A dynamic programming approach to the multi-stream replacement problem

Abstract

Often, in both the military and industrial sectors, the unavailability of essential components renders a complex system inoperable. Therefore, the primary objective of this research is to develop a methodology for determination of feasible strategies for the repair/replace decision. In the general equipment replacement problem, a finite planning horizon may be partitioned into stages such that an end item deteriorates toward a final stage where it is no longer economically or operationally feasible to continue to repair the item, or the item experiences fatal failure. This multi-stage deterioration process is very amenable to a dynamic programming solution methodology where the output from one stage becomes the input to the next stage.

In the multi-stream replacement problem, the population of end items is grouped into streams depending upon such parameters as item age, the number of operational hours, or the environment in which the item operates. The reliability function is used to describe the survivor probability in this population model. A dynamic repair/replace program is formulated where the state functions are characterized by two parameters - item age and current operational condition.

A computerized model is then developed that facilitates evaluation of repair/replacement strategies with respect to total life cycle costs of a logistics system. The solution methodology accommodates both stochastic and/or deterministic demand; different hazard models; a budget constraint; repair capacity constraint; various levels of repair; technological improvement; and organizational implementation issues. The operations impact of a generalized methodology for supporting the repair/replace decision and mode of repair is to provide opportunities for a more efficient use of organizational resources such as capital and repair facilities.