Dynamic Programming Resource Allocation Example

Essays on Dynamic Programming: Resource Allocation Assignment Executive summery: Dynamic programming approach usually offers an optimal solution for complex reservoir operational problems. In this report analysis an attempt to determine the relevance of the dynamic programming in resource allocation scenario as one of the optimizing tool to be relied upon in making decision. A brief overview will include its application, advantages and its shortfalls as well. The final result of module formulation shows the applicability of the dynamic programming in resolving the investment decision. Introduction: The report describes how to formulate and implement by allocating resources using a dynamic programming. The method allows the fund manager to make an informed decision of investing the $10 million on behalf of the pension fund. In addition, it shows the optimal return expected to be earned at different risk levels. The results are tested and confirm through formulating different stages for each product through a simplified scenario. The investment details are illustrated using the scenario bellow. Fund Investment amount must be multiple of * Expected annual return per  £1m of investment Maximum risk exposure to fund A  £3 M  £30,000  £6m B  £4 M  £40,000 none C  £2 M  £60,000  £6m Problem formulation is determined by assuming that at stage 1; product C, stage 2; product A and stage 3; product B. The next step is to determine transformation and returns functional formulas. Therefore, the transformation t n will change all input stages x n to the output stages xn-1 giving an outcome decision d n which can be written as follows; Stage 3: X2 =t3(X3, d3) =X3-2d3 Stage 3 buys Investment B at $ 4M each Stage 2: X1 =t2(X2, d2) =X2-3d2 Stage 2 buys Investment A at $ 3M each Stage 1: X0 =t1(X1, d1) =X1-4d1 Stage 1 buys Investment C at $ 2M each Where as, the expected reward r n which is the total benefits at each stage n which relies on the number of d n of units of production n bought in stage n are as follows; Stage 3: r3(X3, d2) =40d3 Stage 2: r2 (X2, d2) =30d2 Stage 1: r1 (X1, d1) =60d1 The objective function i.e. the total return from investment at this initial stage includes only the total reward r 1 as there is no any other previous stage. Therefore the output as well as the objective function is determined as follows: X 0 = X1-4d1; f1 (X1) = r1(X1, d1) = 60 d1 Where 0 ≠¤ X 1 ≠¤ 9 and 0 ≠¤ d1≠¤ (Appendix table 1) X1 shows the input at stage 1, d1 is the anticipated decisions at this particular stage, where as, d*1 is the optimal decision at a given value of input X1 and f1(x1) is the reward to be earned for making decision d1 using input X1. At stage 2, the decision d2 is the number of units purchases for product C such that 0 ≠¤ d2≠¤ 1(Appendix table 2). The output at this stage is X1=X2-3d2 and the objective function is F2(X2) =30d2+f1(X1) where f1(X1) represents the exact value of objective function calculated in the previous stage. At stage 3 (product B $ 4 M $40K), is the stage where the investment is at its maximum i.e. the value of X3= 9 the result at this stage is as shown in table 3. Where the optimal results are; Stage 3: X3 = 9, d3=1, X2=X3-2d3=9-2=7 Stage 2: X2=7, d2=1, X1=X2-3d2=7-3=4 Stage 1: X1=4, d1=1, X0=X1-4d1=4-4=0 (Appendix table 3). According to the results it shows that the fund manager should consider purchasing the following Stage 3: One unit of product C at a cost of 2 millions Stage 2: One unit of product A at a cost of 3 millions Stage 1: One unit of product B at a cost of 4 millions This will optimize the investment i.e. 2+3+4+9 Millions and the expected returns will be $60,000 per unit of $ 1 million investment from product C $30,000 per unit of $ 1 million investment from product A $40, 000 per unit of $ 1 million investment from product B Thus, the total returns will be $ 190 millions which is the same as the value of the objective function in stage 3 Conclusion: Based on the above results, it is quite clear that, unlike linear programming, dynamic programming is very simple to formulate and solve since there are no complex variables. In addition, the incorporation of different constraints is much easier as compared to linear and non linear programming. Thought that is the case, there are some disadvantages of this method, for instance, designing and formulating the recursive equations may be so frustrating and complex beside not providing one time period solution to various problems as compared to linear programming. Therefore, considering all the above, the manager would be in a better position in making the investment decision using dynamic programming. Appendix 1 Table 1    d1    X1 0 1 2 d*1 F*1(x1) x0 0 0       0 0 0 1 0       0 0 1 2 0       0 0 2 3 0       0 0 2 4 0 60    1 60 0 5 0 60    1 60 1 6 0 60    1 60 1 7 0 60    1 60 3 8 0 60 120 2 120 0 9 0 60 120 2 120 1 Table 2 d2    X2 1 2 d*2 f2(x2) x1 0 0    0 0 0 1 0    0 0 0 2 0    0 0 0 3 0 30 1 30 0 4 60 90 1 90 1 5 60 90 1 90 1 6 60 90 1 90 3 7 60 90 1 90 4 8 120 150 1 150 5 9 120 150 1 150 6 Table 3          d3          X3 0 1 2 3 4 5 6 d*3 f3(x3) X2 9 150 190 150 100 120 150 180 1 190 7 References: Bellman, Richard, 1957, â€Å"Dynamic Programming† Princeton, NJ: Princeton University Press. Breton, Michele, Pascal Francisco 2006, Dynamic programming approach to price installation option, â€Å"European Journal of operational Research, Vol. 169(2), pages 667-676. Elton, Edwin, J, Gruber, Martin J, 1971, â€Å"Dynamic Programming Approach to price installment in Finance, â€Å"Journal of Finance, Vol. 26(2), pages 473-506 Finn E, Edward C. Prescott, 1977, â€Å"Rules rather than the discretion: The Inconsistency Dynamics† Cambridge, MA: Harvard University Press, 198 George G, Rogers, David F, Sweeney Dennis J, 2010, â€Å"Risk management strategies of portfolio optimization,† Euro Journal of operation Research, Vol. 207(1), page 409-419 Handy, A, Tasha, 2006, â€Å"Operational research; Introduction, eighth edition, prentice, hall in India private limited, New Delhi James C, T, Mao Carl E, S, 1966, â€Å"Decision Theory Approach to portfolio selection† Management science, Vol. 12 (8), page B323-B333. Martin R, Young, 1998, â€Å"A minim ax portfolio selection rule with lines Linear Programming solution† Management Science, Vol. 12(8), page B323-B333. Nancy, Robert E, Lucas, Edward C. Prescott, 2009, â€Å"Recursive methods in economic Of optimal plans," Journal of Political Economy, 1977, 85, 473-491 Sharma, J, K, 2007, Operational research; Theory and application, third edition, Macmillan publishers

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HLSC Spiritual and Social Dimensions

Question: Discuss about the HLSCfor Spiritual and Social Dimensions. Answer: Introduction In general, cancer is considered as the occurrence of a chronic stressor that affects the quality of life. This disease diagnosis adversely impacts different dimensions of a womans life, including her psychological, physical, spiritual, and social dimensions, triggering long-term after-effects on the quality of life. This disease diagnosis frequently is accompanied by distress, such as unsolicited disturbing thoughts which can lead to emotional responses and psychological challenges. Coping with this disease after the diagnosis is a vital health concern that results in adjustments to the malady. A woman in this condition has to deal with all of these difficulties to adjust to the diagnosis and with her new life situations. Emotional Responses Diagnosis of any cancer triggers different emotional responses which vary from patient to patient. In this situation, a patient is likely to experience shock and disbelief as the initial responses, followed by a period of distress considered as mixed symptoms of anxiety, depression, and anger. In the course of this time, a woman may experience persistence despondency and irritability (Morse, Pooler, Vann-Ward, Maddox, Olausson, Roche-Dean and Martz, 2014). Upon receiving a cancer diagnosis any woman may develop a sense of guilt that her family has to get through all these. A mother might be terrified for the future of her children and might get more affected than others. She might also fear about how this disease and its treatments might distress her family. These emotional reactions are considered harmful but they are very normal in relation to cancer diagnosis. The emotional state of sorrow about her cancer and the deviations it brings is common and might actually help her to cope( Tamagawa, et al., 2013). Cognitive Responses This disease can cause psychological trauma. A womans diagnosis of this disease can be life-altering. Her cognitive responses of this stressful situation might include confusion, relentless worries, common negative thoughts and outlook, forgetfulness, difficulty in concentration and mental tardiness(Wang, et al., 2014). Cognitive responsesfrequently include mental shock, denial, restriction of interests, alterations in body image and self-esteem, cognitive impairments, sleep disorders, reconsideration of life and mortality, suicidal approaches and ineptness (Janelsins, Kesler, Ahles, Morrow, 2014). When confronted by a diagnosis of this disease, women like a woman typically engross in the cognitive responses of appraising the nature of the stressor (example: risks, real loss or harm). Cognitive responses to this disease have been associated with anxiety and adjustment in that the higher the apparent threat, the poorer the level of well-being and the greater the level of suffering. M ajor depressive condition after this disease diagnosis can cause cognitive impairment. Cognitive impairment predicts poor psychological functioning (Janelsins, Kesler, Ahles, Morrow, 2014). Behavioral Responses Behavioral changes are a usual side effect of this disease diagnosis that takes account of disorders in sleep, mood, energy, and cognition. It can be overwhelming for a woman to deal with cancer. These symptoms source severe disturbance in the quality of life of the patient and perhaps remain for years (Berman, et al., 2014). Fatigue is progressively documented as one of the most typical worrying side effects. Cancer-related fatigue is more enduring, more severe, and more restricting than common fatigue due to overexertion or deficiency of sleep (Galiano-Castillo, et al., 2014). Many kinds of literature suggest that difficulty in sleeping are normal among victims. Sleep disruption causes considerable disturbance in the quality of life of a woman suffering from this disease and is allied with complications like daytime fatigue, the general capability to function, depressed attitude, and agony. Depressive symptoms and psychological distress are usually maximum in the first six months a fter this disease diagnosis and then decline over time as women adjust to the preliminary jolt of diagnosis and critical effects of management (Berman, et al., 2014). Risk Factors The treatment of this disease can be very traumatic for a woman. The situation becomes worse for a mother because of concern for the children. Treatment of this disease can prevent her from breastfeeding which can negatively impact both a woman and the babies. Treatment of early stage this disease involves breast-sparing surgery (lumpectomy and mastectomy) followed by radiation therapies. Lumpectomy carries the risk of side effects such as pain, bleeding, tenderness, the formation of hard scars and change in shape and form of breast. Risk factors of mastectomy include infection, bleeding, lymphedema, pain, numbness, and formation of hard scars at surgical sites (Rakhra, et al., 2016). Risk factors of radiation include skin problems, fatigue, breast and nipple soreness etc. In the case of lactating women like a woman, a large variation in milk output of the irradiated breast has been found. Lumpectomy and any other invasive breast surgeries damage the core tissues of breasts and inter rupt usual drainage of milk. Even though radiation has not completely damaged the lactation capacity, surgically treated breast tends to not lactate normally (Leal, Stuart, Carvalho, 2013). Protective Factors At first, a woman needs her family on her side to cope with this hostile situation. According to (Colby Shifren, 2013), being mentally stable is very much essential for this disease patient. Seeking help from mental health professionals is vital for any woman. They can teach a woman and her family members many problem-solving approaches in a supportive environment. A woman with this disease may not eat poorly, for example, intake smaller number of meals and take foodstuffs with inferior nutritional values. They may also cut back on their required exercise. They may have to suffer receiving proper sleep at night and they may take away themselves from friends and family. Simultaneously, these women may consume alcohol, caffeine, cigarettes and other harmful drugs in an effort to calm themselves (Chlebowski, 2013). Thus, a woman must be restrained from all these things. Getting good nutrition and gentle exercise during her treatment is important. The social cognitive theory may give a helpful system to understanding physical activity among patients with breast cancer amid treatment, however, correlation strength differs with physical action estimation type. Conclusion Getting a diagnosis of this disease can be one of the most upsetting life events any woman ever experiences. Distress naturally lingers even after the primary shock of diagnosis has passed. The patient may be very worried about her symptoms, treatments, and mortality.A womans concern for her infants makes her emotional state ever more challenging. This can contribute to anxiety, chronic stress, and depression. Negative emotional responses can cause her to discontinue from performing things that are good for her and start doing stuff that is unsafe for anyone but particularly worrying for those with this severe malady. Thus, seeking professional help is vital for her as soon as possible. References Berman, M. G., Askren, M. K., Jung, M., Therrien, B., Peltier, S., Noll, D. C., Cimprich, B. (2014). Pre-treatment worry and neurocognitive responses in women with this disease. Health psychology, 222. Colby, D. A., Shifren, K. (2013). Colby, D. A., Shifren, K. (2013). Optimism, mental health, and quality of life: a study among victims. Psychology, health medicine, 18(1), 10-20. Galiano-Castillo, N., Ariza-Garca, A., Cantarero-Villanueva, I., Fernndez-Lao, C., Daz-Rodrguez, L., Arroyo-Morales, M. (2014). Galiano-Castillo, N., Ariza-Garca, A., Cantarero-Villanueva, Depressed mood in this disease survivors: associations with physical activity, cancer-related fatigue, quality of life, and fitness level. European Journal of Oncology Nursing, 18(2), 206-210. Janelsins, M. C., Kesler, S. R., Ahles, T. A., Morrow, G. R. (2014). Janelsins, M. C., Kesler, Prevalence, mechanisms, and management of cancer-related cognitive impairment. Janelsins, M. C., Kesler, S. R., Ahles, T. A., Morrow, G. R. (2014)International Review of Psychiatry, 26(1), 102-113. Leal, S. C., Stuart, S. R., Carvalho, H. D. (2013). Breast irradiation and lactation: a review. Expert review of anticancer therapy, 13(2), 159-164. Morse, J. M., Pooler, C., Vann-Ward, T., Maddox, L. J., Olausson, J. M., Roche-Dean, M., Martz, K. (n.d.). Rakhra, S., Bethke, K., Strauss, J., Hayes, J. P., Hansen, N., Khan, S. A., Donnelly, E. D. (2016). Rakhra, S., Bethke, K., StrauRisk Factors Leading to Complications in Early-Stage This disease Following Breast-Conserving Surgery and Intraoperative Radiotherapy. Annals of Surgical Oncology, 1-4. Tamagawa, R., Giese?Davis, J., Speca, M., Doll, R., Stephen, J., Carlson, L. E. (2013). Tamagawa, R., Giese?Davis, J., Trait mindfulness, repression, suppression, and self?reported mood and stress symptoms among women with this disease. Journal of clinical psychology, 69(3), 264-277. Wang, Y., Yi, J., He, J., Chen, G., Li, L., Yang, Y., Zhu, X. (2014). Cognitive emotion regulation strategies as predictors of depressive symptoms in women newly diagnosed with this disease. Psycho?Oncology, 23(1), 93-99.

Juvenile Offenders Essays - Criminology, Childhood, Crime

Juvenile Offenders Juvinile Should Juveniles be waived to adult court Philosophy 14 Nov 98 Should juveniles be waived to adult court. There has been tension between teens (pre-teens) and adults for thousands of years, and the question how to deal with the youth of a culture, in a punishment sense, has been with us for just as long. Socrates, for example, stated that children show little respect for there elders. Since Socrates time largely due to the spread of guns and drugs, younger and younger children are committing violent crimes. Children that have special needs or have committed a criminal act have been subject to state protection since, 1838. The first juvenile court was established in Chicago in 1890. The assumption, that was made at that time, was that the criminal justice system should work to help youngsters, not to humiliate or punish them. Along with the creation of the juvenile justice system went the creation of status offenses, these are offenses that if committed by an adult, would not be consi dered an offense. In the 1950's and 60's many laws were passed to protect the rights of children, in a court of law. The major decisions of this time were: Kent v. United States, In re Gault, and In re Winship. Since the time that these laws were enacted, the number of juveniles committing violent offenses has risen dramatically. There are two distinct schools of thought in this argument: side A believes that a persons age should not prevent that person from feeling the full effect of the adult court system, while side B feels that you simply cannot apply the same rules to juvenile offenders that you do to adults. I will first present side A's case then B's and finally end with my own opinion. Many states have begun enacting new laws about the transfer of juveniles, that are more harsh on juveniles. Minnesota, for example, has a new law that states a 16 or 17 year old person that has been charged with a violent offense has to prove to court why they should be tried in the juvenile s ystem. In cases where the offender is younger than 16 the prosecutor must show why the juvenile should be waived. One of main issues of side A, is that if the offender is too old the sentence would not be severe enough for the crime that had been committed. Another issue is the overcrowding of the juvenile justice system. Many of the offenders in the juvenile system, if a few years older, would have already been sentenced to life sentences in an adult court. Side A does not believe that a persons age should be the lone determining factor for non-waiver. While side A does believe that there are a great many negative influences on today's youth, they believe that these circumstances do not dismiss that crimes that have been committed. The core belief that most of the side A advocates share is, the belief that the small percentage of the juveniles that are committing the serious crimes are past the point where a juvenile court could be of any help. Side A truly feels that by allowing s erious juvenile offenders to be waived to adult court, thus receiving a stiffer sentence, the community, as a hole, will be much better served. Side B believes, essentially, that no child (juvenile) should be waived. Side B sees several key factors for the rise in juvenile crime. These reasons are ones that are out of the control of the juvenile. The key factors are: (a) Unemployment among teens was 19 percent in 1993, up from 15.3 percent five years earlier, and for black youths the unemployment rates were twice that. (b) Since 1970, Aid to families with dependent children benefits have declined an average of 45 percent in inflation-adjusted dollars, according to the Children's Defense Fund. (c) In 1992, there were 14.6 million children living below the poverty line, the Children's Defense Fund says, about 5 million more than in 1973. (d) In 1993, there were 3 million victims of child abuse, according to the National Committee for the Prevention of Child Abuse- a rate 50 percent hi gher than in 1985.