Production, Manufacturing and Logistics
Innovative menu of contracts for coordinating a supply chain with multiple mean-variance retailers

https://doi.org/10.1016/j.ejor.2015.05.035Get rights and content

Highlights

  • Coordinate multi-retail supply chains.

  • Consider systems with risk-averse retailers.

  • Employ the mean-variance (MV) model.

  • Develop innovative measures.

  • Propose non-MV inferior contracts.

Abstract

We consider the coordination challenge with a risk-neutral manufacturer which supplies to multiple heterogeneou retailers. We find that the manufacturer can maximize its expected profit only if the expected profit of the supply chain is maximized, or equivalently supply chain coordination (SCC) is achieved. The target sales rebate (TSR) contract is commonly used in practice to achieve SCC. However, as we found in this paper, the presence of heterogeneity in retailers’ minimum expected profit requirements is the major cause that a single TSR contract and the related single hybrid contracts all fail to achieve SCC and maximize the manufacturer’s expected profit simultaneously. Thus, we develop an innovative menu of TSR contracts with fixed order quantity (TSR-FOQ) . Although there are multiple contracts in a menu, we find that the manufacturer only needs to decide one basic TSR contract and two newly developed parameters termed as the risk-level indicator and the separation indicator, in applying the sophisticated menu of TSR-FOQ. By adjusting the two indicators, the manufacturer can control the profit variance of the retailers and the separations of the component contracts of the menu. We further propose another sophisticated menu of TSR with minimum order quantity and quantity discount contracts which can give each retailer a higher degree of freedom in the selection of order quantity. Differences between the two menus are analytically examined. Some meaningful managerial insights are generated.

Introduction

In supply chain management, there is no doubt that coordinating a supply chain system with risk sensitive retailers is an important issue (Agrawal, Seshadri, 2000, Chen, Seshadri, 2006, Chiu, Choi, 2013). However, in the literature, there is an absence of a fair and flexible supply contracting mechanism which can help achieve coordination in a supply chain with multiple heterogeneous risk-sensitive retailers. This motivates us to conduct this analytical study. Specifically, we consider a two-echelon (not an n-echelon) supply chain with a single manufacturer (M) and multiple retailers (Rs), where M is risk-neutral and Rs are risk-averse mean-variance seekers. We consider that each retailer faces a separate market of the similar size (noting that separate markets do not necessary mean that the markets are in different countries, they could be in different places of the same country). These assumptions consider the scenario in which the manufacturer finds many retailers to act as its agents to sell its product in separate markets and each retailer serves a market of a similar size. Given different economic conditions, these Rs have different profit targets (i.e., minimum participation requirements on the expected profit), which reflects the heterogeneity of retailers. If the profit target is not satisfied, the individual R will order nothing and may “withdraw from the supply chain”. As a result, the manufacturer will lose the opportunity to sell the product in that particular market. Given the heterogeneous mean-variance Rs, we aim to explore the supply contracting mechanism that will allow M to coordinate the supply chain while maximizing its own expected profit. Besides the economics issues, in order to maintain a good relationship with retailers and to enhance the sustainability of the supply chain, the manufacturer also considers the issues associated with fairness, faithful supply contracting and partnership. Therefore, to avoid (1) any negative effects caused by unfairness among retailers; (2) the legal problem that may arise from price discrimination (Robinson-Patman Act, see Crowley, 1947 for more details); and (3) the risk that may bring an unexpected cost in time and efforts to handle the unfairness and the legal issues, M has to offer the same supply contract scheme to all Rs. In other words, even M can easily find a customized single contract which is designed “just for” a specific R, to maximize its own expected profit, its realization is difficult because this contract must then also be made available to every other R. Therefore, the multiple-retailer problem cannot be considered as separate single-retailer problems, and then be solved in a single retailer setting. Moreover, in order to isolate the effects of the heterogeneity of the retailers, we consider that the markets are independent and identical, which is also adopted in the literature (e.g. Agrawal & Seshadri, 2000), and the manufacturer has sufficient capacity to fulfill all the orders from the retailers. This helps isolate the core problem of having “multiple risk sensitive” retailers and reveal insights on the respective coordination mechanism.

By modeling risk aversion using the mean-variance (MV) approach (Chiu, Choi, 2013, Huang, Simchi-Levi, Song, 2012), we consider that Rs all follow the MV objectives (we call them MV-Rs) and each MV-R aims to minimize the variance of profit subject to the constraint of having the expected profit no less than a given level (i.e., the profit target or the minimum requirement on expected profit is achieved). The MV approach has been adopted extensively for supply chain risk analysis. The advantages of applying the MV approach in modeling risk sensitive supply chain agents include: (i) it is easy to understand even for practitioners such as managers in the industry, (ii) it is analytically tractable, and (iii) it has good literature supports (Agrawal, Seshadri, 2000, Chiu, Choi, 2013, Choi, Chiu, 2012, Choi, Li, Yan, 2008). As it will be shown later, we analytically find that, in a supply chain with multiple MV-Rs, M’s expected profit is maximized only if the expected profit of the entire supply chain is optimized, i.e., the supply chain coordination (SCC) is achieved. Therefore, we will focus on examining the supply contracts to achieve SCC, as this also implies maximizing M’s expected profit.

In the literature, mostly a single retailer is considered in the analysis of SCC with supply contracts, including revenue sharing contract and target sales rebate contract. In this study, we explore how a target sales rebate (TSR) contract can help to achieve SCC while maximizing the expected profit of M. Under a TSR contract, the manufacturer will grant a rebate to a retailer if the sales of the retailer exceeds a pre-specified target (cf. Chiu, Choi, Li, 2011, Taylor, 2002). A sales rebate thus provides an incentive for the retailer to order and sell more, and helps coordinate the supply chain by resolving problems such as double marginalization. We choose to study the TSR contract because (i) many manufacturers have employed the TSR and related contracts in practice (see Chiu, Choi, Li, 2011, Chiu, Choi, Tang, 2011), (ii) it offers a greater flexibility to achieve SCC as there are three control parameters in the contract, (iii) it is intuitively appealing and has a sufficient literature base.

In our analysis, we find that SCC cannot be achieved (and hence M’s expected profit cannot be maximized) if a single TSR contract is employed and the heterogeneity of Rs is the main reason accounting for this. We, therefore, propose and examine two variations of TSR contracts, namely the TSR with fixed order quantity (TSR-FOQ) contract, and the TSR with minimum order quantity and quantity discount (TSR-MQD) contract. In a TSR-FOQ contract, the order quantity is pre-specified, so Rs can only decide to accept or reject it. In a TSR-MQD contract, a minimum order quantity (MOQ) is specified such that Rs can order no less than the given MOQ. In addition, a TSR-MQD contract includes a quantity discount function which offers a lower unit wholesale price for a larger order quantity. Although a TSR-FOQ contract and a TSR-MQD contract allow more control for M than that under a TSR contract, they both fail to guarantee the achievement of SCC. This presents a challenge to the coordination problem. To achieve SCC, we employ the menu of contracts approach, in which M needs to design the menu of contracts in a way that the Rs will react by selecting components for the contract and ordering the “desirable quantity” (which is equivalent to the best quantity for the supply chain). This imposes a challenge on M as the Rs are virtually free to decide their favorable component contracts and ordering quantities. As a remark, in the literature and also in practice, the menu of contracts approach is typically devised to resolve information asymmetry between the players involved. We suggest to adopt the menu of contracts approach in this paper because the single contract approach fails to guarantee the achievement of SCC with multiple heterogeneous retailers. We believe that the menu of contracts approach can also be extended to a more general setting that consider both the heterogeneous retailers and information asymmetry. However, the focuses of this paper are on (1) examining the challenges in coordinating such supply chain multiple heterogeneous retailers with different minimum expected profit preferences, and (2) examining the application of menu of contracts with multiple heterogeneous retailers. As we shall see later on, the problem formulation in our analysis is already very complicated, a more general setting will limit the development of analytical results and insights. Therefore, we leave the information asymmetry extension to future study.

In this paper, we derive two menus of contracts, namely the menu of TSR-FOQ contracts and the menu of TSR-MQD contracts. The sufficient conditions under which the two menus of contracts can coordinate the supply chain and maximize M’s expected profit are obtained. For the case when the sufficient conditions are unattainable, two sub-optimal menus of contracts are derived under which SCC is still achievable. In developing these coordinating menus of contracts, we introduce some innovative concepts. Firstly, we define two new concepts for describing the connections between component contracts of a menu, they are non-dominated component contracts and MV-non-inferior component contracts (see Section 5 for details). We find that the component contracts of a menu which achieves SCC must be non-dominated and MV-non-inferior. Secondly, we propose two new contract terms specifically applied for the menu of contracts, a risk level indicator (for Rs) and a separation indicator (of component contracts of the menu). As the menu of contracts contains multiple supply contracts, it is complicated for M to determine the parameters for achieving SCC. By introducing the risk level indicator and the separation indicator, the contract setting is significantly simplified. More specifically, instead of controlling the contract parameters of all component contracts in the menu, M only needs to control “the component contract” which is specifically designed for one particular R, plus the risk level indicator and the separation indicator. We suggest that the risk level indicator is specific for the supply chain setting (multiple risk-averse retailers) considered in this paper, and the separation indicator is general for applying the menu of contracts. When one considers a similar supply chain coordination model with another kind of heterogeneity of retailers, the risk level indicator will be replaced by another specific indicator, and the separation indicator will remain applicable.

This study contributes to the advancement of both academic research and practice of SCC by extending and generalizing the result on SCC with one manufacturer (i.e., M) and multiple heterogeneous risk averse retailers (i.e., Rs). We reveal that the expected profit of M is maximized only if SCC is achieved. Moreover, we illustrate that for M, the heterogeneity of Rs is the major barrier to achieve SCC and to maximize M’s expected profit simultaneously. The SCC mechanisms under different settings have been established. Some innovative analytical schemes for achieving SCC and expected profit maximization of a manufacturer have been proposed and their performance has been examined. The results provide some important references for manufacturers to employ rebates, menu of contracts, and other associated contracts to achieve SCC while maximizing their own expected profits. In addition, our findings provide useful insights on SCC and suggest ways to extend the traditional coordination mechanism from cases with a single retailer to the case with multiple heterogeneous risk-averse retailers. Our study thus lays the foundation for a new line of research.

The organization of the rest of this paper is as follows. We present the literature review in Section 2. In Section 3, the supply chain model is constructed, and some preliminaries are derived. Then we review the SCC issue for the case of a single MV-R, and examine the performance of several “single TSR” contracts in Section 4. The concepts of non-dominated contracts and MV-non-inferior contracts are introduced in Section 5. In Section 6, we develop the specific menu of TSR-FOQ contracts and the menu of TSR-MQD contracts, and derive the respective sufficient conditions that allow the two menus of contracts to achieve SCC while maximizing the manufacturer’s expected profit. Finally, we conclude the paper and discuss some open research areas for future work in Section 7. To improve presentation, all proofs are shown in Appendix A.

Section snippets

Literature review

There is a vast literature on SCC. In the following, we focus on the most relevant works and present a concise review. First, sales rebates take various forms which can be observed in different industries. For instance, in fashion apparel, suppliers of national brands such as Levi’s used to impose a channel sales rebate scheme on the items that they wanted to push to the market using a rebate known as “push money”. In the auto industry, a kind of channel sales rebate called “dealer incentive”

The model

We consider a two-echelon supply chain with one manufacturer and n retailers. The manufacturer (M) produces a newsboy type product, and sells it to the retailers (Ri, i=1,,n). Then the retailers resell the product in n separate markets. To avoid the unfairness across the supply chain members, the legal problem of price discrimination and the related extra cost in time and efforts to handle it, the manufacturer must provide the same contract package to all retailers.

To maintain the brand image

Single contract

Chiu, Choi, and Li (2011) show that a single basic TSR contract achieves SCC for a supply chain with a single retailer. Therefore, before we derive the menu of contracts that achieves SCC and maximizes E[ΠM], in this section, we first explore the performance of the single basic TSR contract, the single TSR-FOQ contract, and the single TSR-MQD contract. We focus on examining whether or not SCC and E[ΠM]=Π¯M* can be achieved, if M offers a single contract to the Rs.

Non-dominated and MV-non-inferior contracts

Heterogeneity of Rs’ μi increases the complexity of M’s optimization problem. To achieve SCC and E[ΠM]=Π¯M* simultaneously, M should consider a more sophisticated solution scheme. We suggest to design one specific TSR contract for each retailer, and then combine them to form a menu of TSR contracts. However, the menu of TSR contracts approach arises two problems.

Consider a menu of two TSR contracts, θTSR,1=(w=5,u=1,T=1000) and θTSR,2=(w=4,u=1,T=1000). Obviously, all retailers select θTSR, 2

Menu of contracts

We consider two different menus of contracts, the menu of TSR-FOQ contracts and the menu of TSR-MQD contracts. We focus on deriving a menu of TSR-FOQ contracts and a menu of TSR-MQD contracts under which SCC and E[ΠM]=Π¯M* are achieved simultaneously (there may exist other types of menu of contracts to achieve the same goals).

Conclusion and future research

Due to the heterogeneity of the minimum expected profit requirement among mean-variance retailers (Rs), we know that the manufacturer (M) cannot achieve supply chain coordination (SCC) and maximize its expected profit simultaneously by offering a single TSR contract to the Rs. To tackle this problem, we propose that M offers a menu of contracts to the Rs. We introduce two menus of TSR contracts, namely the menu of TSR-FOQ contracts (ΘFOQ) and the menu of TSR-MQD contracts (ΘMQD) for achieving

Acknowledgments

We sincerely thank the editor, and the anonymous reviewers for their many helpful suggestions and kind advice. Chun-Hung Chiu is partially supported by the National Natural Science Foundation of China, China with the grant number of 71371197. Tsan-Ming Choi is partially supported by RGC-HK General Research Fund with the grant numbers of PolyU 5420/10H and PolyU 5424/11H.

References (22)

  • ChoiT.M. et al.

    Risk analysis in stochastic supply chain: A mean-risk approach

    (2012)
  • Cited by (36)

    • Mean-variance analysis of wholesale price contracts with a capital-constrained retailer: Trade credit financing vs. bank credit financing

      2021, European Journal of Operational Research
      Citation Excerpt :

      Among them, Markowitz's mean-variance framework is widely used to explore risk management problems (Markowitz, 1959). In the context of supply chain management, many scholars introduce the mean-variance framework to depict the risk of uncertain market demand (Chiu & Li, 2011, 2015; Gan et al., 2004, 2005; Javier, Melike, & Anna, 2015; Wei & Choi, 2010; Wu, Li, Wang, & T. Cheng, 2009; Zhuo, Shao, & Yang, 2018) and optimize supply chain contracts. Specifically, Gan et al. (2004) propose a definition of supply chain coordination with risk-averse agents and investigate the supply chain coordination problem under the mean-variance framework.

    View all citing articles on Scopus
    View full text