Optimum Operation of a Complex Activity Under Conditions of Uncertainty

The model presented is suitable for determining the optimum manner of operation of a complex activity that depends on the maintenance of each of many subactivities, each subactivity being subject to uncertainty, measurable by a probability distribution. The activity discussed is the flying of planes at a base, the subactivities being the supply of spare parts. The first problem of the base is how many of each part to order. This has been satisfactorily solved by existing literature. The second problem is when to order, if the lack of any one of many different parts can ground an aircraft. It is this problem which the present paper solves. Consistent with stated assumptions, formulas are derived that yield minimum routine supply cost sets of reorder points (one reorder point for each part). Each set gives some specified protection against a plane being grounded because the base lacks one or more parts, at minimum cost, ignoring costs which arise from grounding of planes. Taking into account the costs that arise from the grounding of planes, such as the cost of rush requisitions and the need for additional aircraft and other considerations, a procedure is developed for choosing one set among all minimum cost sets which is optimum in an over-all sense. The solution is put in a form which can be used on a decentralized basis and under changing conditions. The use of the model under dynamic conditions is discussed. A variant of the main model is described which should be extremely useful for combat situations. Operations Research , ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.