Feasibility of scheduling lot sizes of two frequencies on one machine

The paper considers the Economic Lot Scheduling Problem of finding a feasible schedule that allows cyclic production of several products on a single facility so as to minimise holding and set-up costs. We consider the case when products are produced in a given fixed lot size and at regular intervals with at most two cycle lengths between them. Our main results are, for the multi-product case: necessary and sufficient condition for existence of a feasible schedule; and necessary and sufficient conditions for 100% utilization of the production line; and for the two product case: a characterization of all feasible schedules. It is envisaged that the results will be used to help construct production schedules which utilise the production line well and keep down holding costs, by using two regular intervals.