Coordination of inbound and outbound transportation schedules with the production schedule

This paper studies the coordination of production and shipment schedules for a single stage in the supply chain. The production scheduling problem at the facility is modeled as belonging to a single process. Jobs that are located at a distant origin are carried to this facility making use of a finite number of capacitated vehicles. These vehicles, which are initially stationed close to the origin, are also used for the return of the jobs upon completion of their processing. In the paper, a model is developed to find the schedules of the facility and the vehicles jointly, allowing for effective utilization of the vehicles both in the inbound and the outbound. The objective of the proposed model is to minimize the sum of transportation costs and inventory holding costs. Issues related to transportation such as travel times, vehicle capacities, and waiting limits are explicitly accounted for. Inventories of the unprocessed and processed jobs at the facility are penalized. The paper contributes to the literature on supply chain scheduling under transportation considerations by modeling a practically motivated problem, proving that it is strongly NP-Hard, and developing an analytical and a numerical investigation for its solution. In particular, properties of the solution space are explored, lower bounds are developed on the optimal costs of the general and the special cases, and a computationally-efficient heuristic is proposed for solving large-size instances. The qualities of the heuristic and the lower bounds are demonstrated over an extensive numerical analysis.