Multiproduct lot sizing for finite production rate

This article deals with the situation where the producer manufactures several products with given production rates on a single machine. Only one product can be produced at a time on the machine. As an example, the producer may use higher or lower quality components in the production. Also, the products may have different holding costs. We present a model, where the demand appears at discrete points in time, and all demand must be met. We assume a deterministic, varying demand. By a production batch we mean a sequence of individual demands that is possible to manufacture in a continuous run to satisfy all the demands on time. A production run consists of a sequence of batches. There is a fixed set-up cost associated with each production run. By a production schedule we mean a sequence of ‘run’ intervals such that each of them is partitioned into parts – for each product. This paper is concerned with the problem of how to determine the production schedule that minimizes the total production and holding cost over a finite time horizon.