O.R. Applications
Coordinated decisions for substitutable products in a common retailer supply chain

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Abstract

This paper studies coordination mechanisms in a supply chain which consists of two suppliers with capacity uncertainties selling differential yet substitutable products through a common retailer who faces price-sensitive random demand of these two products. We develop in a noncompetitive setting three coordination models – revenue sharing, return policy, and combination of revenue sharing and return policy – and contrast them with a basic and uncoordinated model. We are able to establish the ordinal relationship among the retailer’s ordering and pricing decisions and analytically compare the performances between certain models when two suppliers are identical. We find that the retailer’s ordering and pricing decisions in the model with return policy in the case of identical suppliers are independent of demand or supply uncertainty. Our numerical results reveal that the performances of coordination models in the case of nonidentical suppliers resemble those in the case of identical suppliers. We find that the retailer will place a larger order quantity in models where her average cost per unit sold is smaller. We also find that product substitutability and uncertainties have different effects on chain performances.

Introduction

Ameliorating ineffectiveness of a decentralized supply chain, which, in particular, results from supply chain members’ independent decision-making, has gained increasing attention in recent years. Efforts have been made in the development of coordination mechanisms, aiming to allow a decentralized supply chain to perform as effectively as a centralized one does by aligning chain members’ objectives with a chainwide objective (Thomas and Griffin, 1996). Efforts have also been made in exploring sourcing strategies in a decentralized supply chain, as multiple sourcing is not uncommon in various industrial sectors (Agrawal et al., 2002, Chiang and Benton, 1994, Hong and Hayya, 1992, Treleven and Scheikhart, 1988), and in analyzing the dynamics of interaction among chain members (Cachon and Zipkin, 1999, Leng and Parlar, 2005, Moses and Seshadri, 2000). This paper adds to these growing efforts of improving supply chain effectiveness by analyzing a two-supplier supply chain in which the suppliers with capacity uncertainties sell their differential but substitutable products through a common retailer facing price-sensitive random demand of these two products. Many real-world examples fit the scenario considered in this paper. For instance, a specialty retailer of consumer electronics, e.g. Best Buy, sells two handheld game consoles made by Sony and Nintendo, which are the remaining two suppliers in the handheld game platform space (Gonsalves, 2007, O’Rourke, 2006).

Numerous studies have explored coordination mechanisms, such as revenue sharing and return policy, for improving the performances of decentralized channels (Cachon and Lariviere, 2005, Heish and Wu, 2008, Jeuland and Shugan, 1983, Krishnan et al., 2004, Narayanan et al., 2005, Padmanabhan and Png, 1997, Taylor, 2001, Weng, 1997, Weng, 1999). Cachon and Lariviere (2005), for instance, investigated revenue-sharing contracts in a general supply chain with revenues determined by retailers’ purchase quantities and prices, paralleled them with existing supply chain contracts, and showed that revenue-sharing and buy-back contracts in some settings generate equivalent cash flows. Padmanabhan and Png (1997) on the other hand, examined full return policies, i.e. full refund for unsold items, in the supply chain with a single manufacturer marketing through one or more competing retailers, and showed that, with sufficiently low production costs and demand uncertainty, return policies benefit the manufacturer because retail competition intensifies. Narayanan et al. (2005) further extended the work of Padmanabhan and Png (1997) by allowing the manufacturer to decide an optimal return price and a fixed payment (e.g. franchise fees) under uniformly and normally distributed random demand. Yet, caution shall be given to implementing coordination contracts. As pointed out by Krishnan et al. (2004), return policies can improve supply chain effectiveness, but the sole existence of return policies may lead to a double marginalization problem which neutralizes retailers’ incentives for promotional effort.

The focus of the above-cited literature is on coordination efforts in general settings considering demand uncertainty. Uncertainty on the supply side shall, however, never be neglected (Anupindi and Akella, 1993, Heish and Wu, 2008, Hsu and Bassok, 1999, Kouvelis and Milner, 2002, Tomlin, 2006, Zimmer, 2002, Tomlin, 2006 for instance, studied a firm’s disruption-management strategy in a dual-sourcing setting in which its two independent suppliers have heterogeneous capacities, realiabilities, flexibilities, and cost structures. Anupindi and Akella (1993) considered a quantity allocation problem in a single-product setting with one buyer and two suppliers with different production uncertainties, and derived the buyer’s optimal ordering policies in three models, each characterizing a particular delivery contract a buyer has with the suppliers. Note that multiple sourcing strategies are often adopted in face of supplier uncertainties, and the benefits of multiple sourcing are well documented in several recent articles (Anupindi and Akella, 1993, Fong et al., 2000, Ganeshan et al., 1999, Gurnani et al., 2000, Ha et al., 2003, Lau and Zhao, 1994, Parlar and Perry, 1996, Tomlin, 2006, Van Mieghem, 2004, Yan et al., 2003). It is thus worthwhile to further probe into chain members’ decisions in a two-supplier setting in which both supply and demand uncertainties are present.

In our setting, two suppliers sell differential yet substitutable short-life-cycle (or seasonal) products through a common retailer. Each supplier has capacity uncertainty and the demand of his product is random. The literature on product substitutability in common-retailer chains has typically focused on deterministic or random demand. For example, Choi (1991) analyzed different power structures in a supply chain with two manufactures selling differential but substitutable products through a common retailer under deterministic demand. Trivedi (1998) extended Choi’s model (Choi, 1991) by considering two manufacturers, two retailers, and substitutability at both product and retail levels. Unlike these studies, our work calls for both supply and demand uncertainties and focuses on coordinated decisions in a noncompetitive setting with product differentiation, which is in line with Boyaci and Ray (2003). This noncompetitive setting is applicable when lack of information disables certain supply chain members from interacting with the others properly. We construct two single-mode coordination models, revenue sharing (RS) and return policy (RP), and one two-mode coordination model (termed model RR), which integrates revenue sharing and return policy, and contrast them with a basic and uncoordinated model (model U). We are able to derive the closed-form solutions of the retailer’s ordering and pricing decisions in all four models, and, in the case of identical suppliers, establish the ordinal properties of these decisions, and compare the performances between certain models analytically. A unique finding in the case of identical suppliers is that the retailer’s ordering and pricing decisions in the RP model are independent of demand or supply uncertainty. Although analytical assessment of the performances of coordination models in the case of nonidentical suppliers is intractable, the numerical study reveals that they resemble those in the case of identical suppliers. We find that product substitutability and uncertainties have different effects on chain performances. In particular, with higher product substitutability, the supply chain profits in all models increase, the performances of the coordination models over the uncoordinated model become less significant, and the models incorporating return policy will perform better than the revenue-sharing model. Higher demand or supply uncertainty, on the other hand, leads to lower supply chain profits in all models. Further, at low demand uncertainty or at high supply uncertainty, the revenue-sharing model could perform better than the RR model.

The remainder of this paper is organized as follows. The next section establishes a basic and uncoordinated supply chain model, formulates the supply chain members’ profit functions, and derives their optimal decisions. Section 3 develops three coordination models, and obtains the closed-form solutions for the chain members’ decisions in each coordination model. It further provides an analytical comparison of the retailers’ decisions in four models under the scenario of identical suppliers. Section 4 conducts a numerical analysis and discusses the effects of product substitutability, and demand and supply uncertainties on supply chain performances. The final section concludes with a brief summary and points to potential research directions.

Section snippets

The basic model

This paper studies a single-period model in which two suppliers sell their products through a common independent retailer who is assumed to be the monopolist in the considered market area. We assume that each supplier produces only one product and has uncertainty of allocating capacity when retailer order arrives, and the products of both suppliers possess certain degree of substitutability. Allocation uncertainty captures a supplier’s problem of matching fixed capacity to variable demand in

Coordination models

We develop three coordination models intended to improve supply chain performance: (1) revenue-sharing (RS) model in which the suppliers provide their average production costs as their unit sales prices, and the retailer then determines the ordering and pricing decisions through channel profit-maximization and shares a portion of the profit with each supplier; (2) return policy (RP) model in which the suppliers deliver all the produced quantity, including the overproduced quantity, to the

Numerical examples

To further study the effects of varying parameters on the supply chain profits in the proposed models with identical and nonidentical suppliers, we resort to numerical approaches. We focus in this section on the effects of the retailer’s attitude toward risk, product substitutability, and demand and supply uncertainties on supply chain profits. In the numerical experiments, we consider that the random variable xi,i=1,2, is uniformly distributed over [1-ti,1+ti], and the random variable yi,i=1,2

Summary

We have established one uncoordinated model and three coordinated models for a supply chain which consists of two suppliers with capacity uncertainties selling differential yet substitutable products through a common retailer who faces random demand of these two products, analyzed the retailer’s ordering and pricing decisions in all models, and compared the supply chain profits between certain models. In the case of identical suppliers, we derive the ordinal relationship of the retailer’s

Acknowledgement

The authors thank anonymous referees for their constructive comments and suggestions that significantly enhanced the paper. This research was partly supported by National Science Council, Taiwan, R.O.C. under Grant #NSC95-2416-H-006-027-MY2.

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