# School of Mathematics and Statistics

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2011/2012 Sem. 1

## 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

Dr I B J Goudie