1 The Economic Lot Scheduling Problem

Economies of scale often dictate the choice of a single high speed machine capable of producing a given set of items over the choice of one dedicated machine for each item in the set. A scheduling problem arises when the high speed machine can only produce one item at a time. The problem is further complicated when the machine needs to be setup (often at a cost of both time and money) before a different item can be produced. The Economic Lot Scheduling Problem (ELSP) is that of scheduling the production of a set of items in a single machine to minimizing the long run average holding and set up cost under the assumptions of known constant demand and production rates. Unfortunately, the ELSP belongs to a class of problems, known as NP-hard, see Gallego and Shaw [3], for which it is unlikely that an efficient solution procedure would ever be developed. What makes the ELSP hard is the coordination problem that needs to be resolved among the items competing for the machine capacity. Thus, much of the research effort on the ELSP (over 40 published papers) has dealt with the problem of finding low cost schedules via heuristics. Fortunately, good heuristics have been developed to obtain feasible production schedules whose average cost is often (but not guaranteed to be) close to the optimal. See Dobson [1]. Recently the research focus has shifted to deal with the more practical issues of real time scheduling, setup time reduction and the cost of offering variety. We will start by presenting a lower bound on the long run average cost. This bound will be later used to assess the performance of the rotation schedule (RS) heuristic which calls for setting up and producing the items once per cycle in a given order. Our next goal is to discuss issues that arise in trying to implement feasible ELSP schedules. Our third goal is concerned with a brief discussion of the cost of offering variety and the effect of reducing setup times. The data for the problem are: