Dominance Conditions for Optimal Order-Lot Matching in the Make-To-Order Production System

Order-lot matching is the process of assigning items in lots being processed in the make-to-order production system to meet the due dates of the orders. In this study, an order-lot matching problem (OLMP) is considered to minimize the total tardiness of orders with different due dates. In the OLMP considered in this study, we need to not only determine the allocation of items to lots in the production facility but also generate a lot release plan for the given time horizon. We show that the OLMP can be considered as a special type of machine scheduling problem with many similarities to the single machine total tardiness scheduling problem (1 parallel to Sigma Ti). We suggest dominance conditions for the OLMP by modifying those for 1 parallel to Sigma Ti and a dynamic programming (DP) model based on the dominance conditions. With two example problems, we show that the DP model can solve small-sized OLMPs optimally.