Robust inventory routing under demand uncertainty

Oǧuz Solyali, Jean François Cordeau, Gilbert Laporte

Research output: Contribution to journalArticlepeer-review

92 Citations (SciVal)


This paper introduces a robust inventory routing problem where a supplier distributes a single product to multiple customers facing dynamic uncertain demands over a finite discrete time horizon. The probability distribution of the uncertain demand at each customer is not fully specified. The only available information is that these demands are independent and symmetric random variables that can take some value from their support interval. The supplier is responsible for the inventory management of its customers, has sufficient inventory to replenish the customers, and distributes the product using a capacitated vehicle. Backlogging of the demand at customers is allowed. The problem is to determine the delivery quantities as well as the times and routes to the customers, while ensuring feasibility regardless of the realized demands, and minimizing the total cost composed of transportation, inventory holding, and shortage costs. Using a robust optimization approach, we propose two robust mixed integer programming (MIP) formulations for the problem. We also propose a new MIP formulation for the deterministic (nominal) case of the problem. We implement these formulations within a branch-and-cut algorithm and report results on a set of instances adapted from the literature.

Original languageEnglish
Pages (from-to)327-340
Number of pages14
JournalTransportation Science
Issue number3
Publication statusPublished - Aug 2012


  • Branch-and-cut
  • Integer programming
  • Inventory routing problem
  • Lot sizing
  • Robust optimization

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


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