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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.
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: 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.
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, Addison-Wesley.
Assessment2 Hour Examination = 100%
PrerequisitesMT2004 (or MT2001 and MT1007)
AvailabilityAcademic year 2012/13 in semester 2 at 12
LecturerDr I B J Goudie
Click here for access to past examination papers via iSaint.
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Revised: PMH (October 2012)