Integer programming solution approach for inventory–production–distribution problems with direct shipments

We construct an integrated multi-period inventory–production–distribution replenishment plan for three-stage supply chains. The supply chain maintains close relationships with a small group of suppliers, and the nature of the products (bulk, chemical, etc.) makes it more economical to rely upon a direct shipment, full-truck load distribution policy between supply chain nodes. In this paper, we formulate the problem as an integer linear program that proves challenging to solve due to the general integer variables associated with the distribution requirements. We propose new families of valid cover inequalities, and we derive a practical closed-form expression for generating them, upon the determination of a single parameter. We study their performances through benchmarking several branch-and-bound and branch-and-cut approaches.