Integrated Production Scheduling and Shipping Problem for a Single Manufacturer and Multiple Customers

In this paper, we investigate a supply chain scheduling problem involving a single manufacturer and multiple customers. Our aim is to integrate the production and shipping functions of the manufacturer so as to minimize the total cost incurred due to tardiness of customer orders and shipping of orders to customers. Since this problem is NP-hard (which we show), we solve it by appropriately decomposing it into subproblems, one of which is solvable in polynomial time. A branch-and-bound-based methodology is developed for the solution of the overall problem that exploits its structural properties. Results of an extensive computational experimentation are also presented that show the efficacy of our algorithm.