Optimal Service Policies and Finite Time Horizons

This paper characterizes optimal service policies in terms of the frequency and timing of services which are intended to maintain a stock of assets. The model is non-stochastic. The results are obtained by a two-stage step-wise minimization procedure wherein dynamic programming is first used to characterize sub-optimal policies and then the calculus of finite differences is utilized to select the optimal policy. The effect of the time horizon on the optimal policy is emphasized throughout and, in two specific interpretations of the model, the classical results of the economic lot-size and equipment replacement policy are shown to be limits of more general policies.