Multiproduct optimal batch sizes with in-process inventories and multi work centres

In this paper we extend the classical economic batch size model of Camp to situations where a range of products is made to stock and where the products are manufactured in a production shop consisting of a number of work centers of functionally grouped machines. Assuming that the flow times of the batches along the work centers can be modelled as a queueing process, it is shown that the batch sizes influence the batch waiting times in the shop, and the amount of work in process. The cost function to be minimized consists of ordering costs, final inventory holding costs, and work-in-process carrying costs. We show that the cost function is strictly convex and that the optimal batch sizes can be found by means of well-known numerical methods. We present an outline of an iterative procedure in which the batch size optimization procedure is combined with a shop load optimization procedure to achieve a good overall performance. Using a simplified model that assumes that the products are homogeneous in all respects, we also show that there exists an upper limit for the optimal batch size, which is determined by the ordering costs and the work-in-process carrying costs. Finally, we show that not taking into account work-in-process carrying costs may result in substantial errors in both batch size and cost