A branch and bound algorithm to minimize the total weighted number of tardy jobs and delivery costs with late deliveries for a supply chain scheduling problem

In this paper, we study a supply chain scheduling problem that simultaneously considers production scheduling and product delivery.  jobs have to be scheduled on a single machine and delivered to  customers for further processing in batches. The objective is to minimize the sum of the total weighted number of tardy jobs and the delivery costs. In this paper, we present a heuristic algorithm (HA) and a branch and bound (B&B) method for the restricted case, where the tardy jobs are delivered separately, and compare these procedures with an existing dynamic programming (DP) algorithm by computational tests. The results of computational tests show significant improvement of the B&B over the dynamic programming algorithm.