Economic lot scheduling with resources in parallel

In this paper 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 Dj per unit time, a holding cost hj per unit time, and a setup cost Kj . The machines have different speeds. The speed of machine i is vi: Machine i can produce item j at rate viPj . We consider three different models. The objective in all three models is to find an assignment of items to machines that minimizes 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.