Single-Period Cutting Planes for Inventory Routing Problems

IRP involves the distribution of one or more products from a supplier to a set of clients over a discrete planning horizon. Each client has a known demand to be met in each period and can only hold a limited amount of stock. The product is shipped through a distribution network by one or more vehicles of limited capacity. The objective is to find replenishment decisions minimizing the sum of the storage and distribution costs. In this paper we present reformulations of IRP, under the Maximum Level replenishment policy, derived from a single-period substructure. We define a generic family of valid inequalities, and then introduce two specific subclasses for which the separation problem of generating violated inequalities can be solved effectively. A basic Branch-and-Cut algorithm has been implemented to demonstrate the strength of the single-period reformulations. Computational results are presented for the benchmark instances with 50 clients and three periods and 30 clients and six periods.

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

[2]  Maurice Queyranne,et al.  Optimal pits and optimal transportation , 2015 .

[3]  Gérard Cornuéjols,et al.  Polyhedral study of the capacitated vehicle routing problem , 1993, Math. Program..

[4]  Laurence A. Wolsey,et al.  Single‐item reformulations for a vendor managed inventory routing problem: Computational experience with benchmark instances , 2015, Networks.

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

[6]  Pierre Pestieau,et al.  Aging, Social Security Design, and Capital Accumulation , 2015, SSRN Electronic Journal.

[7]  Juan D. Moreno-Ternero,et al.  Normative foundations for equity-sensitive population health evaluation functions , 2014 .

[8]  Mathieu Van Vyve,et al.  A conic optimization approach for SKU rationalization , 2014 .

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

[10]  H. Donald Ratliff,et al.  A Graph-Theoretic Equivalence for Integer Programs , 1973, Oper. Res..

[11]  Giovanni Rinaldi,et al.  Branch-And-Cut Algorithms for the Capacitated VRP , 2001, The Vehicle Routing Problem.

[12]  François Maniquet,et al.  Social ordering functions , 2016 .

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

[14]  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..

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

[16]  Dirk Neumann,et al.  Does the Choice of Well-Being Measure Matter Empirically? An Illustration with German Data , 2014, SSRN Electronic Journal.

[17]  M. Fischetti,et al.  A Branch-and-Bound Algorithm for the Capacitated Vehicle Routing Problem on Directed Graphs , 1994, Oper. Res..

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

[19]  Maria Grazia Speranza,et al.  Optimal solutions for routing problems with profits , 2013, Discret. Appl. Math..