Formulation of a tactical logistics decision analysis problem using an optimal control approach

Abstract

In recent years, engineers, economists, and military commanders amongst others have placed increasing emphasis on decision making under conditions of uncertainty. Much of life involves making choices under uncertainty, that is, choosing from some set of alternative courses of action in situations where we are uncertain about the actual consequences that will occur for each course of action being considered. It is the field of Decision Analysis that is concerned with the making of rational, consistent decisions, notably under conditions of uncertainty. That is, Decision Analysis helps the decision maker to analyse a complex situation with many different alternatives, states and consequences and to choose the best alternative in light of the information available. The objective of Decision Analysis is to choose a course of action consistent with the basic preferences and knowledge of the decision maker. In this paper we investigate the problem of decision making for the direction of resources within a network of support. This network seeks to mimic how logistic support might be delivered in a military area of operations. It is shown that transitions in the state variables depend upon the status of the network at the end of the previous cycle, the physical distribution decisions taken in the current and previous cycle and the demand for support experienced in the current cycle. By using control theory we are able to formulate the above problem as an optimal control problem, that is, the state variables $X(t)$ are governed by a certain transition function $F$, and we are seeking the decision stream (optimal controller) for physical distribution actions such that a given Combat Power Cost function is optimised. This latter function is fashioned on some contemporary measures of effectiveness adopted for military logistics. Furthermore, the problem of decision making under uncertainty is also studied by using robust optimal control techniques to formulate the effects of changing situational awareness. A simple case study is given to show the potential of the proposed techniques.