The Economic Lot Production and Delivery Scheduling Problem.

Abstract

This study deals with a manufacturing system with several (supplier) facilities that produce multiple component parts in batches, and one (assembly) facility at which these components are used at a constant rate while being assembled into finished goods. At each supplier, a set of components is produced on a single production line in a batch mode because of the time or cost involved in changeovers. The components are transported from the suppliers to the assembly facilities in mixed-component shipments at regular intervals. In practice, the production schedules at the suppliers and the inter-facility delivery schedules are well coordinated, resulting in cost penalties. We develop optimization-based procedures to determine coordinate production and delivery schedules while minimizing the total cost of production, inventory, and transportation for the entire system. We consider an infinite horizon problem and determine a schedule which can be repeated indefinitely. The decisions are the detailed production schedule which specifies both the timing and quantities of each production run of each component, and the time between deliveries. We develop an optimal solution procedure for the case of a single component. We then develop a heuristic procedure for the multiple component case in which the time between production runs (production interval) is the same for all components, and equal to the time between deliveries (delivery interval). We also develop error bounds for this heuristic procedure. This multiple-component model is then generalized to allow more frequent deliveries, while maintaining equal production intervals for all components. Finally, we consider the most general case where the delivery interval and the production intervals of all components may differ. For this case, we restrict our attention to "power-of-two" policies in which each delivery interval is a power-of-two multiple of the delivery interval. For the last two cases, heuristic solution procedures are developed. In computational tests, the new procedures provided solutions with costs up to 60% less than those from less coordinated solutions. These results suggest that considerable savings can be achieved by coordinating the production and delivery schedules. Our research represents a first step toward understanding how this coordination can be achieved most economically.