A single-machine multi-product lot scheduling problem with consideration of product-dependent transportation

This paper investigates the lot scheduling problem for multiple products processes on a single machine, under a cyclical production sequence and deterministic demand rate. The problem is formulated in the form of a demand and supply balance equation, with consideration of the method by which each product produced is transported from the single machine’s location to spatially different multiple demand locations. The paper identifies conditions that ensure the existence of a feasible production lot schedule, and proves that the ‘balanced lot size’ is a unique form of lot sizes for a feasible schedule over an infinite planning horizon. It is clarified that the balanced lot size is not affected by the transportation method assigned to each product. The difference in transportation method only affects the amount of initial inventory required at the beginning of the horizon. These results are applied to the problem of finding a feasible production schedule over a finite planning period, and two methods, utilization of the balanced lot size and application of the balance equation, are presented and advantages of each method are discussed.