https://hal.archives-ouvertes.fr/hal-00653647Li, JianxiangJianxiangLiDepartment of Automatic Control - BIT - Beijing Institute of TechnologyLOSI - Laboratoire d'Optimisation des Systèmes Industriels - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueChu, FengFengChuIBISC - Informatique, Biologie Intégrative et Systèmes Complexes - UEVE - Université d'Évry-Val-d'EssonneChen, HaoxunHaoxunChenLOSI - Laboratoire d'Optimisation des Systèmes Industriels - ICD - Institut Charles Delaunay - UTT - Université de Technologie de Troyes - CNRS - Centre National de la Recherche ScientifiqueA solution to the inventory routing problem in a three-level distribution systemHAL CCSD2011[INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO]Davesne, Frédéric2011-12-19 21:28:112022-08-30 17:14:202011-12-19 21:28:11enJournal articles10.1016/j.ejor.2010.10.0201We consider the infinite horizon inventory routing problem in a three-level distribution system with a vendor, a warehouse and multiple geographically dispersed retailers. In this problem, each retailer faces a demand at a deterministic, retailer-specific rate for a single product. The demand of each retailer is replenished either from the vendor through the warehouse or directly from the vendor. Inventories are kept at both the retailers and the warehouse. The objective is to determine a combined transportation (routing) and inventory strategy minimizing a long-run average system-wide cost while meeting the demand of each retailer without shortage. We present a decomposition solution approach based on a fixed partition policy where the retailers are partitioned into disjoint and collectively exhaustive sets and each set of retailers is served on a separate route. Given a fixed partition, the original problem is decomposed into three sub-problems. Efficient algorithms are developed for the sub-problems by exploring important properties of their optimal solutions. A genetic algorithm is proposed to find a near-optimal fixed partition for the problem. Computational results show the performance of the solution approach. 2010 Elsevier B.V. All rights reserved.