Solving a Real-World Supply Chain by Matheuristics: Challenges and Practical Solutions

Abstract

As a company grows, strategic policies may be needed to raise service levels, often prompting decisions about opening new industrial facilities. Facility location choices require large financial investments and commitments and influence other network design decisions. The production-distribution optimization problem, framed as Location Inventory Problems (LIPs), models these interdependent choices. This paper presents a case study using data from a food manufacturer to locate capacitated distribution centers (DCs) and determine product flows from factories to DCs and from DCs to customers across a multi-period horizon, capturing demand and capacity variations. Objectives include meeting given demands and minimizing total costs while addressing tactical issues such as fleet composition and production planning that share resources across product families. The paper proposes an integer programming model and a matheuristic solution: a Variable Neighborhood Search (VNS) selects DCs to open; the IP model is then solved with those DCs fixed to obtain flows and inventories; finally, a Variable Size Bin Packing (VSBP) model defines fleet composition for each factory and warehouse. The paper emphasizes practical adaptations required for large real-world instances: client aggregation, cost approximations from clustering, and inventory terminal conditions, and discusses implementation challenges and lessons for future researchers and practitioners.