TITLE

# A Branch-and-Cut Algorithm for a Vendor-Managed Inventory-Routing Problem

AUTHOR(S)
Archetti, Claudia; Bertazzi, Luca; Laporte, Gilbert; Speranza, Maria Grazia
PUB. DATE
August 2007
SOURCE
Transportation Science;Aug2007, Vol. 41 Issue 3, p382
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We consider a distribution problem in which a product has to be shipped from a supplier to several retailers over a given time horizon. Each retailer defines a maximum inventory level. The supplier monitors the inventory of each retailer and determines its replenishment policy, guaranteeing that no stockout occurs at the retailer (vendor-managed inventory policy). Every time a retailer is visited, the quantity delivered by the supplier is such that the maximum inventory level is reached (deterministic order-up-to level policy). Shipments from the supplier to the retailers are performed by a vehicle of given capacity. The problem is to determine for each discrete time instant the quantity to ship to each retailer and the vehicle route. We present a mixed-integer linear programming model and derive new additional valid inequalities used to strengthen the linear relaxation of the model. We implement a branch-and-cut algorithm to solve the model optimally. We then compare the optimal solution of the problem with the optimal solution of two problems obtained by relaxing in different ways the deterministic order-up-to level policy. Computational results are presented on a set of randomly generated problem instances.
ACCESSION #
26400001

## Related Articles

• Integrated Production-Inventory-Distribution System Design with Risk Pooling: Model Formulation and Heuristic Solution. Vidyarthi, Navneet; Ã‡elebi, Emre; Elhedhli, Samir; Jewkes, Elizabeth // Transportation Science;Aug2007, Vol. 41 Issue 3, p392

In this paper, we consider a multiproduct two-echelon production-inventory-distribution system design model that captures risk-pooling effects by consolidating the safety-stock inventory of the retailers at distribution centers (DCs). We propose a model that determines plant and DC locations,...

• Convergence to Equilibrium in Dynamic Traffic Networks when Route Cost Is Decay Monotone. Mounce, Richard // Transportation Science;Aug2007, Vol. 41 Issue 3, p409

This paper addresses the issue of convergence to equilibrium in dynamic traffic assignment. Within-day time is considered to be a continuous variable, so that traffic flows and costs are functions of within-day time. Flow propagates along routes connecting origin-destination (OD) pairs with the...

• An application of genetic and tabu searches to the freight railroad operating plan problem. Gorman, Michael Francis // Annals of Operations Research;1998, Vol. 78 Issue 1-4, p51

This paper addresses the joint train-scheduling and demand-flow problem for a major US freight railroad. No efficient optimization techniques are known to solve the NP-hard combinatorial optimization problem. Genetic search is used to find acceptable solutions; however, its performance is found...

• Promise of the night riders. Lewis, Mark // Cabinet Maker;8/27/2004, Issue 5403, p8

Reports on the plans drawn by the British Cabinet Office's business regulation team which will allow retailers to receive late night deliveries. Benefits provided by night supplies to retailers; Provisions of the plan; Reasons why night time deliveries were not allowed before in the retailer...

• AN INVENTORY THEORETIC MODEL OF FREIGHT TRANSPORT DEMAND. Baumol, W. J.; Vinod, H. D. // Management Science;Mar70, Vol. 16 Issue 7, p413

The model in this paper is intended to explain the choice of transport made by shippers, as well as their total demand for transportation services. The optimal choice of mode is shown to involve a trade-off among freight rates, speed, dependability (variance in speed) and en-route lossage. It is...

• Effective Heuristics for Multiproduct Partial Shipment Models. Dawande, Milind; Gavirneni, Srinagesh; Tayur, Sridhar // Operations Research;Mar/Apr2006, Vol. 54 Issue 2, p337

Motivated by real applications, we consider the problem of shipping products to multiple customers from limited inventory. After formulating the optimization problems under different restrictions on partial shipments, we find that commercially available packages, applied directly, are...

• A kink in supply chain. Tita, Bob // Crain's Chicago Business;7/26/2004, Vol. 27 Issue 30, p3

The outsourcing mania washing over the U.S. manufacturing is overwhelming the nation's freight transportation system and undermining the reliability of supply chains. After years of perfecting production operations built on short lead times and lean inventories, manufacturers are creating safety...

• Around Africa with a fridge.  // Truck & Driver;Jun2008, p18

The article describes the transport of a 50-meter-long, 40-tonne cold box from England to Zambia. The giant cooler traveled by ship to Walvis Bay in Namibia. It was then attached to two 10-axle Goldhofer heavy-duty trailer modules hauled by Mercedes Actros Titan tractors and took the 2,400...

• Pricing in Dynamic Vehicle Routing Problems. Figliozzi, Miguel Andres; Mahmassani, Hani S.; Jaillet, Patrick // Transportation Science;Aug2007, Vol. 41 Issue 3, p302

The principal focus of this paper is to study carrier pricing decisions for a type of vehicle routing problems defined in a competitive and dynamic environment. This paper introduces the vehicle routing problem in a competitive environment (VRPCE) as an extension of the traveling-salesman...

Share