On the discrete time-proportional demand inventory problem

Abstract

This paper discusses a lot-size model with a very specific time-varying demand pattern, namely a time proportional demand which occurs only at discrete and equal intervals of time throughout a given planning horizon. The complexity and importance of the problem were recognized by Sasieni, Yaspan, and Friedman (1959), but remained basically ignored until Jaiswal and Shah (1979) provided some heuristics under the simplifying assumptions of equal intervals between consecutive orders and, in one case, equal lot sizes. More recently, Arcelus and Srinivasan have developed an optimal solution algorithm (1985a) as well as some heuristics (1985b) for the more general problem, where both the intervals between orders and the lot sizes are allowed to vary simultaneously. Three basic aspects of the discrete demand case will be considered in this paper, namely, (i) an examination of the characteristics that differentiate the discrete from the continuous demand cases; (ii) a discussion of the ways in which these characteristics can be exploited to find solution algorithms and heuristics for the discrete case; and (iii) a report on computational experience with these models. The comparison of the characteristics of the discrete and the continuous cases is useful for the potential contribution of the latter and better known problem to the solution of the former. Examples of work devoted to the continuous case during the last