Integrated production, inventory, and outbound distribution operations with fixed departure times in a three-stage supply chain

This study considers an integrated production, inventory, and outbound distribution scheduling model that arises in a three-stage supply chain consisting of three parts: a supplier, a manufacturer, and several customers. The manufacturer receives a set of two-stage orders to process a specific set of jobs (products) for the customers. These jobs are first partly processed by the supplier, and delivered to the manufacturer by vehicles immediately at additional delivery costs depending on the delivered jobs. The partly processed jobs are then processed by the manufacturer, and delivered to their respective customers by transporters with fixed delivery departure times. A finished job is either kept in a temporary warehouse before it is delivered at an inventory cost, or delivered to its customer immediately. Each job is associated with a desired due date, and late deliveries are not accepted. The objective is to determine schedules for processing the jobs, and identify delivery schedules from the manufacturer to all customers such that the weighted sum of the weighted number of late jobs, inventory cost, and delivery cost is minimized. For each considered problem, we investigate its computational complexity, and develop pseudo-polynomial or polynomial-time solution algorithm, if viable. Using randomly generated data, we conduct extensive numerical studies to evaluate the performance of the proposed algorithms.