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MT3833 UTILITIES DECISIONS AND INVENTORIESAims To provide an introduction to the formulation and solution of problems of decisiontaking and problems in the management of inventory systems for a single item. To motivate the need for utility functions, and to explain how they are assessed and employed.
ObjectivesBy the end of the course students are expected to be able to formulate a decision problem, identifying actions and states of nature, and draw up a utility table;  apply the concept of dominance and identify admissible actions and decision rules;  determine Bayes rules using expected worths or posterior expected utilities;  represent and analyse a decision problem using a decision tree;  realise that the value of money is not its face value;  determine the expected utility of an investment or gamble;  assess an individual's attitude to risk by inspection of his utility function;  derive the optimal order quantity in a deterministic inventory problem;  solve deterministic dynamic programming problems by forward or backward induction;  formulate a probabilistic inventory problem and establish the optimal policy.
Syllabus Decision theory: Elements of decision problems. Maximin and Bayesian approaches. Randomised actions. Decision rules and their worths. Bayes Theorem. Decision trees. Sequential decision problems. Bellman's optimality principle. Utility theory: Nonlinearity of value of money. St Petersburg paradox. Utility functions. Attitudes to risk. Risk premiums. Axioms of coherence. Assessment of utility functions.  Inventory theory: Economic order quantity models. Quantity discounts. Deterministic dynamic programming and its application to multiperiod models. Probabilistic demand models. Newsboy problem. Ss models. Continuous review models.
TextbooksOperations Research, an introduction, 9th ed.: H A Taha, Pearson.Operations Research, applications and algorithms, 4th ed.: W. L. Winston, Thomson/ Brooks / Cole. An introduction to management science: quantitative approaches to decision making, 13th ed.: D.R. Anderson, D.J. Sweeney, T.A. Williams & R.K. Martin, Cengage Learning. Choice Against Chance: J Aitchison, AddisonWesley.
Assessment2 Hour Examination = 100%
PrerequisitesMT2004 (or MT2001 and MT1007)
AvailabilityAcademic year 2012/13 in semester 2 at 12
LecturerDr I B J GoudieClick here for access to past examination papers via iSaint.
Click here to see the University Course Catalogue entry. Revised: PMH (October 2012)
