A Mixed-Integer Programming Model for Optimizing the Distribution Network of a Packaging Company

Abstract

Designing a distribution network for a company is critical as it determines how efficiently and cost-effectively prod ucts are transported. An optimized distribution network should minimize costs and delivery times while maximizing service levels. In this context, the location and number of facilities such as warehouses and factories, as well as the choice of transportation modes, play a significant role in the network’s performance. This study examines a distribution network design problem experienced by a packaging company. Currently, the company operates a single warehouse shipment management system for its operations in France. However, the company’s sales group in France believes that replacing the single-warehouse system with a two-warehouse system could optimize transportation costs while ensuring on-time deliveries. Therefore, the company analyzes the feasibility of such a transition. To achieve this, mixed-integer linear programming (MILP) models are developed, minimizing total distribution costs between the manufacturing plants and the warehouses while determining the distribution of deliveries through three transportation modes—trucks, trains, and ships—that ensures timely delivery of demands. The results indicate that the company should maintain its current single warehouse policy but can favor reduction in transportation costs by focusing on production lead times and delivery prices of transportation modes.

Keywords

• Mixed Integer Linear Programming
• Distribution Network Design Problem
• Transportation Mode Selection
• Supply Chain Network Design Problem

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