Discrete Optimization
A location-routing problem for the conversion to the “click-and-mortar” retailing: The static case

https://doi.org/10.1016/j.ejor.2007.01.048Get rights and content

Abstract

The static conversion from brick-and-mortar retailing to the hybrid click-and-mortar business model is studied from the perspective of distribution logistics. Retailers run warehouses and brick-and-mortar stores to meet the demand of their walk-in customers. When they decide to operate on the Web as an e-tailer, also click-and-mortar stores are needed which can serve both walk-in and online customers. While the distance between home and the nearest open store is used as a proxy measure for walk-in customers, a quality of service (QoS) guarantee for online customers is timely delivery of their orders. We describe and solve a static location-routing based problem for companies that embrace the clicks-and-bricks strategy in their retail operations. An augmented Lagrangian relaxation method embedded in a subgradient optimization procedure generates lower bounds, whereas a heuristic method finds feasible solutions. The performance of the Lagrangian-based solution method is tested on a number of randomly generated test problems.

Introduction

Most national retailers in the USA are selling today their products and goods online, and the term e-tailing has been now widely accepted as a synonym for online retailing. It all started in the first era of e-commerce (1995–2000) where we saw an infusion of pure-play (or Internet-only) businesses. These businesses offered Web ordering and delivery, and operated with one or more warehouses, but without retail storefronts. In the second era of e-commerce, which is said to commence in January 2001, many firms began to use a mixed “clicks-and-bricks” strategy, combining traditional sales channels such as physical stores, order-by-phone and printed catalogs with online efforts. This strategy led to the birth of a hybrid store type called click-and-mortar. Consumers’ desire for companies’ real-world presence with physical facilities was the main motive behind this transformation. They wanted to touch-and-feel, try and talk before they agreed to pay the merchants. The shift to a click-and-mortar strategy is often found in the grocery segment of retailing since late 1990’s (Hays et al., 2005). Mentioned in Hays et al. as the most prominent brand-name grocery stores now online are Albertsons, Publix and Safeway in the USA, Fairprice and Cold Storage in Singapore, and Wellcome Supermarkets and Park’n Shop in Hong Kong. Van Mieghem (2001) considers UK’s biggest Internet grocer Tesco.com a thriving click-and-mortar business outside the USA. Tesco’s successful Internet shopping services eventually steered the company to the USA, and led to a partnership with Safeway in June 2001.

In this paper, we study a static location-routing based optimization problem to model the conversion of a traditional retailer that embraces the clicks-and-bricks strategy. The solution of the problem under investigation, which we call CMBP-S, reveals a location–allocation profile for the stores of the retailer, and a routing plan for its delivery vehicles. These entities of the retailer serve two customer types, namely walk-in and online customers. We propose a Lagrangian relaxation method embedded in a subgradient optimization procedure to solve the problem CMBP-S. The paper is organized as follows. Section 1.1 dwells on the conversion to click-and-mortar retailing operations while Section 1.2 gives the complete description and underlying assumptions of the CMBP-S. Section 2 provides an extensive review of location routing and distribution network design problems in the literature, and stresses the characteristics of the CMBP-S. In Section 3 we present a mixed integer programming (MIP) formulation of our problem. This is followed by the discussion of the Lagrangian relaxation and the solution of the resulting subproblems in Section 4. Section 5 features computer experiments with the proposed solution methodology and the results thereof. The paper concludes with future research directions in Section 6.

We consider a traditional brick-and-mortar retailer that operates two types of facilities and serves only one type of customers. Its facilities comprise warehouses (WH’s) and physical stores, where goods are transferred from the former to the latter in direct shipments. Goods are then sold to walk-in type customers who are assumed to go to the nearest physical store for shopping. When the retailer opens a website for the online shopping convenience, it will need the capability of receiving, processing and then delivering orders placed by online customers at that website. Some of its present brick-and-mortar stores (BM’s) might have to be reconfigured, or several new stores might be opened with that capability. A physical store is designated as a click-and-mortar store (CM) if it is Internet-enabled, equipped with the necessary hardware, software and personnel such that it can effectively handle online orders. A physical store can serve online customers only then if it is opened as a CM or if it is a BM that is reconfigured as (converted to) a CM. Online customers have different expectations and service requirements than walk-in customers. Most of the time, their orders are delivered to their residences while walk-in customers visit the stores in person. Sometimes, these two types might exchange their roles. An online customer places his or her order on the website of the retailer, but prefers going to the nearest store to pick up the order. On the other hand, a walk-in customer can buy a bulky good in the store, and might need it delivered home. Our criterion in determining the customer type is whether or not the purchased good is to be delivered subject to a time restriction. In this case, we consider him or her an online customer.

Customers and facilities of the retailer in the static click-and-mortar business problem (CMBP-S) are given symbolically in Fig. 1 along with the direction of travel between these. Any CM can serve both customer types as shown in Fig. 1. BM’s, on the other hand, can only serve walk-in customers. The orders of online customers can be delivered only from CM’s. The retailer may decide to open one or more new stores. These will be built as CM’s by default. There are three options regarding any of the already present physical stores (BM’s):

  • (i)

    It can be preserved as is. In this case, it cannot deliver orders to online customers.

  • (ii)

    It can be reconfigured as a CM, which would enable it to serve online customers as well.

  • (iii)

    It can be closed, as a result of which some walk-in customers in its vicinity could be lost.

The CMBP-S is applicable especially in the retailing of non-durable goods. Customers who order on the Web such items as flowers or groceries usually expect fast and prompt delivery. Typical temporal constraints upon the deliveries are time windows. In the CMBP-S, however, we assume that deliveries to online customer addresses are restricted by time deadlines only. Depending on the limited capacity of the homogeneous vehicle fleet and on the time deadlines, customers are visited on one or more arc-disjoint tours. A single tour consolidating all orders at a CM will most likely be infeasible. Instead, multiple tours should be constructed. The conversion is as a whole a stochastic and dynamic problem. However, the following simplifying assumptions reduce the problem into a single period static problem.

  • Facilities bear unlimited storage space, which implies that they can supply/transship any volume of demand. Moreover, stores act as no-inventory transit-depots.

  • The reconfiguration of a BM as a CM is associated with some fixed cost. The alternative of shipping orders from a WH is studied in the scenario analyses in Aksen and Altınkemer (2003).

  • In order for a store to serve a walk-in customer, it must be located within the maximum driving (walking) distance of that customer. If there is no such store, the retailer loses his or her demand. Walk-in customers will always choose the nearest among multiple open stores within the maximum distance. This is only a proxy measure since in reality a customer may visit multiple stores in one shopping trip.

  • Any BM can be closed at some fixed cost or gain. Likewise, opening a new CM incurs a fixed cost. All fixed costs and gains are known a priori. They are amortized with a discount factor to a daily basis so that they match with the variable costs of operating the stores.

  • At each store delivering online orders, special vehicles have to be acquired at a fixed acquisition cost per vehicle in order to carry these orders. Trucks currently used by the retailer for the bulk shipping of goods from WH’s to stores are unsuitable for home deliveries since such deliveries are small-size.

  • Shipments from WH’s to stores go in trucks on direct replenishment routes. No two stores are visited on the same replenishment route.

  • Each vehicle should return to its own store. No open route is permitted between stores and customers.

  • The complete matrix of distances is also known a priori.

  • The flow of goods from WH’s to stores will have to match the amount of goods sold or delivered from stores to customers. We assume that these two flows are synchronized. Hence, no inventories build up, and inventory holding costs are ignored.

  • Online orders are pooled before all vehicles are dispatched at the same time.

The last assumption implies that orders are not received on a real-time basis. Stores wait until a certain hour of the day to get all orders. No order is accepted afterward. Each deadline is assumed to be after that time. Therefore, CMBP-S is a single-period static problem. This situation is different than the home delivery problem (HDP) of consumer direct full-line grocery services. First introduced by Campbell and Savelsbergh (2005), the HDP is quite a new problem where the vendor dynamically decides which deliveries to accept or reject and the time slot for the delivery, if it is accepted, to maximize expected profits. The HDP also involves determining cost-effective incentive schemes for customers to choose less stringent time slots for their deliveries. In this aspect, it supports operational decisions of very short terms, but does not make long-term decisions like opening new stores or Internet-enabling existing stores.

Section snippets

Literature review and problem characteristics

The problem CMBP-S basically combines a multisource facility location-allocation problem (FLAP) with a network design problem which involves vehicle routing decisions. The newest annotated literature review of the location-routing problem (LRP) and its extensions is currently due to Ahipaşaoğlu et al. (2003). A perfect synthesis and survey of the LRP is accomplished earlier by Min et al. (1998). They write: “The concept of integrated logistics systems recognizes the interdependence among the

Formulation of the CMBP-S

A mathematical model of the CMBP-S comprises the following index sets, parameters, and decision variables.

    Index sets

    Io

    set of online customers = {1, …, No}

    Iw

    set of walk-in customers = {No + 1, …, No + Nw}

    I

    set of customers = Io  Iw = {1, …, N} where N = No + Nw

    JB

    set of BM’s (locations) = {1, …, MB}

    JC

    set of potential CM’s (locations) = {MB + 1, …, MB + Mc}

    JS

    set of all present and potential stores = JB  JC = {1, …, MB + Mc}

    JW

    set of warehouses (locations) = {MB + MC + 1, …, MB + MC + MW}

    J

    set of all present and potential facility locations = Jw  JB  JC = {1, …, M} where M = M

Lagrangian relaxation for CMBP-S

The Lagrangian relaxation (LR) method embedded in a subgradient optimization can be used for a variety of NP-hard optimization problems to bracket the true optimal solution between a lower and an upper bound [Zlb, Zub]. In minimization problems of the form P: Z = minxX f(x) the upper bound constitutes a good heuristic feasible solution to the problem. The quality of this solution is measured as ∣(Zub  Zlb)/Zlb∣, the relative percentage gap between the final bound values. Since the true optimal

Computer experiments and results

Our composite Lagrangian relaxation method has been coded in C and compiled with Microsoft Visual C++ 6.0® on an Intel Pentium® 4 HT 3.40 GHz processor with 2 GB RAM. We tested our method’s performance in terms of the Lagrangian gap and solution time on a test bed of randomly generated problems. In Section 5.1, we describe how we generated the problems, and give the parameters used in the implementation of our method. In Section 5.2, we present the test results.

Conclusions and future research

In this paper, we propose a static location-routing model (CMBP-S) for the conversion from the traditional brick-and-mortar to the hybrid click-and-mortar retailing business. The model entities consist of online and walk-in customers, warehouses and stores. The model combines store location and customer allocation decisions with vehicle routing decisions into an integrated problem. The transshipment of goods from warehouses to stores with unlimited storage capacity and from there to customers

Acknowledgements

The authors would like to thank the editors of the European Journal of Operational Research, Jacques Teghem and Lorenzo Peccati, and two anonymous referees for their insightful comments which improved the readability and the theoretical soundness of the paper.

References (24)

  • A.M. Campbell et al.

    Decision support for consumer direct grocery initiatives

    Transportation Science

    (2005)
  • J.F. Cordeau et al.

    VRP with time windows

  • Cited by (0)

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