On the Feasibility of Scheduling Lot Sizes for Two Products on One Machine

We are concerned with scheduling several products that, require processing or a single machine. Routine application of the economic lot size formula to each product separately, often yields an infeasiable schedule in the sense that there are times when it specifies simultaneous production of two or more products. Feasibility is guaranteed if a common cycle length (and thus equal set-ups per year per product) is chosen. However it is possible to find schedules by allowing variations in the number of set-ups among the products which cost less than the cost of the common cycle length schedule. In this paper we present a necessary and sufficient condition for the feasibility of scheduling two products, when the number of set-ups for each product are givers. Also a method of constructing the schedules is discussed.