# Column Generation based Solution for a Tactical Inventory Routing Problem

1 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Inventory routing problems combine the optimization of product deliveries (or pickups) with inventory control at customer sites. Our application concerns the planning of single product pickups over time; each site accumulates stock at a deterministic rate; the stock is emptied on each visit. At the tactical planning stage considered here, our objective is to minimize a surrogate measure of routing cost while achieving some form of regional clustering by partitioning the sites between the vehicles. The fleet size is given but can potentially be reduced. Planning consists in assigning customers to vehicles in each time period, but the routing, i.e., the actual sequence in which vehicles visit customers, is considered as an operational'' decision. The planning is due to be repeated over the time horizon with constrained periodicity. We develop a truncated branch-and-price-and-cut algorithm combined with rounding and local search heuristics that yields both primal solutions and dual bounds. On a large scale test problem coming from industry, we obtain a solution within 6.25% deviation from the optimal. A rough comparison between an operational routing resulting from our tactical solution and the industrial practice shows a 10% decrease in number of vehicles as well as in travel distance. The key to the success of the approach is the use of a state-space relaxation technique in formulating the master program to avoid the symmetry in time.
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Reports

https://hal.inria.fr/inria-00169311
Contributor : François Vanderbeck <>
Submitted on : Friday, November 14, 2008 - 7:51:12 PM
Last modification on : Tuesday, February 5, 2019 - 11:41:17 AM
Long-term archiving on : Thursday, September 23, 2010 - 5:13:32 PM

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• HAL Id : inria-00169311, version 3

### Citation

Sophie Michel, François Vanderbeck. Column Generation based Solution for a Tactical Inventory Routing Problem. [Research Report] 2008. ⟨inria-00169311v3⟩

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