Stochastic inventory routing with time-based shipment consolidation

Danja R. Sonntag, Albert H. Schrotenboer, Gudrun P. Kiesmüller

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Inspired by the retail industry, we consider a stochastic inventory routing problem where retailers are replenished from a central warehouse using a time-based shipment consolidation policy. Such a time-based dispatching policy, where retailers facing stochastic demand are repetitively replenished at fixed times, is essential in practice. It allows for easy incorporation with dependent up- and downstream planning problems such as personal staffing and warehouse operations, and has become a standard part of transportation contracts. We provide a new chance-constrained model that determines an optimal clustering of retailers in groups, their associated routing and shipment interval, and each retailers’ optimal inventory level. A newly developed branch-price-and-cut algorithm solves our model to optimality. Its efficiency comes from a tailored labeling algorithm for solving the pricing problem that relies, among others, on an optimality pruning criterion based on the approximate solution of a 0,1-knapsack problem. Computational experiments show that our exact method can solve instances of up to 60 retailers to optimality. Besides, we accommodate practitioners by providing a fast heuristic that provides excellent solutions with an optimality gap of less than 1%. Finally, we show that incorporating uncertainty already in the planning process is essential for stochastic inventory routing with time-based shipment consolidation, as it results in overall cost-savings of 7.7% compared to the current state-of-the-art.

Original languageEnglish
Pages (from-to)1186-1201
Number of pages16
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 1 May 2023


  • Branch-price-and-cut
  • Inventory control
  • Stochastic inventory routing
  • Time-based shipment consolidation
  • Transportation


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