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Decision Networks is a technique for solving problems which involve a sequence of decisions. It is similar in style to critical path analysis in that it consists of arrow diagrams which give a visual representation of the problem and are used as a basis for a simple calculation procedure. The technique can deal with deterministic and stochastic problems and in the latter case is more general than decision trees. The decision network approach meets the need for a method of solution for multi-stage decision problems which is easily understood, helps the user to visualize the nature of the problem and is routine in application.

Insurance companies charge reduced premiums to motorists who go through a period of one or more years without making a claim. When an accident occurs the insured frequently finds himself with the option of either making a claim and reverting to a higher premium or paying for the repair himself. Most motorists operate an informal system of "no-claim limits", whereby they only claim for repairs which exceed a certain cost. In this paper it is shown how, under reasonable assumptions regarding the rate of accidents and the distribution of repair costs, optimal no-claim limits can be determined. These minimise the long run average cost of premiums and repairs and show significant savings over the case where all claims are made. The effect of an "excess clause", whereby the insured agrees to pay a first amount of any claim is also studied, and rules for determining whether it is profitable to accept such a clause are presented in the form of a graph.

A method of scheduling machines is presented which incorporates the facility of providing proven optimum solutions for minimum throughput time. The method employs branch and bound procedures and includes a new, job based, bounding procedure which is well suited to the situation where all jobs are not processed by all machines. Comparisons are made with well known bounding procedures and computational experience is reported with examples taken from real applications.

The problem of minimising the overall duration of a project subject to constraints on the availability of resources is considered with particular reference to the use of branch and bound methods. A new resource based bound, new dominance rules and an innovatory network breakdown technique which preserves optimality are reported. Computational experience and comparisons with schedules obtained by decision rule methods are given.

This paper describes two complementary studies concerning the maintenance and replacement of heavy haul railway track. Minimum cost policies are derived using decision networks in one case and a group replacement model in the other. The results indicate relatively large cost savings on current practice.

In the repair limit replacement method when an item requires repair it is first inspected and the repair cost is estimated. Repair is only then undertaken if the estimated cost is less than the "repair limit". Dynamic programming methods are used in this paper as a general approach to the problem of determining optimum repair limits. Two problems are formulated and the cases of finite and infinite planning horizons and discounted and undiscounted costs are discussed. Methods are given for allowing for equipment availability and for the introduction of new types of equipment. An improved general formulation for finite time horizon, stochastic, dynamic programming problems is developed.

In the first section a modification to Howard's policy improvement routine for Markov decision problems is described. The modified routine normally converges the more rapidly to the optimal policy. In the second section a particular form of recurrence relation, which leads to the rapid determination of improved policies is developed for a certain type of dynamic programming problem. The relation is used to show that the repair limit method is the optimal strategy for a basic equipment replacement problem.

The problem of scheduling activities so as to minimize project duration in the presence of resource constraints is considered. A branch and bound algorithm is described and some limited computational experience is reported.

The report is based on a study of the replacement of Army vehicles. These vehicles are currently phased out of service by a system of decision rules called repair limits. Existing repair limit systems, although superior to group replacement policies, appear to be sub-optimum. A theory of repair limits is proposed. This leads to the determination of optimum repair limits by a simulation method. A second optimization method is introduced based on the use of certain frequency distributions which are found to represent the repair cost data. The results show that the methods proposed can be expected to lead to financial savings.