Vehicle routing problem in omni-channel retailing distribution systems

Abstract

This paper introduces a variant of the vehicle routing problem where a group of retail stores are served from a distribution center using a fleet of vehicles. Moreover, products are distributed to consumers from some of these retail stores based on product availability at inventory and by means of the same fleet of vehicles. This variant of the vehicle routing problem can be found in omni-channel retail distribution systems. Retail distribution systems are considered omni- or multi-channel systems when consumers can either place orders online or physically visit the stores to buy the products. In this problem, the decisions of assigning consumers to retail stores based on inventory availability are combined with finding the routes of vehicles. The new problem can be considered a generalization of both capacitated vehicle routing problem and the pickup and delivery problem. The paper presents a mathematical formulation to describe this problem and proposes two solution approaches (two-phase heuristic and multi-ant colony algorithm). We also generate new benchmark problem instances to evaluate the performance of the proposed solution approaches.

Keywords: Routing, Metaheuristic, Heuristic, Logistics, Omni-channel routing

1. Introduction

Transportation of goods through supply chains has attracted significant interest in the optimization research throughout the last decades. Transportation has been a key element of the competition between organizations as it can denote 10% to 20% of the cost of any product (Toth and Vigo, 2002). Operations research has been employed in planning efficient transportation systems by optimizing the distribution of goods. The vehicle routing problem (VRP) is an operational decision in the supply chain. The VRP is the problem of distributing goods between depots and customers. In this class of problems, the demands of customers are fulfilled with the products originating from a depot and transported using a fleet of vehicles such that the total traveling cost of all vehicles is minimized. There are many variants of the VRP according to the different classifications of customers and vehicles characteristics. For recent research work in the area of the VRP and its variants refer to (Cordeau et al., 2007; Golden et al., 2008; Laporte, 2009; Eksioglu et al., 2009; Toth and Vigo, 2014; Lahyani et al., 2015).

The problem considered in this paper is motivated by the product distribution system found in most retail chain stores following the omni-channel business model. Recently, e-commerce has been a global trend and an important tool for every business worldwide. Economies have started to rely on e-commerce, and companies have been forced to adopt different strategies and policies to adapt to this change in the market. Nowadays, most businesses try to increase their sales by using a recent business model called omni-channel retailing (e.g., John Lewis Partnership, a major retailer in the UK (Rowell, 2013)). The retail industry has evolved from multi-channels toward omni-channels (Verhoef et al., 2015). This development is helping retail stores reach more consumers and expand their market. It allows consumers to go shopping seven days a week, twenty-four hours a day. Omni-channel retailing is a seamless experience in which there is no difference between physical and online shopping (Brynjolfsson et al., 2013).

The proposed problem is considered a generalization of the CVRP, TSP and PDP. The problem reduces to the CVRP if the demands of all online orders are considered zero. Moreover, the problem reduces to the TSP for unlimited vehicle capacity and without route length constraints. The problem reduces to the PDP if the demands of all retail stores are considered zero. The TSP, CVRP and PDP are considered NP-hard problems, and hence, the proposed problem will also be NP-hard. To the best of our knowledge, this is the first paper that addresses the VRP in omni-channel distribution systems.

The main contribution of this paper can be stated as follows: A new variant of the VRP arising in omni-channel distribution systems is presented. This problem has practical applications in most retail distribution systems. The mathematical formulation of the described problem is presented. In addition, we present two solution approaches to solve the problem (two-phase heuristic and multi-ant colony (MAC) algorithm). New benchmark problem instances are presented that can be used to compare the results of new solution approaches in future research work. We also illustrate the benefit of using the integrated distribution system instead of the two existing distribution systems. The purpose of this paper is to introduce and formulate a new variant of the VRP in omni-channels. Thus, one heuristic and one metaheuristic are used to solve the problem. Other metaheuristics and exact algorithms like branch and price can be considered in future research and then compared with the reported results in this paper.

The paper is organized as follows: Section 2 presents the literature related to the proposed problem. In Section 3, the problem assumptions and a mathematical formulation are presented. In Section 4, two solution approaches are described. The computational experiment results are presented in Section 5. Finally, Section 6 concludes the paper.

2. Problem description

The problem investigated in this paper considers a giant retailing company running in different cities. In a given city, it owns a central warehouse and a group of retail stores. The company offers its consumers the choice of purchasing products in two ways: physically visiting the stores or ordering the products online. The proposed model considers the distribution system for this giant retailing company in a particul

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