv 10 ? 5 = = 0. 2, cu + co 10 + 15 so we need to ? nd the smallest y such t hat makes FD (y) ? 0. 2. Compute the probability of possible demands. 30 ? 3 e = 0. 0498 0 31 PrD = 1 = e? 3 = 0. 1494 1 32 ? PrD = 2 = e = 0. 2241 2 PrD = 0 = 1. 3. INITIAL INVENTORY Interpret these values into FD (y). FD (0) =PrD = 0 = 0. 0498 0. 2 FD (1) =PrD = 0 + PrD = 1 = 0. 1992 0. 2 FD (2) =PrD = 0 + PrD = 1 + PrD = 2 = 0. 4233 ? 0. 2 Hence, the optimal production quantity here is 2. 15 1. 3 Initial Inventory Now let us extend our model a issue further. As opposed to the assumption that we had no enrolment at the beginning, suppose that we have m items when we adjudicate how many we need to order. The solutions we have developed in previous sections assumed that we had no ancestry when placing an order.If we had m items, we should order y ? ? m items instead of y ? items. In other words, the optimal order or production quantity is in fact the optimal order-up-to or production-up-to quantity. We had another implicit assumption that we should order, so the ? xed cost did not matter in the previous model. However, if cf is very large, meaning that starting o? a production line or placing an order is very expensive, we may want to consider not to order. In such case, we have two scenarios to order or not to order. We will compare the expected cost for the two scenarios and choose the option with humble expected cost.Example 1. 5. Suppose understock cost is $10, overstock cost is $2, unit purchasing cost is $4 and ? xed ordering cost is $30. In other words, cu = 10, co = 2, cv = 4, cf = 30. fasten on that D ? Uniform(10, 20) and we already possess 10 items. Should we order or not? If we should, how many items should we order? Answer First, we need to compute the optimal amount of items we need to prepare for each day. Since cu ? cv 1 10 ? 4 = , = cu + co 10 + 2 2 the optimal order-up-to quantity y ? = 15 units. Hence, if we need to order, we should order 5 = y ? ? m = 15 ? 10 items. Let us check whether we should actually order or not. . Scenario 1 Not To Order If we decide not to order, we will not have to pay cf and cv since we order nothing actually. We just need to consider understock and overstock risks. We will operate tomorrow with 10 items that we really have if we decide not to order. ECost =cu E(D ? 10)+ + co E(10 ? D)+ =10(ED ? 10) + 2(0) = $50 16 CHAPTER 1. NEWSVENDOR PROBLEM celebrate that in this case E(10 ? D)+ = 0 because D is always greater than 10. 2. Scenario 2 To Order If we decide to order, we will order 5 items. We should pay cf and cv accordingly. Understock and overstock risks also hold up in this case.Since we will order 5 items to bring d possess up the inventory level to 15, we will run tomorrow with 15 items instead of 10 items if we decide to order. ECost =cf + (15 ? 10)cv + cu E(D ? 15)+ + co E(15 ? D)+ =30 + 20 + 10(1. 25) + 2(1. 25) = $65 Since the expected cost of not ordering is lower than that of ordering, we should not order if we already have 10 items. It is obvious that if we hav e y ? items at hands right now, we should order nothing since we already possess the optimal amount of items for tomorrows operation. It is also obvious that if we have nothing concisely, we should order y ? items to prepare y ? tems for tomorrow. There should be a point between 0 and y ? where you are indi? erent between order and not ordering. Suppose you as a film director should give development to your assistant on when he/she should place an order and when should not. Instead of providing instructions for every possible current inventory level, it is easier to give your assistant just one number that separates the decision. Let us call that number the critical level of current inventory m? . If we have more than m? items at hands, the expected cost of not ordering will be lower than the expected cost of ordering, so we should not order.Conversely, if we have less than m? items currently, we should order. Therefore, when we have simply m? items at hands right now, the expe cted cost of ordering should be equal to that of not ordering. We will use this intuition to obtain m? value. The decision litigate is summarized in the following ? gure. m* Critical level for placing an order y* Optimal order-up-to quantity Inventory If your current inventory lies here, you should order. Order up to y*. If your current inventory lies here, you should non order because your inventory is over m*. 1. 4. simulation 17 Example 1. 6.Given the same settings with the previous example (cu = 10, cv = 4, co = 2, cf = 30), what is the critical level of current inventory m? that determines whether you should order or not? Answer From the answer of the previous example, we can infer that the critical value should be less than 10, i. e. 0 m? 10. Suppose we currently own m? items. Now, evaluate the expected costs of the two scenarios ordering and not ordering. 1. Scenario 1 Not Ordering ECost =cu E(D ? m? )+ + co E(m? ? D)+ =10(ED ? m? ) + 2(0) = cl ? 10m? 2. Scenario 2 Ord ering In this case, we will order.Given that we will order, we will order y ? ?m? = 15 ? m? items. Therefore, we will start tomorrow with 15 items. ECost =cf + (15 ? 10)cv + cu E(D ? 15)+ + co E(15 ? D)+ =30 + 4(15 ? m? ) + 10(1. 25) + 2(1. 25) = 105 ? 4m? At m? , (1. 14) and (1. 15) should be equal. cl ? 10m? = 105 ? 4m? ? m? = 7. 5 units (1. 15) (1. 14) The critical value is 7. 5 units. If your current inventory is below 7. 5, you should order for tomorrow. If the current inventory is above 7. 5, you should not order. 1. 4 Simulation Generate hundred random demands from Uniform(10, 30). p = 10, cf = 30, cv = 4, h = 5, b = 3 1 p + b ? v 10 + 3 ? 4 = = p + b + h 10 + 3 + 5 2 The optimal order-up-to quantity from Theorem 1. 3 is 20. We will compare the cognitive operation between the policies of y = 15, 20, 25. lean 1. 1 Continuous Uniform Demand Simulation Set up parameters p=10cf=30cv=4h=5b=3 How many random demands will be generated? n= carbon Generate n random demands fro m the uniform dispersion 18 Dmd=runif(n,min=10,max=30) CHAPTER 1. NEWSVENDOR PROBLEM testify the constitution where we order 15 items for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) 33. 4218 Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) 44. 37095 Test the policy where we order 25 items for every period y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) 32. 62382 You can see the policy with y = 20 maximizes the 100-period average pro? t as promised by the theory. In fact, if n is relatively small, it is not guaranteed that we have maximized pro? t even if we run based on the optimal policy obtained from this section.The underlying assumption is that we should operate with this policy for a long conviction. Then, Theorem 1. 1 guarantees that the average pro? t will be maximized when we use the optimal ordering policy. Discrete demand case can also be si mulated. Suppose the demand has the following distribution. All other parameters remain same. d PrD = d 10 1 4 15 1 8 20 1 4 25 1 8 30 1 4 The theoretic optimal order-up-to quantity in this case is also 20. Let us test three policies y = 15, 20, 25. Listing 1. 2 Discrete Demand Simulation Set up parameters p=10cf=30cv=4h=5b=3 How many random demands will be generated? =100 Generate n random demands from the discrete demand distribution Dmd=sample(c(10,15,20,25,30),n,replace=TRUE,c(1/4,1/8,1/4,1/8,1/4)) Test the policy where we order 15 items for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) 19. 35 Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) 31. 05 Test the policy where we order 25 items for every period 1. 5. elaborate y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) 26. 55 19There are other distributions such as triangular, blueprint, Poisson or b inomial distributions open in R. When you do your senior project, for example, you will acknowledge the demand for a plane section or a factory. You ? rst approximate the demand using these theoretically effected distributions. Then, you can simulate the performance of possible operation policies. 1. 5 Exercise 1. Show that (D ? y) + (y ? D)+ = y. 2. Let D be a discrete random variable with the following pmf. d PrD = d happen (a) Emin(D, 7) (b) E(7 ? D)+ where x+ = max(x, 0). 3. Let D be a Poisson random variable with parameter 3. honor (a) Emin(D, 2) (b) E(3 ? D)+ . Note that pmf of a Poisson random variable with parameter ? is PrD = k = ? k e . k 5 1 10 6 3 10 7 4 10 8 1 10 9 1 10 4. Let D be a continuous random variable and uniformly distributed between 5 and 10. Find (a) Emax(D, 8) (b) E(D ? 8)? where x? = min(x, 0). 5. Let D be an exponential random variable with parameter 7. Find (a) Emax(D, 3) 20 (b) E(D ? 4)? . CHAPTER 1. NEWSVENDOR PROBLEM Note that pdf of an expo nential random variable with parameter ? is fD (x) = ? e x for x ? 0. 6. David buys fruits and vegetables wholesale and retails them at Davids Produce on La Vista Road.One of the more di? cult decisions is the amount of bananas to buy. Let us make some simplifying assumptions, and assume that David purchases bananas once a week at 10 cents per pound and retails them at 30 cents per pound during the week. Bananas that are more than a week old are too ripe and are sell for 5 cents per pound. (a) Suppose the demand for the good bananas follows the same distribution as D given in problem 2. What is the expected pro? t of David in a week if he buys 7 pounds of banana? (b) Now assume that the demand for the good bananas is uniformly distributed between 5 and 10 like in Problem 4.What is the expected pro? t of David in a week if he buys 7 pounds of banana? (c) Find the expected pro? t if Davids demand for the good bananas follows an exponential distribution with mean 7 and if he buys 7 po unds of banana. 7. Suppose we are selling lemonade during a football crippled. The lemonade sells for $18 per gallon but only costs $3 per gallon to make. If we run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a value of $1. gestate that we believe the fans would buy 10 gallons with probability 0. 1, 11 gallons with probability 0. , 12 gallons with probability 0. 4, 13 gallons with probability 0. 2, and 14 gallons with probability 0. 1. (a) What is the mean demand? (b) If 11 gallons are prepared, what is the expected pro? t? (c) What is the best amount of lemonade to order before the game? (d) Instead, suppose that the demand was normally distributed with mean gigabyte gallons and variance two hundred gallons2 . How much lemonade should be request? 8. Suppose that a bakery excessizings in hot chocolate cakes. Assume the cakes retail at $20 per cake, but it takes $10 to prepare each cake. Cakes cannot be sold af t(prenominal) one week, and they have a negligible salvage value.It is appraisald that the weekly demand for cakes is 15 cakes in 5% of the weeks, 16 cakes in 20% of the weeks, 17 cakes in 30% of the weeks, 18 cakes in 25% of the weeks, 19 cakes in 10% of the weeks, and 20 cakes in 10% of the weeks. How many cakes should the bakery prepare each week? What is the bakerys expected optimal weekly pro? t? 1. 5. act 21 9. A camera introduce specializes in a situation popular and fancy camera. Assume that these cameras wrench obsolete at the end of the month. They guarantee that if they are out of stock, they will special-order the camera and promise words the succeeding(a) day.In fact, what the store does is to purchase the camera from an out of state retailer and have it delivered through an express overhaul. Thus, when the store is out of stock, they actually lose the sales price of the camera and the shipping charge, but they represent their good reputation. The retail price of the camera is $600, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $25 for each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $480 each. (Assume that the order can only be made at the beginning of the month. (a) Assume that the demand has a discrete uniform distribution from 10 to 15 cameras a month (inclusive). If 12 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or shortage cost? What is the expected come cost? (b) What is optimal number of cameras to order to minimize the expected intact cost? (c) Assume that the demand can be approximated by a normal distribution with mean 1000 and meter aberrance 100 cameras a month. What is the optimal number of cameras to order to minimize the expected come up cost? 10.Next months production at a manufacturing party will use a certain f irmness for part of its production process. Assume that there is an ordering cost of $1,000 incurred whenever an order for the resultant is placed and the solvent costs $40 per liter. Due to short product life cycle, un apply solvent cannot be used in following months. There will be a $10 disposal charge for each liter of solvent left over at the end of the month. If there is a shortage of solvent, the production process is seriously disrupted at a cost of $100 per liter short. Assume that the sign inventory level is m, where m = 0, 100, three hundred, 500 and 700 liters. a) What is the optimal ordering quantity for each case when the demand is discrete with PrD = 500 = PrD = 800 = 1/8, PrD = 600 = 1/2 and PrD = 700 = 1/4? (b) What is the optimal ordering policy for arbitrary sign inventory level m? (You need to delineate the critical value m? in addition to the optimal order-up-to quantity y ? . When m ? m? , you make an order. Otherwise, do not order. ) (c) Assume optimal qua ntity will be ordered. What is the total expected cost when the initial inventory m = 0? What is the total expected cost when the initial inventory m = 700? 22 CHAPTER 1. NEWSVENDOR PROBLEM 11.Redo Problem 10 for the case where the demand is governed by the continuous uniform distribution varying between four hundred and 800 liters. 12. An self-propelled corporation will make one prevail production run of move for violate 947A and 947B, which are not interchangeable. These part are no longer used in new cars, but will be needed as replacements for endorsement work in existing cars. The demand during the imprimatur period for 947A is approximately normally distributed with mean 1,500,000 parts and standard deviation 500,000 parts, while the mean and standard deviation for 947B is 500,000 parts and 100,000 parts. (Assume that two demands are item-by-item. Ignoring the cost of setting up for producing the part, each part costs only 10 cents to engender. However, if additional parts are needed beyond what has been bring outd, they will be purchased at 90 cents per part (the same price for which the automotive confederation sells its parts). Parts remaining at the end of the warranty period have a salvage value of 8 cents per part. There has been a marriage proposal to produce Part 947C, which can be used to replace either of the other two parts. The unit cost of 947C jumps from 10 to 14 cents, but all other costs remain the same. (a) Assuming 947C is not produced, how many 947A should be produced? b) Assuming 947C is not produced, how many 947B should be produced? (c) How many 947C should be produced in order to recompense the same component of demand from parts produced in-house as in the ? rst two parts of this problem. (d) How much money would be saved or lost by producing 947C, but meeting the same subdivision of demand in-house? (e) Is your answer to question (c), the optimal number of 947C to produce? If not, what would be the optimal number of 947C to produce? (f) Should the more expensive part 947C be produced instead of the two existing parts 947A and 947B. Why? tactile sensation compare the expected total costs.Also, suppose that D ? Normal(, ? 2 ). q xv 0 (x? )2 1 e? 2? 2 dx = 2 q (x ? ) v 0 q (x? )2 1 e? 2? 2 dx 2 + = 2 v 0 (q? )2 (x? )2 1 e? 2? 2 dx 2 t 1 v e? 2? 2 dt + Pr0 ? D ? q 2 2 where, in the 2nd step, we changed variable by letting t = (x ? )2 . 1. 5. EXERCISE 23 13. A warranty plane section manages the after-sale overhaul for a critical part of a product. The department has an obligation to replace any damaged parts in the next 6 months. The number of damaged parts X in the next 6 months is assumed to be a random variable that follows the following distribution x PrX = x 100 . 1 cc . 2 three hundred . 5 400 . 2The department currently has 200 parts in stock. The department necessarily to decide if it should make one last production run for the part to be used for the next 6 months. To start the pro duction run, the ? xed cost is $2000. The unit cost to produce a part is $50. During the warranty period of next 6 months, if a replacement request comes and the department does not have a part available in house, it has to buy a part from the spot-market at the cost of $100 per part. Any part left at the end of 6 month sells at $10. (There is no holding cost. ) Should the department make the production run? If so, how many items should it produce? 4. A store sells a particular brand of fresh juice. By the end of the day, any unsold juice is sold at a discounted price of $2 per gallon. The store gets the juice day-to-day from a local producer at the cost of $5 per gallon, and it sells the juice at $10 per gallon. Assume that the daily demand for the juice is uniformly distributed between 50 gallons to 150 gallons. (a) What is the optimal number of gallons that the store should order from the distribution each day in order to maximize the expected pro? t each day? (b) If 100 gallons are ordered, what is the expected pro? t per day? 15. An auto federation is to make one ? al purchase of a rare railway locomotive oil to ful? ll its warranty serve for certain car models. The current price for the engine oil is $1 per gallon. If the company runs out the oil during the warranty period, it will purchase the oil from a supply at the market price of $4 per gallon. Any leftover engine oil after the warranty period is useless, and costs $1 per gallon to get rid of. Assume the engine oil demand during the warranty is uniformly distributed (continuous distribution) between 1 million gallons to 2 million gallons, and that the company currently has half million gallons of engine oil in stock (free of charge). a) What is the optimal amount of engine oil the company should purchase now in order to minimize the total expected cost? (b) If 1 million gallons are purchased now, what is the total expected cost? 24 CHAPTER 1. NEWSVENDOR PROBLEM 16. A company is obli renderd to pr ovide warranty profit for Product A to its nodes next year. The warranty demand for the product follows the following distribution. d PrD = d 100 . 2 200 . 4 300 . 3 400 . 1 The company needs to make one production run to satisfy the warranty demand for entire next year. each unit costs $100 to produce the penalisation cost of a unit is $500.By the end of the year, the woman chaser value of each unit is $50. (a) Suppose that the company has currently 0 units. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. (b) Suppose that the company has currently 100 units at no cost and there is $20000 ? xed cost to start the production run. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. 17. Suppose you are running a restaurant having only one menu, lettuce salad, in the Tech Square.You should order lettuce every day 10pm after closing. Then, your supplier delivers the ordered amount of lettuce 5am next morning. Store hours is from 11am to 9pm every day. The demand for the lettuce salad for a day (11am-9pm) has the following distribution. d PrD = d 20 1/6 25 1/3 30 1/3 35 1/6 One lettuce salad requires two units of lettuce. The selling price of lettuce salad is $6, the buying price of one unit of lettuce is $1. Of course, leftover lettuce of a day cannot be used for future salad and you have to pay 50 cents per unit of lettuce for disposal. (a) What is the optimal order-up-to quantity of lettuce for a day? b) If you ordered 50 units of lettuce today, what is the expected pro? t of tomorrow? Include the purchasing cost of 50 units of lettuce in your calculation. Chapter 2 Queueing Theory Before acquiring into Discrete- clock Markov Chains, we will learn about frequent issues in the come uping theory. Queueing theory deals with a set of schemes having postponement space. It is a very powerful tool that can model a bro ad range of issues. Starting from analyzing a simple align, a set of queues connected with each other will be covered as well in the end. This chapter will give you the screen background knowledge when you read the required book, The Goal.We will revisit the queueing theory once we have more move modeling techniques and knowledge. 2. 1 Introduction Think about a dish out brass. All of you must have experienced wait in a help carcass. One example would be the Student pore or some restaurants. This is a charitable dust. A bit more automated expediency ashes that has a queue would be a call center and automated answering moulds. We can depend a manufacturing clay instead of a inspection and repair system. These waiting systems can be generalized as a set of bu? ers and master of ceremoniess. There are key factors when you try to model such a system.What would you need to analyze your system? How frequently guests come to your system? Inter-comer Times How fast you r servers can serve the clients? Service Times How many servers do you have? Number of Servers How large is your waiting space? Queue size of it If you can collect data about these metrics, you can characterize your queueing system. In general, a queueing system can be denoted as follows. G/G/s/k 25 26 CHAPTER 2. QUEUEING THEORY The ? rst garner characterizes the distribution of inter-comer multiplication. The second letter characterizes the distribution of assistance propagation.The third number denotes the number of servers of your queueing system. The fourth number denotes the total capacity of your system. The fourth number can be omitted and in such case it meat that your capacity is in? nite, i. e. your system can contain any number of people in it up to in? nity. The letter G represents a general distribution. Other candidate characters for this position is M and D and the meanings are as follows. G General Distribution M Exponential Distribution D settled Distr ibution (or constant) The number of servers can vary from one to many to in? nity.The size of bu? er can also be either ? nite or in? nite. To simplify the model, assume that there is only a single server and we have in? nite bu? er. By in? nite bu? er, it core that space is so wide of the mark that it is as if the limit does not exist. Now we set up the model for our queueing system. In terms of analysis, what are we interested in? What would be the performance measures of such systems that you as a manager should know? How long should your guest wait in line on average? How long is the waiting line on average? There are two concepts of average. One is average over succession.This applies to the average number of clients in the system or in the queue. The other is average over people. This applies to the average waiting time per guest. You should be able to distinguish these two. Example 2. 1. Assume that the system is empty at t = 0. Assume that u1 = 1, u2 = 3, u3 = 2, u4 = 3, v1 = 4, v2 = 2, v3 = 1, v4 = 2. (ui is ith nodes inter- arriver time and vi is ith customers inspection and repair time. ) 1. What is the average number of customers in the system during the ? rst 10 proceeding? 2. What is the average queue size during the ? rst 10 transactions? 3.What is the average waiting time per customer for the ? rst 4 customers? Answer 1. If we d un treat the number of people in the system at time t with respect to t, it will be as follows. 2. 2. LINDLEY EQUATION 3 2 1 0 27 Z(t) 0 1 2 3 4 5 6 7 8 9 10 t EZ(t)t? 0,10 = 1 10 10 Z(t)dt = 0 1 (10) = 1 10 2. If we d gross the number of people in the queue at time t with respect to t, it will be as follows. 3 2 1 0 Q(t) 0 1 2 3 4 5 6 7 8 9 10 t EQ(t)t? 0,10 = 1 10 10 Q(t)dt = 0 1 (2) = 0. 2 10 3. We ? rst need to compute waiting measure for each of 4 customers. Since the ? rst customer does not wait, w1 = 0.Since the second customer arrives at time 4, while the ? rst customers renovation ends at time 5. So , the second customer has to wait 1 minute, w2 = 1. Using the similar logic, w3 = 1, w4 = 0. EW = 0+1+1+0 = 0. 5 min 4 2. 2 Lindley Equation From the previous example, we now should be able to compute each customers waiting time given ui , vi . It requires too much e? ort if we have to draw graphs every time we need to compute wi . Let us generalize the logic behind shrewd waiting clock for each customer. Let us determine (i + 1)th customers waiting 28 CHAPTER 2. QUEUEING THEORY time.If (i + 1)th customer arrives after all the time ith customer waited and got served, (i + 1)th customer does not have to wait. Its waiting time is 0. Otherwise, it has to wait wi + vi ? ui+1 . propose 2. 1, and envision 2. 2 explain the two cases. ui+1 wi vi wi+1 Time i th arrival i th service start (i+1)th arrival i th service end Figure 2. 1 (i + 1)th arrival before ith service completion. (i + 1)th waiting time is wi + vi ? ui+1 . ui+1 wi vi Time i th arrival i th service start i th service end ( i+1)th arrival Figure 2. 2 (i + 1)th arrival after ith service completion. (i + 1)th waiting time is 0.Simply put, wi+1 = (wi + vi ? ui+1 )+ . This is called the Lindley Equation. Example 2. 2. Given the following inter-arrival clock and service times of ? rst 10 customers, compute waiting times and system times (time spent in the system including waiting time and service time) for each customer. ui = 3, 2, 5, 1, 2, 4, 1, 5, 3, 2 vi = 4, 3, 2, 5, 2, 2, 1, 4, 2, 3 Answer Note that system time can be obtained by adding waiting time and service time. Denote the system time of ith customer by zi . ui vi wi zi 3 4 0 4 2 3 2 5 5 2 0 2 1 5 1 6 2 2 4 6 4 2 2 4 1 1 3 4 5 4 0 4 3 2 1 3 2 3 1 4 2. 3. TRAFFIC INTENSITY 9 2. 3 Suppose Tra? c Intensity Eui =mean inter-arrival time = 2 min Evi =mean service time = 4 min. Is this queueing system stable? By stable, it means that the queue size should not go to the in? nity. Intuitively, this queueing system will not last because average service t ime is greater than average inter-arrival time so your system will soon explode. What was the logic behind this judgement? It was basically study the average inter-arrival time and the average service time. To simplify the judgement, we come up with a new quantity called the tra? c fanaticism. De? nition 2. 1 (Tra? Intensity). Tra? c intensity ? is de? ned to be ? = 1/Eui ? = 1/Evi where ? is the arrival rate and is the service rate. Given a tra? c intensity, it will fall into one of the following three categories. If ? 1, the system is stable. If ? = 1, the system is unstable unless both inter-arrival times and service times are deterministic (constant). If ? 1, the system is unstable. Then, why entert we call ? employ instead of tra? c intensity? Utilization seems to be more spontaneous and user-friendly name. In fact, drill just happens to be same as ? if ? 1.However, the problem arises if ? 1 because consumption cannot go over 100%. Utilization is bounded above by 1 and that is why tra? c intensity is regarded more general notation to compare arrival and service rates. De? nition 2. 2 (Utilization). Utilization is de? ned as follows. Utilization = ? , 1, if ? 1 if ? ? 1 Utilization can also be interpreted as the long-run fraction of time the server is put ond. 2. 4 Kingman nearness Formula Theorem 2. 1 (Kingmans High-tra? c estimation Formula). Assume the tra? c intensity ? 1 and ? is sozzled to 1. The long-run average waiting time in 0 a queue EW ? Evi CHAPTER 2. QUEUEING THEORY ? 1 c2 + c2 a s 2 where c2 , c2 are square coe? cient of conversion of inter-arrival times and service a s times de? ned as follows. c2 = a Varu1 (Eu1 ) 2, c2 = s Varv1 (Ev1 ) 2 Example 2. 3. 1. Suppose inter-arrival time follows an exponential distribution with mean time 3 minutes and service time follows an exponential distribution with mean time 2 minutes. What is the expected waiting time per customer? 2. Suppose inter-arrival time is constant 3 mi nutes and service time is also constant 2 minutes. What is the expected waiting time per customer?Answer 1. Tra? c intensity is ? = 1/Eui 1/3 2 ? = = = . 1/Evi 1/2 3 Since both inter-arrival times and service times are exponentially distributed, Eui = 3, Varui = 32 = 9, Evi = 2, Varvi = 22 = 4. Therefore, c2 = Varui /(Eui )2 = 1, c2 = 1. Hence, s a EW =Evi =2 ? c2 + c2 s a 1 2 2/3 1+1 = 4 minutes. 1/3 2 2. Tra? c intensity remains same, 2/3. However, since both inter-arrival times and service times are constant, their variances are 0. Thus, c2 = a c2 = 0. s EW = 2 2/3 1/3 0+0 2 = 0 minutes It means that none of the customers will wait upon their arrival.As shown in the previous example, when the distributions for both interarrival times and service times are exponential, the squared coe? cient of variation term becomes 1 from the Kingmans approximation formula and the formula 2. 5. slightS LAW 31 becomes study to compute the average waiting time per customer for M/M/1 qu eue. EW =Evi ? 1 Also note that if inter-arrival time or service time distribution is deterministic, c2 or c2 becomes 0. a s Example 2. 4. You are running a highway collecting money at the entering toll gate. You reduced the utilization level of the highway from 90% to 80% by adopting car pool lane.How much does the average waiting time in front of the toll gate decrease? Answer 0. 8 0. 9 = 9, =4 1 ? 0. 9 1 ? 0. 8 The average waiting time in in front of the toll gate is reduced by more than a half. The Goal is about identifying bottlenecks in a plant. When you become a manager of a company and are running a expensive machine, you normally want to run it all the time with unspoiled utilization. However, the implication of Kingman formula tells you that as your utilization approaches to 100%, the waiting time will be skyrocketing. It means that if there is any uncertainty or random ? ctuation input to your system, your system will greatly su? er. In lower ? region, increase ? is no t that bad. If ? near 1, increasing utilization a little bit can lead to a disaster. Atlanta, 10 years ago, did not su? er that much of tra? c problem. As its tra? c infrastructure capacity is acquire closer to the demand, it is getting more and more fragile to uncertainty. A clump of strategies presented in The Goal is in fact to decrease ?. You can do various things to reduce ? of your system by outsourcing some process, etc. You can also strategically manage or balance the cargo on di? erent parts of your system.You may want to utilize customer service organization 95% of time, while utilization of sales people is 10%. 2. 5 Littles Law L = ? W The Littles Law is much more general than G/G/1 queue. It can be applied to any black disaster with de? nite boundary. The Georgia Tech campus can be one black box. ISyE building itself can be another. In G/G/1 queue, we can slow get average size of queue or service time or time in system as we di? erently draw box onto the queueing sy stem. The following example shows that Littles law can be applied in broader context than the queueing theory. 32 CHAPTER 2. QUEUEING THEORY Example 2. 5 (Merge of I-75 and I-85).Atlanta is the place where two interstate highways, I-75 and I-85, merge and cross each other. As a tra? c manager of Atlanta, you would like to estimate the average time it takes to drive from the north con? uence point to the south con? uence point. On average, 100 cars per minute enter the merged area from I-75 and 200 cars per minute enter the same area from I-85. You also dispatched a chopper to take a aery snapshot of the merged area and counted how many cars are in the area. It turned out that on average 3000 cars are within the merged area. What is the average time between entering and exiting the area per vehicle?Answer L =3000 cars ? =100 + 200 = 300 cars/min 3000 L = 10 minutes ? W = = ? 300 2. 6 Throughput Another focus of The Goal is set on the throughput of a system. Throughput is de? ned as follows. De? nition 2. 3 (Throughput). Throughput is the rate of output ? ow from a system. If ? ? 1, throughput= ?. If ? 1, throughput= . The bounding constraint of throughput is either arrival rate or service rate depending on the tra? c intensity. Example 2. 6 (Tandem queue with two stations). Suppose your factory production line has two stations linked in series. Every raw material coming into your line should be processed by Station A ? rst.Once it is processed by Station A, it goes to Station B for ? nishing. Suppose raw material is coming into your line at 15 units per minute. Station A can process 20 units per minute and Station B can process 25 units per minute. 1. What is the throughput of the entire system? 2. If we double the arrival rate of raw material from 15 to 30 units per minute, what is the throughput of the whole system? Answer 1. First, obtain the tra? c intensity for Station A. ?A = ? 15 = = 0. 75 A 20 Since ? A 1, the throughput of Station A is ? = 15 units per minute. Since Station A and Station B is linked in series, the throughput of Station . 7. SIMULATION A becomes the arrival rate for Station B. ?B = ? 15 = = 0. 6 B 25 33 Also, ? B 1, the throughput of Station B is ? = 15 units per minute. Since Station B is the ? nal stage of the entire system, the throughput of the entire system is also ? = 15 units per minute. 2. Repeat the same steps. ?A = 30 ? = = 1. 5 A 20 Since ? A 1, the throughput of Station A is A = 20 units per minute, which in turn becomes the arrival rate for Station B. ?B = A 20 = 0. 8 = B 25 ?B 1, so the throughput of Station B is A = 20 units per minute, which in turn is the throughput of the whole system. 2. 7 SimulationListing 2. 1 Simulation of a Simple Queue and Lindley Equation N = 100 Function for Lindley Equation lindley = function(u,v) for (i in 1length(u)) if(i==1) w = 0 else w = append(w, max(wi-1+vi-1-ui, 0)) return(w) u v CASE 1 Discrete Distribution Generate N inter-arrival times and servic e times = sample(c(2,3,4),N,replace=TRUE,c(1/3,1/3,1/3)) = sample(c(1,2,3),N,replace=TRUE,c(1/3,1/3,1/3)) Compute waiting time for each customer w = lindley(u,v) w CASE 2 settled Distribution All inter-arrival times are 3 minutes and all service times are 2 minutes Observe that nobody waits in this case. 4 u = rep(3, 100) v = rep(2, 100) w = lindley(u,v) w CHAPTER 2. QUEUEING THEORY The Kingmans approximation formula is exact when inter-arrival times and service times follow iid exponential distribution. EW = 1 ? 1 We can con? rm this equation by simulating an M/M/1 queue. Listing 2. 2 Kingman Approximation lambda = arrival rate, mu = service rate N = 10000 lambda = 1/10 mu = 1/7 Generate N inter-arrival times and service times from exponential distribution u = rexp(N,rate=lambda) v = rexp(N,rate=mu) Compute the average waiting time of each customer w = lindley(u,v) mean(w) 16. 0720 Compare with Kingman approximation rho = lambda/mu (1/mu)*(rho/(1-rho)) 16. 33333 The Ki ngmans approximation formula becomes more and more true as N grows. 2. 8 Exercise 1. Let Y be a random variable with p. d. f. ce? 3s for s ? 0, where c is a constant. (a) get a line c. (b) What is the mean, variance, and squared coe? cient of variation of Y where the squared coe? cient of variation of Y is de? ned to be VarY /(EY 2 )? 2. Consider a single server queue. Initially, there is no customer in the system.Suppose that the inter-arrival times of the ? rst 15 customers are 2, 5, 7, 3, 1, 4, 9, 3, 10, 8, 3, 2, 16, 1, 8 2. 8. EXERCISE 35 In other words, the ? rst customer will arrive at t = 2 minutes, and the second will arrive at t = 2 + 5 minutes, and so on. Also, suppose that the service time of the ? rst 15 customers are 1, 4, 2, 8, 3, 7, 5, 2, 6, 11, 9, 2, 1, 7, 6 (a) Compute the average waiting time (the time customer overlook in bu? er) of the ? rst 10 departed customers. (b) Compute the average system time (waiting time plus service time) of the ? st 10 departed cust omers. (c) Compute the average queue size during the ? rst 20 minutes. (d) Compute the average server utilization during the ? rst 20 minutes. (e) Does the Littles law of hold for the average queue size in the ? rst 20 minutes? 3. We want to decide whether to employ a human operator or buy a machine to paint steel beams with a rust inhibitor. Steel beams are produced at a constant rate of one every 14 minutes. A skilled human operator takes an average time of 700 seconds to paint a steel beam, with a standard deviation of 300 seconds.An automatic lynx takes on average 40 seconds more than the human painter to paint a beam, but with a standard deviation of only 150 seconds. reckon the expected waiting time in queue of a steel beam for each of the operators, as well as the expected number of steel beams waiting in queue in each of the two cases. Comment on the e? ect of variability in service time. 4. The arrival rate of customers to an ATM machine is 30 per hour with exponentially distirbuted in- terarrival times. The transaction times of two customers are independent and identically distributed.Each transaction time (in minutes) is distributed according to the following pdf f (s) = where ? = 2/3. (a) What is the average waiting for each customer? (b) What is the average number of customers waiting in line? (c) What is the average number of customers at the localize? 5. A production line has two machines, forge A and simple machine B, that are arranged in series. Each job needs to processed by automobile A ? rst. Once it ? nishes the bear on by Machine A, it moves to the next station, to be processed by Machine B. Once it ? nishes the processing by Machine B, it leaves the production line.Each machine can process one job at a time. An arriving job that ? nds the machine picky waits in a bu? er. 4? 2 se? 2? s , 0, if s ? 0 otherwise 36 CHAPTER 2. QUEUEING THEORY (The bu? er sizes are assumed to be in? nite. ) The processing times for Machine A are iid h aving exponential distribution with mean 4 minutes. The processing times for Machine B are iid with mean 2 minutes. Assume that the inter-arrival times of jobs arriving at the production line are iid, having exponential distribution with mean of 5 minutes. (a) What is the utilization of Machine A?What is the utilization of Machine B? (b) What is the throughput of the production system? (Throughput is de? ned to be the rate of ? nal output ? ow, i. e. how many items will exit the system in a unit time. ) (c) What is the average waiting time at Machine A, excluding the service time? (d) It is cognise the average time in the entire production line is 30 minutes per job. What is the long-run average number of jobs in the entire production line? (e) Suppose that the mean inter-arrival time is changed to 1 minute. What are the utilizations for Machine A and Machine B, respectively?What is the throughput of the production system? 6. An auto collision shop has slightly 10 cars arriving pe r week for repairs. A car waits after-school(prenominal) until it is brought inside for bumping. after(prenominal) bumping, the car is painted. On the average, there are 15 cars waiting outside in the yard to be repaired, 10 cars inside in the bump area, and 5 cars inside in the exposure area. What is the average length of time a car is in the yard, in the bump area, and in the photograph area? What is the average length of time from when a car arrives until it leaves? 7. A small bank is sta? d by a single server. It has been observed that, during a normal business day, the inter-arrival times of customers to the bank are iid having exponential distribution with mean 3 minutes. Also, the the processing times of customers are iid having the following distribution (in minutes) x PrX = x 1 1/4 2 1/2 3 1/4 An arrival ? nding the server busy joins the queue. The waiting space is in? nite. (a) What is the long-run fraction of time that the server is busy? (b) What the the long-run ave rage waiting time of each customer in the queue, excluding the processing time? c) What is average number of customers in the bank, those in queue plus those in service? 2. 8. EXERCISE (d) What is the throughput of the bank? 37 (e) If the inter-arrival times have mean 1 minute. What is the throughput of the bank? 8. You are the manager at the Student Center in charge of running the food court. The food court is represent of two parts prep station and abolishs desk. Every person should go to the cooking station, place an order, wait there and pick up ? rst. Then, the person goes to the cashiers desk to check out. After checking out, the person leaves the food court.The coo