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Courses in Mathematics and Statistics Level 1 Modules Level 2 Modules Level 3 Modules Level 4 Modules Level 5 Modules Honours timetable 2011/2012 Sem. 1 2011/2012 Sem. 2 2012/2013 Sem. 1 & Sem. 2 2013/2014 Sem. 1 & Sem. 2

MT3833 UTILITIES DECISIONS AND INVENTORIES Aims - To provide an introduction to the formulation and solution of problems of decision-taking 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. Objectives By 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: Non-linearity 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 multi-period models. Probabilistic demand models. Newsboy problem. S-s models. Continuous review models. Textbooks Operations 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, Addison-Wesley. Assessment 2 Hour Examination = 100% Prerequisites MT2004 (or MT2001 and MT1007) Availability Academic year 2012/13 in semester 2 at 12 Lecturer Dr I B J Goudie Click here for access to past examination papers via iSaint. Click here to see the University Course Catalogue entry. Revised: PMH (October 2012)