Lot sizes in a capacity constrained facility: a simulation study of stationary stochastic demand

This paper considers the scheduling of several different items on a single machine, in literature known as the economic lot scheduling problem, ELSP. One of the characteristics of this problem is that the demand rate is deterministic and constant. However, in a practical situation demand usually varies. In this paper we examine if a deterministic model can be used if demand is stationary stochastic. A dynamic programming approach from Bomberger and a heuristic method from Segerstedt are used to calculate lot sizes for four items. The production of these items is simulated with different variations in demand rates. Our conclusion is that a deterministic model of this kind can be used in a practical situation where the demand rate is stationary stochastic, but the models must be complemented by a decision rule; which item to produce and when to produce it. In our tests the heuristic method and the dynamic programming approach perform rather similarly with respect to costs and inventory levels, but the dynamic programming results in more backorders when there is small variation in demand rates. This study indicates that the model used for determination of lot sizes is of less importance than the decision rule used for identification of the item to produce and when to produce it.