Dynamic Lot Size Problem with Multiple Customers: Customer-Specific Shipping and Backlogging Costs

This paper considers a dynamic lot size problem faced by a producer who supplies a single product to multiple customers. Characterized by their backorder costs as well as shipping costs, the customer with a high backorder cost is the one whose need for the product is more critical than the need of a customer with a low backorder cost. We show that the general problem with time-varying, customer-dependent backlogging and shipping costs is NP-hard in the strong sense. We then develop an efficient dynamic programming algorithm for an important instance of the problem when there is no speculative motive for backlogging. We also establish forecast-horizon results for the case of stationary production and shipping costs, which help the decision maker determine proper forecast horizon in a rolling-horizon planning process. Subject classifications: dynamic lot size model, dynamic programming, forecast horizon, multiple customers.