A Branch and Bound Algorithm to Minimize the Total Weighed Number of Tardy Jobs and Delivery Costs

This paper addresses the production and delivery scheduling integration problem; a manufacturer receives ₋ orders from one customer while the orders need to be processed on one or two machines and be sent to the customer in batches. Sending several jobs in batches will reduce the transportation cost but it may increase the number of tardy jobs. The objective is to minimize the sum of the total weighted number of tardy jobs and the delivery costs. The structural properties of the problem for a single machine and special cases of the two-machine flow shop problem are investigated and used to set up a new branch and bound algorithm. A heuristic algorithm for upper bound calculation and two approaches for lower bound calculation are also introduced. Results of computational tests show significant improvement over an existing dynamic programming method.