Single item reformulations for a vendor managed inventory routing problem: computational experience with benchmark instances

Pasquale Avella, Maurizio Boccia and Laurence Wolsey ()
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Pasquale Avella: Universita del Sannio
Maurizio Boccia: Universita del Sannia
Laurence Wolsey: Université catholique de Louvain, CORE, Belgium

No 2013045, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: The Inventory Routing Problem (IRP) involves the distribution of one or more products from a supplier to a set of customers over a discrete planning horizon. The version treated here, the so- called Vendor Managed Inventory Routing Problem (VMIRP), is the Inventory Routing problem arising when the replenishment policy is decided a priori. We consider two replenishment policies. The first is known as Order-Up (OU): if a client is visited in a period, then the amount shipped to the client must bring the stock level up to the upper bound. The latter is called Maximum Level (ML): the maximum stock level in each period cannot be exceeded. The objective is to find replenishment decisions minimizing the sum of the storage and distribution costs. VMIRP contains two important subproblems: a lot-sizing problem for each customer and a classical vehicle routing problem for each time period. In this paper we present a-priori reformulations of VMIRP-OU and VMIRP-ML derived from the single-item lot-sizing substructure. In addition we introduce two new cutting plane families - the Cut Inequalities - deriving from the interaction between the Lot-Sizing and the Routing substructures. A Branch-and-Cut algorithm has been implemented to demonstrate the effectiveness of Single-Item reformulations. Computational results on the benchmark instances with 50 customers and 6 periods with a single product and a single vehicle are presented.

Keywords: : mixed integer programming; inventory routing; lot-sizing; reformulations; vendor management (search for similar items in EconPapers)
JEL-codes: C11 C57 C90 (search for similar items in EconPapers)
Date: 2013-09-11
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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