Production-Planning Algorithms for the Inventory-Overtime Tradeoff

This paper develops planning-horizon theorems and algorithms for determining optimal production in period 1 when there are linear costs associated with overtime and inventory, and demand is deterministic. If overtime in each period is unrestricted and no shortages are permitted, then it is easily shown that the firm will have to know future demand for at most the next k* periods, where k* is determined by the ratio of the wage differential between overtime and regular time to the per unit holding cost per period. Using the k* concept, the paper determines planning horizons when both storage and backlogging of demand are allowed. If overtime constraints are imposed, a planning algorithm is proposed that requires less information on future demand than a linear programming model. Economic implications of this approach for decision-making and information processing in firms are discussed.