Ordering policy and coordination of a supply chain with two-period demand uncertainty

Abstract

We develop a two-period game model of a one-manufacturer and one-retailer supply chain to investigate the optimal decisions of the players, where stock-out and holding costs are incorporated into the model. The demand at each period is stochastic and price sharply drops in mid-life. We assume the retailer has a single order opportunity, and decides how much inventory to keep in the middle of selling season. We show that both the price-protection mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme may achieve channel coordination and access a ‘win–win’ situation under some conditions. The larger the lowest expected profit of the retailer, the lower the possibility of ‘win–win’ situation will be. Combined with the analysis of feasible regions for coordination policies, we find that PME scheme is not always better than ME scheme from the perspective of implementable mechanism. Finally, we find that adopting the dispose-down-to (DDT) policy can bring a larger improvement of the expected channel profit in the centralized setting, and it is interesting that by using DDT policy, double marginalization occurs only at Period 1, and however, does not plague the retailer in Period 2.

Introduction

Supply chain coordination management has been extensively studied in the operations management literature. A supply chain is coordinated when the players, acting rationally, make the decisions that are optimal for the whole supply chain. Some coordination schemes such as quantity discount and revenue-sharing are used to regulate the relationship among the supply chain’s members. Mechanisms are often designed for the static environment with stochastic demand and exogenous selling price. However, owing to the rapid development of technology and the change in consumer taste, some products such as personal computer, electronic component and automobile not only have different short life cycles but also experience sharp price drops in mid-life. For example, the average retail price of a personal computer (PC) drops by 50–58% within the first year of its product life cycle (Anon, 1998, Lee et al., 2000). Gartner Research reports that average selling prices for Apple PCs sold in the first quarter have fallen as much as 20% due to cheap netbooks, cutting box assemblers’ revenues (Philip, 2009). In China, according to the report of Zhongguancun online research center, it shows that the notebook and desktop computer prices monthly have flat decreased by 0.63%, and the price of digital camera has fallen at a rate of 2.27% per month, while mobile phone price has dropped by about 7.05% per month at the second quarter of 2007 (Zhang and Jiang, 2009).

Owing to declining retail prices, price protection becomes a common business practice, especially in the high-technology industries. The early practice of price protection is an unlimited price protection policy where retailers are reimbursed for price reductions on all unsold inventory (Zarley, 1994). Later, this is followed by attempting to shorten the price-protection period combined with additional incentives for retailers. In 1994, Apple and HP attempted to change the terms by limiting the length of time for which price protection would be offered. And later, in 1997, IBM reduced the price protection period to 30 days for their second tier resellers and combined this new rule with the other incentives such as wholesale price discount of 2.5% for the resellers who accepted 15 days of price protection (Zarley and Bliss, 1997, Sourirajan et al., 2008). These actions at the end of the 1990s have marked the stabilization of the price protection terms, and these price-protection actions have two primary impacts: (1) shifting sales forward in time and (2) increasing total sales.

With high and new technology of increasing innovation, retailers may stock too little of a product to satisfy the market demand due to double marginalization, which refers to the fact that a party’s relative cost structure is distorted by the transfer price within the supply chain. Price protection is intended to effectively offset the negative impact of double marginalization effect. From the channel’s perspective, price protection is a tool for channel coordination, achieving the maximum efficiency for the whole supply chain.

This paper assumes that product has a long manufacturing lead-time, so that the retailer has a single order opportunity. The manufacturer (supplier) usually provides some incentives to the retailer to stock more. In particular, price protection (P), mid-life returns (M) and end-of-life returns (E) policies are often used by the supplier to encourage the retailer to order more, especially in the PC industry. Specifically, price protection is a policy under which the manufacturer pays the retailer a portion of the difference in the retail price from one period to the next for inventory held at the end of Period 1; mid-life returns policy allows the retailer to return part of units through the life cycle at some rebate; and end-of-life returns policy allows the retailer to return unsold units at the end of the life cycle. We show that a proper price protection scheme can coordinate the supply chain. From the perspective of practical operations, many companies in the high-tech industry have adopted the price protection policy for their marketing channels, for example, IBM, Hewlett Packard, Seagate, Apple, Compaq, and Maxtor, offer various price protection and return terms to ensure the availability of their products in the market (Zarley and Bliss, 1997, Vizard and Moltzen, 2004, Callioni et al., 2005).

A salient characteristic of the PC industry is that computer hardware and component firms have the opportunity to dispose of the product during the life cycle and at the end of the life cycle. For example, Dell sells overstock components and computers in the end of each selling period through the overstock.com website. An actual dispose-down-to (DDT) policy in the mid-life will be investigated in this paper. Mid-life returns policy and end-of-life returns policy are commonly used in specific industries where the retail price is relatively stable, say books, recorded music, CD and video.

Unlike Lee et al. (2000), we explore the role of various channel policy combinations when firms can dispose the excess product during Period 1 and Period 2. In our model, the decision-maker has a chance to execute DDT policy and decide the inventory level in the middle of selling season. That is, the retailer may dispose some items if the stock level at the end of Period 1 is high enough; otherwise, she keeps all of leftover items for Period 2. We focus on the following issues: the effects of DDT policy on the assignment of items in the two periods and the expected channel profit. Our numerical experiments show that DDT policy can bring a larger improvement of the expected channel profit of centralized system by comparing with Lee et al. (2000).

We evaluate channel policy combinations by two criteria. First, policy combinations should guarantee channel coordination, i.e., it can maximize the expected profit of the whole supply chain. Second, policy combinations should guarantee a ‘win–win’ situation, i.e., the expected profit of each party under the channel policy is strictly greater than that under no channel policy. The second criterion is critical. If the combination can guarantee channel coordination but cannot assure a ‘win–win’ situation, then the combination is infeasible because achieving coordination may result in one of the parties to be worse off.

In this paper, we consider a one-manufacturer and one-retailer supply chain in a declining price environment to investigate the effects of the mid-life returns and end-of-life returns policies on coordination of the supply chain. Shortage or stock-out costs are incurred at the ends of Period 1and Period 2.We study the motivation of the manufacturer to use price protection policy over the declining retail prices. It is discovered that both the price protection plus mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme can coordinate the supply chain. However, can it guarantee a ‘win–win’ situation? In our paper, we will investigate the ‘win–win’ situation of the coordination by computing the lower-bound of the retailer’s expected profit from the coordination mechanism, that is, the larger the lower-bound, the less the possibility of ‘win–win’ will be.

The remainder of this paper is organized as follows. The related literature is reviewed in Section 2. Model formulation and problem description are described in Section 3. The benchmark, the centralized supply chain, is analyzed in Section 4. Section 5 studies coordination mechanisms, PME scheme and ME scheme. Section 6 carries out a numerical analysis. Finally, in Section 7 we summarize the results and point out possible directions for future research.