Economic lot scheduling with resources in parallel

Abstract

In this article we consider the economic lot scheduling problem with m machines (or facilities) in parallel. There are n different types of items. Item j has a demand D j per unit time, a holding cost h j per unit time, and a setup cost K j . The machines have different speeds. The speed of machine i is v i . Machine i can produce item j at rate v i P j . We consider three different models. The objective in all three models is to find an assignment of items to machines that minimises the total cost per unit time of the entire system. In the first model, each machine operates according to a rotation or cyclical schedule and the cycle lengths of the rotation schedules of the m machines have to be the same. In the second model, each machine again operates according to a rotation schedule, but the rotation schedules are allowed to have different cycle lengths. In the third model, the machines do not have to operate according to rotation schedules. For each model, we consider a number of special cases that provide some insights into the role each parameter plays. Based on the results of the special cases, we formulate for each model a heuristic that can be applied to arbitrary instances. In the concluding remarks, we discuss the significance of our results for problems that occur in practice.