Cyclical Schedules for Capacitated Lot Sizing with Dynamic Demands

Cyclical scheduling, where the time between production periods for each item is constant, offers simplicity and ease of control compared with noncyclical scheduling, where production periods are irregularly spaced. However, when demands are dynamic, flexibility in the spacing of production periods permits noncyclical scheduling to result in lower total costs. This study investigates the additional cost of cyclical scheduling. We focus upon the capacitated lot sizing problem (CLSP), which deals with planning production on a single, capacitated machine serving multiple items with dynamic demands. To establish cyclical schedules, a mathematical programming model is developed along with a heuristic solution technique and a Lagrangian-based lower bounding procedure. For problems solved in this study, differences between solution costs and lower bounds average less than 1%. Experiments are performed to evaluate the heuristic technique and to compare cyclical schedules with noncyclical ones. For comparison purposes, a noncyclical heuristic and problem sets from the literature are used. New problems based upon operating data from Ford Motor Company are also generated and solved. In this study, cyclical schedules average 4.4% higher in cost than noncyclical ones. Coefficient of demand variation most seriously influences differences in costs. Other significant factors include capacity utilization, setup time, time between orders, and number of items.