Retail–collection network design under deposit–refund

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Abstract

This paper studies the interplay between industrial firms and government concerning the collection of used products from households. The focus is on the use of a deposit–refund requirement by the government when the collection rate voluntarily achieved by the firms is deemed insufficient. We present a continuous modeling framework for designing a drop-off facility network and determining the sales price that maximize the firm's profit under a given deposit–refund. The customers’ preferences with regards to purchasing and returning the product are incorporated via a discrete choice model with stochastic utilities. Through parametric analyses, we determine the net value that can be recovered from a returned product as a key driver for the firm to voluntarily engage in collection. We show that a minimum deposit–refund requirement would not achieve high collection rates for products with low return value and point out two complementary policy tools that can be used by the government.

Introduction

Resource recovery involves diverting used products from the waste stream and seizing their remaining value via reuse, recycling and/or re-manufacturing. This reduces the use of virgin natural resources, mitigates environmental pollution and eases the burden on limited landfill space for the waste stream. Providing a means for minimizing the environmental externalities of the consumption-oriented economies, resource recovery programs have attracted the attention of many regulatory bodies and governments. The European Parliament, for example, enacted a new Directive in February 2003 that requires the manufacturers to assume financial responsibility for the reuse and/or recycling of waste electrical and electronic equipment (WEEE). Although such requirements constitute an additional liability for manufacturers, the value recovered from used products provides an economic opportunity in some cases. For example, in 1991 Xerox Corporation launched its Asset Recycle Management Program that aimed at managing the increasing volume of products returned to Xerox through customer trade-ins and lease expirations. The resulting savings in the purchasing costs of new parts and raw materials were reported to be in the order of several hundred million dollars in 1995.

In this paper, we focus on the collection of used products from households. This is a common first phase for many resource recovery initiatives, and it provides the input for re-manufacturing and recycling processes. Collection effectiveness depends on the consumers’ willingness to return used products at the time of disposal. Therefore, it is important to provide the consumers with convenience and, if necessary, incentives to participate in the collection program. A common example of convenience is the pick-up services offered in the case of heavy and bulky commodities, such as used household appliances. When transportation costs associated with pick-up are excessive, firms typically establish collection facilities for consumers to drop-off the used products. Since customers perform the transport task in this case, accessibility of the collection facilities is crucial. Incentives, such as a certain rebate at the time of return, can complement convenience in increasing the return rate. In order to study the interplay between accessibility and incentives, we focus on the use of a drop-off policy for collection. Note that implementation of pick-up policies also involves the routing of collection vehicles [1]. A detailed account of the collection policies used in the US can be found in McMillen and Skumatz [2].

The regulators’ aspiration with regards to environmental sustainability frequently translates into required rates for resource recovery. The WEEE Directive, for example, establishes target recycling rates for refrigerators and washing machines at 75%, cathode ray tubes used in TV and computer monitors at 70% and computer equipment at 55%. When resource recovery is not economically viable for the industry, voluntary collection programs may not be sufficient to achieve the target recovery rates. In such cases, governments can resort to a wide spectrum of policy tools to facilitate achievement of their targets. Mandatory take-back legislation, such as Germany's packaging recycling law implemented via the well-known Green Dot program, constitutes the most radical approach that is typically difficult to enforce. Price-based policies constitute a less challenging option in terms of implementation and monitoring. Examples of such policies include taxes on the use of virgin materials, recycling subsidies, disposal fees and deposit–refund requirements [3]. Economics literature provides evidence that deposit–refund is the most preferable policy in terms of the total cost of accomplishing a certain disposal reduction [4], [5], [6]. Motivated by this fact, in this study we represent government's involvement in the collection activity via a minimum deposit–refund requirement.

A deposit–refund system requires consumers to pay a certain deposit at the time of purchase, which is refunded upon the return of the used product. Such systems have been commonly used in promoting return and reuse of product packages and containers, e.g., aluminum cans and glass bottles [7]. Other examples of government-initiated deposit–refund systems include car batteries and tires [8]. In his seminal work, Bohm [9] argued that deposit–refund can be used by regulators as an effective policy tool in a wide range of industries. Many industry representatives, however, expressed concern over the impact of deposit on retail price and often lobbied against deposit–refund requirements pointing out a possible reduction in sales. In Germany, for example, the January 2003 deposit law is perceived to have caused a 20–60 percent drop in sales by can and bottle manufacturers [10]. Although the macrobenefits of deposit–refund systems are well studied by economists, there is no published research analyzing their impact on the manufacturers’ operations. A solid understanding of the firm-level impact of deposit–refund requirements, however, is crucial for their overall effectiveness. Our study is motivated by the need for analytical approaches that foster such an understanding.

In this paper, we develop a methodology for designing a drop-off facility network under deposit–refund requirements. We adopt a continuous modeling approach and assume constant population density over the market area. Although approximate in nature, continuous models allow for the development of closed-form expressions that facilitate analytical insights regarding the impact of problem parameters. Daganzo [11] has devised this approach for the analysis of (forward) logistics systems. Continuous modeling has been used also for determining optimal market areas [12] and production–distribution network design [13]. Recently, Fleischmann [14] presented a continuous model for the design of reverse logistics networks. In representing the collection activity, he assumed a constant return rate over the market area. We extend this approach by incorporating the impact of deposit–refund on both the sales rate and the return rate. Given a deposit–refund requirement, we provide a model to determine the optimal sales price and collection area radius so as to maximize the expected profit of the firm. The variation among consumers in terms of their response to a certain deposit–refund is explicitly modeled in estimating the sales and return rates.

In terms of incorporating the variability of individuals’ choices in the analysis of deposit–refund systems, Kulshreshtha and Sarangi [15] constitutes the most relevant study in the economics literature. The authors, however, are focused on the use of deposit–refund systems as a price discrimination mechanism rather than the optimal design of collection facility networks. In contrast, the earlier research for reverse logistics network design is based on mixed integer programming formulations, where the variability in the amount of return at each customer location is ignored (e.g., [16], [17], [18], [19]).

In a recent paper, Guide and Van Wassenhove [20] called on the industry to adopt a proactive approach to used product acquisition, rather than passively accepting the returns. Deposit–refund constitutes an effective means for the firm (as well as the government) to influence the quantity, timing, and possibly the quality of returns. In Section 2, we present an analytical framework that incorporates deposit–refund in the collection system design decisions of the firm. Section 3 demonstrates the versatility of the proposed methodology by adapting it to the integrated retail–collection network design problem. In Section 4 we present an illustrative example to show that the firm can achieve considerable additional profit by optimizing sales price under deposit–refund rather than simply adding the deposit onto the retail price. Our parametric analyses also indicate that the net value recovered from a returned product is a key driver for the firm to offer voluntary deposit–refund. Section 5 points out that a minimum deposit–refund requirement would not achieve high collection rates for products with low return value and studies the impact of two additional requirements that can be used by the government. Realizing the inadequacy of a price-based policy (i.e., deposit–refund), these policy tools are designed to improve collection rate by imposing that the firm offers a certain level of accessibility to its collection facilities. We provide some concluding remarks in Section 6.

Section snippets

Designing a collection system with deposit–refund

In this section, we focus on the design of a collection system to complement an existing retail network. Most companies have a retail network in place when they decide to launch a collection program, either on a voluntary basis or as a result of regulatory requirements. The collection facilities can be located anywhere in the market area while the retail network usually remains unaltered during this process. The accessibility of retail facilities and the retail price are among the key factors

Re-designing the retail network under deposit–refund

The proposed analytical framework is quite versatile for studying the collection facility network design problem under different structural assumptions. Note that the model in Section 2 allows for the location of collection facilities anywhere in the market area. When resource recovery is not a significant economic opportunity for the firm, establishment of facilities dedicated to collection may not be viable. In this case, firms may agree to offer collection services only at their retail

Firm-initiated deposit–refund: An illustrative example

We have done extensive numerical studies with the models proposed in Sections 2 and 3. Our objective for the remainder of this paper is to highlight the main insights we gained through these analyses. This section illustrates the firm's perspective on deposit–refund systems via a set of hypothetical examples. We first analyze a firm that has an existing retail facility network and optimizes its collection facility network design while simply adding the deposit onto the retail price. We compare

Government-initiated deposit–refund

In the previous section, we showed that the proposed methodology can be used for identifying the deposit–refund that maximizes the firm's profit. It is safe to assume that the firm will offer this deposit–refund voluntarily. Our analysis also identified returned product value p as a key factor in profitability of the collection activity. In order to approach the problem from the government's perspective, this section presents a parametric analysis of the voluntary deposit–refund with respect to

Concluding remarks

In this paper, we present an analytical framework that incorporates deposit–refund in the firm's collection facility network design and pricing decisions. We use the proposed methodology for modeling the launch of a collection program as well as the establishment of integrated retail–collection facilities. Our computational analyses on an illustrative example show that the returned product value is a key factor that determines the nature of collection in an industry. For products with high

Acknowledgements

This research has been supported in part by a grant from the Social Sciences and Humanities Research Council of Canada (410-02-0705). The comments and suggestions of an anonymous referee were very helpful in improving the paper. This submission was handled by Gilbert Laporte.

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