Formulations for an inventory routing problem

Claudia Archetti, Nicola Bianchessi, Stefan Irnich, M. Grazia Speranza

    Research output: Contribution to JournalArticleAcademicpeer-review


    In this paper, we present and compare formulations for the inventory routing problem (IRP) where the demand of customers has to be served, over a discrete time horizon, by capacitated vehicles starting and ending their routes at a depot. The objective of the IRP is the minimization of the sum of inventory and transportation costs. The formulations include known and new mathematical programming formulations. Valid inequalities are also presented. The formulations are tested on a large set of benchmark instances. One of the most significant conclusions is that the formulations that use vehicle-indexed variables are superior to the more compact, aggregate formulations.

    Original languageEnglish
    Pages (from-to)353-374
    Number of pages22
    JournalInternational Transactions in Operational Research
    Issue number3
    Publication statusPublished - 1 Jan 2014


    • Branch-and-cut algorithm
    • Integer programming
    • Routing problems
    • Supply chain management


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