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Integer Programming Solution Approach for Inventory-Production-Distribution Problems with Direct Shipments

Miguel A. Lejeune (mlejeune***at***andrew.cmu.edu)
Francois Margot (fmargot***at***andrew.cmu.edu)

Abstract: 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. Computational testing is done using a large-scale planning problem faced by a North American company.

Keywords: cover inequality, binary-integer knapsack constraint, production-distribution planning, supply chain management

Category 1: Applications -- OR and Management Sciences (Supply Chain Management )

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Combinatorial Optimization (Branch and Cut Algorithms )

Citation: Forthcoming in International Transactions in Operational Research.

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Entry Submitted: 01/13/2007
Entry Accepted: 01/14/2007
Entry Last Modified: 11/19/2007

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