A Matheuristic for the Multivehicle Inventory Routing Problem

We consider the inventory routing problem, in which a supplier has to replenish a set of customers by means of a limited fleet of capacitated vehicles over a discrete time horizon. The goal is to minimize the total cost of the distribution that comprises the inventory cost at the supplier and at the customers and the routing cost. We present a matheuristic that combines a tabu search and mathematical programming formulations. When compared with two exact methods on 640 small instances, the matheuristic finds 192 (48%) optima over the 402 instances with known optima and improves 125 upper bounds. Tested on 240 large instances (with up to 200 customers) for which no optimal solutions are known, it improves the best solution for 220 (92%) of the 240 instances. The online supplement is available at https://doi.org/10.1287/ijoc.2016.0737.

[1]  Demetrio Laganà,et al.  A decomposition-based heuristic for the multiple-product inventory-routing problem , 2015, Comput. Oper. Res..

[2]  Yossiri Adulyasak,et al.  Formulations and Branch-and-Cut Algorithms for Multivehicle Production and Inventory Routing Problems , 2012, INFORMS J. Comput..

[3]  Jean-François Cordeau,et al.  Optimization-Based Adaptive Large Neighborhood Search for the Production Routing Problem , 2011, Transp. Sci..

[4]  Leandro C. Coelho,et al.  The exact solution of several classes of inventory-routing problems , 2013, Comput. Oper. Res..

[5]  Haldun Süral,et al.  A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem , 2011, Transp. Sci..

[6]  Leandro C. Coelho,et al.  Improved solutions for inventory-routing problems through valid inequalities and input ordering , 2014 .

[7]  Leandro C. Coelho,et al.  A Branch-Price-and-Cut Algorithm for the Inventory-Routing Problem , 2014, Transp. Sci..

[8]  Gilbert Laporte,et al.  Thirty Years of Inventory Routing , 2014, Transp. Sci..

[9]  El-Houssaine Aghezzaf,et al.  The Inventory-routing problem with transshipment , 2017 .

[10]  Gilbert Laporte,et al.  The inventory-routing problem with transshipment , 2012, Comput. Oper. Res..

[11]  Luca Bertazzi,et al.  Inventory routing problems: an introduction , 2012, EURO J. Transp. Logist..

[12]  Luca Bertazzi,et al.  A Hybrid Heuristic for an Inventory Routing Problem , 2012, INFORMS J. Comput..

[13]  Hanif D. Sherali,et al.  Improving Discrete Model Representations via Symmetry Considerations , 2001, Manag. Sci..

[14]  Luca Bertazzi,et al.  Analysis of the maximum level policy in a production-distribution system , 2011, Comput. Oper. Res..

[15]  Stefan Irnich,et al.  Formulations for an inventory routing problem , 2014, Int. Trans. Oper. Res..

[16]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[17]  Zeger Degraeve,et al.  Alternative formulations for a layout problem in the fashion industry , 2002, Eur. J. Oper. Res..

[18]  Luca Bertazzi,et al.  Inventory routing problems with multiple customers , 2013, EURO J. Transp. Logist..

[19]  Luca Bertazzi,et al.  A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem , 2007, Transp. Sci..

[20]  Giovanni Rinaldi,et al.  A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

[21]  Gilbert Laporte,et al.  Consistency in multi-vehicle inventory-routing , 2012 .

[22]  Martin W. P. Savelsbergh,et al.  An Optimization-Based Heuristic for the Split Delivery Vehicle Routing Problem , 2008, Transp. Sci..