Dynamic Programming and Equipment Resetting Decision Rules

HALL AND EILON consider the problem of determining optimum production runs on a process which deteriorates, in a linear manner, with time, and hence eventually becomes so uneconomic that it may be worthwhile to reset the process. In this paper Hall and Eilon consider the case where the resetting of the process initiates runs with the same statistical behaviour for each run. In general, however, this will not be the case; for not only will there be human variations in each setting up, but also, if components (e.g. cutting tools, etc.) are to be replaced, these will have their own variations in many ways. It seems natural to extend the model to cater for such variations and to consider the problem of minimizing the total expected cost of satisfying an order for n items. This problem can be expressed as one of determining decision rules for the length of a production run once the current values of the variable resetting characteristics have been identified.