Synchronizing production and air transportation scheduling using mathematical programming models

Traditional scheduling problems assume that there are always infinitely many resources for delivering finished jobs to their destinations, and no time is needed for their transportation, so that finished products can be transported to customers without delay. So, for coordination of these two different activities in the implementation of a supply chain solution, we studied the problem of synchronizing production and air transportation scheduling using mathematical programming models. The overall problem is decomposed into two sub-problems, which consists of air transportation allocation problem and a single machine scheduling problem which they are considered together. We have taken into consideration different constraints and assumptions in our modeling such as special flights, delivery tardiness and no delivery tardiness. For these purposes, a variety of models have been proposed to minimize supply chain total cost which encompass transportation, makespan, delivery earliness tardiness and departure time earliness tardiness costs.