Two-period pricing and strategy choice for a supply chain with dual uncertain information under different profit risk levels

Highlights

• A concept of PRLS is proposed to depict the profit risk caused by uncertain demand.

• The retail price in period 2 is lower than that in period 1 for a give PRLS.

• The retail price in period 2 is convex on PRLS contrary to intuition.

• Differential pricing of supplier with stage pricing response of retailer is best.

• The suggested optimal PRLS shows expectation criterion is not always appropriate.

Abstract

With the rapid development of e-commerce and Internet technology, multi-period dynamic pricing is a natural choice that conforms to the demand trend of customers who make product purchase decisions based on current prices, past observed prices (reference prices) and past product reviews in a repeated market. This study considers a problem of two-period pricing and strategy choice for a supply chain consisting of a supplier and a retailer in the presence of uncertain basic market demand and uncertain product review. The supplier adopts a price commitment or differential pricing strategy and the retailer responds with a stage pricing or first-period pricing strategy, which constitutes four strategies. A concept of the profit risk level of a supply chain (PRLS) is proposed to characterize the profit risk of the supply chain due to dual uncertain information. Under the four strategies and different PRLSs, we find that the retailer prefers to set a lower retail price in the second period than in the first period to obtain more profits. Interestingly, although the profits of participants in the supply chain increase with the PRLS, the retail price in the second period is convex about the PRLS, which is contrary to the intuition that high risks imply high prices. Furthermore, our results reveal that the strategy under which the supplier uses a differential pricing strategy and then the retailer responds with a stage pricing strategy is the best under the four strategies for a given PRLS because it is win-win for the supplier and retailer. Finally, an optimal PRLS is suggested to balance the profits and risks, which shows that the expectation is not always an appropriate decision rule.

Introduction

With the rapid development of technology, short life-cycle products, such as computers, smart phones, etc., have more and more full of people’s lives and may be long enough to provide multiple production and sales opportunities for upstream and downstream firms in a supply chain (i.e., production and sales of multiple periods). In multiple periods, the demand of products is different from that in a single period because in a single period, consumers make product purchase decisions according to current prices, whereas, with the rapid development of e-commerce and Internet technology, customers make decisions not only based on current prices but also on past observed prices (reference prices) and past product reviews in a market with multiple periods. For example, in the two-period setting, for most seasonal products such as fashion clothes and fashionable mobile phones, the retailers stimulate customer demand by reducing the retail price in the second period (Maiti and Giri, 2017, Zhang et al., 2013). Although the prices may be reduced for many different reasons, the decision makers of a supply chain could benefit from using a reference price strategy (Zhang et al., 2014, Chen et al., 2016). All these show that more and more consumers, firms and scholars are aware of the importance of reference prices and product reviews in multi-period (especially two-period) product pricing.

However, on the one hand, in the two-period supply chain mentioned above, a supplier (he) and a retailer (she) will take different action sequence and timing for dynamic pricing, which will have different impact on the interests of customers and firms. Specifically, a supplier may use a price commitment strategy or a differential pricing strategy. The price commitment strategy means that the supplier announces an only wholesale price based on his total profit of both periods in the beginning of the first period. The differential pricing strategy refers to that a supplier sets a wholesale price in each period based on his total profit of both periods in the beginning of the first period, or announces it based on his profit of each period in the beginning of each period. According to the supplier’s wholesale price(s) under different action timing, a retailer may respond with a stage pricing strategy or a first-period pricing strategy. The stage pricing strategy represents that the retailer sets a retailer price based on her profit of this period in the beginning of each period. And the first-period pricing strategy implies that the retailer announces a retail price of each period based on her total profit of both periods in the beginning of the first period. For example, throughout the sales season, the wholesale prices of products remain basically unchanged when there has been no major technological innovation in smart phones such as Samsung and Huawei, whereas they are changed periodically when a bigger change in technology happens. A retailer, such as Wal-Mart Stores or JD.com, uses a complex dynamic pricing strategy that it sets different retail prices in different periods. Sometimes, in the first period, Wal-Mart Stores or JD.com sets a normal price for a product and offers introductory discount price via promotional offers or coupons for the next period.

On the other hand, the basic market demand and product review are often uncertain in a two-period supply chain in real life. For example, in a new smart phone market, the decision makers of firms can only estimate the basic market demand according to the location of the product but do not know it exactly, implying that the basic market demand is uncertain. After the first selling period, some people are reluctant to comment on the product they buy, and some comments are casual and do not really reflect what they think of the product, which means that the product review is uncertain. The example also implies that the uncertain information with no or little available useful data exists in the real world. People can not exactly predict the uncertain information accurately in advance, but can only estimate it by subjective judgement methods. This makes probability theory unsuitable for dealing with such uncertain information. Moreover, most of the work with uncertain information utilizes conventional expected utility maximization criterion to describe the profits of the participants in a supply chain. Nevertheless, Ellsberg (1961) suggests that using the expectation maximization criterion is not always appropriate. Therefore, it is realistic and necessary to adopt the decision criterion different from the expected value maximization and the uncertain information processing method different from the probability theory to study two-period pricing problems with dual uncertain information.

Based on both motivations mentioned above, this paper investigates a problem of two-period pricing and strategy choice for a supply chain with dual uncertain information. The sales season is divided into two periods. In the two periods, a supplier as a Stackelberg leader adopts a price commitment or differential pricing strategy and a retailer as a follower responds with a stage pricing or first-period pricing strategy. This leads to four strategies: price commitment and stage pricing (strategy PS), differential pricing and stage pricing (strategy DS), price commitment and first-period pricing (strategy PF), and differential pricing and first-period pricing (strategy DF). Under the four strategies, the basic market demand and the product review made by the first-period customers with little or no observed data are assumed to be uncertain. We apply uncertainty theory (Liu, 2007), which is an effective tool for processing unknown information with expert experience, to characterize the uncertain information and propose a decision rule based on confidence levels instead of a conventional expected value rule. The confidence level is the degree of belief in a successful result and can be defined as a percentage. Its value reflects the individual’s attitude toward risk during a decision-making process (Liu et al., 2017, Liu et al., 2018). The difference between one and confidence level is used to characterize the participants’ risk attitudes to profits in a supply chain. We call it the profit risk level of the supply chain (PRLS). Under the four strategies and different PRLSs, we consider a two-period pricing and strategy choice problem for a supply chain. Specifically, the following questions are worth studying: (i) Should the wholesale price (for a differential pricing strategy) and the retail price in the second period be set high or low compared with those in the first period under different PRLSs? (ii) How does the PRLS affect two-pricing decisions and the profits of the participants in a supply chain under the four strategies? (iii) Which is the best of the four strategies for a given PRLS? (iv) Is there an optimal PRLS that balances profits and risks under the four strategies?

To solve these questions, we consider a two-period supply chain with one supplier and one retailer under the four strategies and different PRLSs. The demand in the second period depends on the current retail price, the retail price and product review in the first period where the basic market demand and the past product review are assumed to be uncertain. Under the four strategies and different PRLSs, the corresponding models are established and solved. We compare the prices in two periods and analyze the impact of the PRLS on the two-periods pricing decisions and the participants’ profits under each of the four strategies. Comparing the equilibria under the four strategies, we derive the best of the four strategies for a given PRLS. To balance profits and risks, an optimal PRLS is suggested under strategy PS, DS, PF or DF.

Compared with the existing literature, the most important contributions of our paper lies in two aspects. On the one hand, we introduce the risk attitude of decision makers into the literature on two-period dynamic pricing and extend Maiti and Giri (2017)’s work and obtain many different management insights. On the other hand, we have filled some gaps in the supply chain risk management literature. Many scholars, such as Gan et al., 2005, Chernonog and Kogan, 2014, Yao et al., 2016, only study the risk management of one-dimension uncertain information and consider only a single situation of different decision makers’ risk attitudes (one is risk-averse and the other is risk-neutral). Whereas, we simultaneously investigate the case of two-dimensional uncertain information and all different risk attitudes of decision makers. Furthermore, we provide a suggestion to the decision makers who have no special preference for risk, which indicates that the expectation maximization is not always an appropriate decision criterion. The main specific conclusions that differ from the existing literature are detailed below.

First, for any given risk attitude for the supplier and retailer (i.e., PRLS), the retailer (supplier) prefers to set a lower retail price (wholesale price for a differential pricing strategy) in the second period than that in the first period under all the four strategies. This is because the demand in the second period increases with the decrease of the current retail price, and it further increases when the product review is considered and the retail price in the second period is lower than that in the first period. This leads to an increase in the respective profits of the supplier and retailer in both periods.

Second, under each of the four strategies, an increase in the PRLS will increase the wholesale price(s), the retail price in the first period and the profits of the supplier, retailer and total supply chain. Interesting, the retail price in the second period is convex about the PRLS, that is, it decreases first and then increase, and the convexity is determined by the ratio between the sensibilities of the uncertain basic market demand and product review to the PRLS. The conclusion is contrary to intuition because it shows that high risks do not imply high prices. This finding provides an important theoretical basis for decision makers who have no special preference for risk to choose a rational risk attitude to best meet customer demand for products.

Third, from the actual theoretical results, comparing the equilibria under the four strategies for a given PRLS, we find that strategy DS is the best of the four strategies, that is, under strategy DS, the supplier and the retailer can obtain most profits and provide best service to customers due to highest profits, most market supply and lowest prices under the four strategies. Under strategy DS, the lowest wholesale price in each period results in the lowest retail price in each period, and then the demand in each period increases to the highest level, implying that the supplier’s, retailer’s and supply chain’s profits increase to the highest level. From the actual intuitive experience, strategy DS dominates the other three strategies because the supplier and retailer will dynamically adjust their respective pricing decisions in each period under the former strategy, while they will not do so under the other strategies. Therefore, the supplier and the retailer can achieve win–win results under strategy DS.

Finally, we suggest an optimal PRLS that attempts to maximize the retail price in the second period under each of the four strategies. Our results show that the expectation is not always appropriate to be as individuals’ decision rule because the suggested optimal PRLS can better balance the profits and risks of the participants in a supply chain.

The remainder of our paper is organized as follows. Section 2 reviews the most relevant literature and compares our study with them. Section 3 describes and builds the models under the four strategies: PS, DS, PF and DF. Section 4 compares the two-period pricing decisions under the four strategies and provides the optimal strategy choice. Section 5 suggests a proper PRLS for balancing profits and risks under the four strategies. Section 6 extends the models in Section 3. Section 7 concludes our paper.