تصمیم گیری پویا در زنجیره تامین دو مرحله ای با معاملات مکرر

This research investigates how the experience learned in repeated transactions by consumers and manufacturers would affect supply-chain partners' strategic decisions such as price, order quantity and service level. Consumer demand depends on two factors: (1) retailer price and (2) service level provided by the manufacturer in the past and current transaction periods. Game theory is used to understand interactions between the horizontally competitive suppliers and their vertical interactions to the common retailer in the one-period looking-ahead decision environment. Dynamic-system concepts are integrated into the game-theoretic model for understanding the evolution of the strategic decisions over multiple time periods. The research shows that the manufacturer with any type of cost-advantage for providing more services to its customers will capture a larger market than its competitor. Comparison of our model to the myopic model indicates that the myopic suppliers, who ignore the customer learning effect on future periods, shrink their market sizes and earn less profit over time. The manufacturers who use the learning experience to plan future investment can prevent this phenomenon from happening and enhance their competitiveness.

Faced with marketplace factors like cross-channel behavior, media fragmentation and advertising saturation, companies today are faced with the difficulty of retaining empowered, demanding and media-savvy customers. As a result a new term has emerged: Customer Experience Management (CEM). CEM's premise is the reverse of Customer Resource Management (Gurney, 2002). It states that every interaction between the company and customer results in the customer learning something about the company. Depending on the experience, customers may alter their behavior in ways that affect the company's profitability. Thus, by managing these experiences companies can orchestrate more profitable relations with customers. A superior customer experience means both cost and service efficiency. Service is defined as any action that a manufacturer takes to help customers obtain maximum value from their purchases (Goffin, 1999). Examples of service include end-to-end online services (e.g., financing, insurance, and customer support) or product-related merchandise to strengthen customer experience with the company (e.g., discount coupons, and rebates). Most savvy executives recognize that forging long-term relationships with their key customers is the route to success in an increasingly competitive and dynamic marketplace. These companies routinely use their transaction data to identify new customer segments, improve the profitability of existing customer segments, enhance each customer interaction and build customer relationships. Customer retention is not only a cost effective and profitable strategy, but in today's business world it is necessary especially when we remind ourselves that 80% of the sales in any business come from 20% of the customer and clients. When a customer buys a product he looks for how well the product fits his needs. He also evaluates the quality and service of the product. If any of the attributes does not fit well with the customer's expectation, he may choose a competitor's product. In doing so he is willing to undertake risk associated with trying a new product. On the other hand if the customer is satisfied with the product he will be feel less uncertain about it in the next period and repeat the transaction. The motivation for the paper was the observation that between 1971 and 1990, total sales of Japanese cars in the US increased by 427% while total new car sales increased only 9%. Experience learned from past transactions about product price, quality and service can help consumers decide what brand of products to buy and what price he/she is willing to pay. The same experience can also help manufacturers decide on their future investments for improving their market share and hence their competitiveness. Keaveney (1995), Wojcik (2001) and Gurney (2002) discuss how customer learning experience can impact the demand of a product.1 This research focuses on the problem of deciding product price, order quantity and service level from the experience gained from (1) supply-chain partners' repeated transactions and (2) consumer's memory of price and service difference between the product brands. To limit the scope of research, the supply chain considered in this article has two manufacturers producing competing products and selling them through a common retailer. This article analyzes the behavior of each firm over time when faced with learning demands as shown in Fig. 1. In our model, the market base for each product in any given period is affected by two types of components: (1) inter-temporal factors, i.e., the difference in price, service and investment between the two products in the previous period and (2) the amount of investment by each manufacturer in the given period to expand the market base of its product (or brand). Each period can be viewed as one selling season or a span over one product generation, e.g., one quarter or one year. The decision on the amount of investment is made at the very beginning of each period. The decisions on the wholesale price and service level are taken by each manufacturer after the market has been influenced by the investment. Finally, the retailer makes its decision on the retail price of both products at the end of each period. The decision cycle is repeated over time in this order. Fig. 2 shows the timeline of decisions made within each transaction. To investigate the strategy and impact of investment made by manufacturers, we use the Manufacturer Stackelberg model.2In the real world both the manufacturer and the retailer offer services. For our paper we assume that the end customers do not distinguish between these services. We do not model the services offered by the retailers in this paper. This seems to be a reasonable assumption in most scenarios. For example, if a single facility owns both the manufacturer and the retailer then service is set for both the facilities jointly. Even if separate entities own them, the manufacturer has a financial incentive mechanism to reward the retailer for improving sales and service. Thus, all the costs are factored into the manufacturer's cost. Manufacturer incentives to the retailer to improve sales and service is a vast area in itself and is outside the scope of this research. The model in our research can be applied to both durable goods (e.g., compact diskettes, computer parts, etc.) and non-durable goods such as food grains. The only assumptions we make are (1) manufacturers produce products with overlapping generation of customers and (2) there is no switching cost for customers. Assumption (1) means that we consider products with life cycle greater than one period. It is important as we want to model the consumer learning effect from one period into future periods. Switching costs (assumption (2)) occur when consumers incur a cost while switching manufacturers of a good. Companies in areas such as computers, banking and telephony aggressively exploit switching costs. They lure customers with attractive introductory offers and then lock them in with higher rates, new fees, and fewer perks so that switching to a new firm would be very expensive. See Fornell (1992) and Klemperer (1995) for studies in this area. It is only recently that learning through repeated transactions has been integrated into multi-period models. Petruzzi and Dada, 2001 and Petruzzi and Dada, 2002 and Cachon and Porteus (1999) are among the studies in this area which regard learning as a process of updating information on demand function. Petruzzi and Dada (2001) analyze inventory and pricing decisions in a two-period retail setting when an opportunity to refine information about uncertain demand is available. Petruzzi and Dada (2002) extend the problem by considering multiple periods. The authors use dynamic programming techniques to solve their optimization problems. Another stream of research embeds learning into the demand function. For example, Vilcassim et al. (1999) use this approach in their analysis of price and advertising competition among firms in a given product market. Our study introduces a new methodology by integrating game theory with dynamic-system concepts. This allows us to understand the behavior (and impact) of horizontal and vertical firms during the multi-period decision-making process under the learning effect. This article answers the following questions: (i) How do the manufacturers make their pricing (or investment) decisions over time? (ii) How are the price and service levels in the second period affected by those in the first period? (iii) How does the whole supply chain behave over time? What indication(s) is there to learn about firms' interaction and system's temporal (inter-temporal) behaviors? In Section 2 we provide a brief review of the relevant literature. Section 3 presents notations and models for learning demands. Analysis of the model using game theory and dynamic-system concepts is presented in 4 and 5, respectively. Numerical examples are given in Section 6. Comparison of results from our model and a myopic model is presented in Section 7. All proofs are deferred to the appendix for the clarity of exposition. The appendix also contains the table for the possible range of parameter values. 2. Literature review It is only recently that learning through repeated transactions has been integrated into multi-period models. There are two streams of research on learning in the literature. Petruzzi and Dada, 2001 and Petruzzi and Dada, 2002 and Cachon and Porteus (1999) are among the studies in the first group which regard learning as a process of updating the demand function. For instance, Petruzzi and Dada (2001) analyzed inventory and pricing decisions in a two-period retail setting when an opportunity to refine information about uncertain demand is available. Specifically, they determined the optimal stocking and pricing policies over time when a given market parameter of the demand process, though fixed, is initially unknown. Petruzzi and Dada (2002) extended the problem by considering multiple periods. The second stream of research embeds learning into the demand function. For example, Vilcassim et al. (1999) used this approach in their analysis of price and advertising competition among firms in a given product market. Firm (or brand) level demand functions account for the contemporaneous and carry-over effects of these marketing activities, and also allow for the effects of competitors' actions. This approach enables them to quantify both the direction and magnitude of competitive reactions, and also to identify the form of market conduct that generates a specific pattern of interaction. Our research follows this approach of learning to study the repeated transactions problem. This paper is related to the literature of multi-period dynamic competition. In the marketing literature demand is modeled as a diffusion of acceptance with adoption (sales) rate and focuses on consumer adoption process of a new product. The research on diffusion models originated with the Bass (1969) model, where the main focus was short-run profit maximization. Robinson and Lakhani (1975) were the first to incorporate the variable of price into the Bass model. They analyzed the Dynamic Pricing strategy with demand and cost varying with past sales. Dockner (1985) generalized the Robinson–Lakhani model to a duopoly and applied a game-theoretic approach to find a Nash Equilibrium on the decision of product price. However, this group of literature focuses only on price as the main decision variable, i.e., no service level decision. Neither does it consider the role of retailer in the supply chain during dynamic competition. In the recent work, the cost function has been introduced on the production side; hence there are learning effects on both demand and cost. Most applications deal with durable goods where each adopter represents one unit of sales. Only some of these works have included repeated purchases in their models. See Jeuland and Dolan (1982) and Mahajan et al. (1983). Tsay and Agrawal (2000) study a supply chain with two retailers competing on price and service for customers. Their work completely ignores the manufacturers and develops insights for retailers profit and demand. Vilcassim et al. (1999) study dynamic price and advertising competition among firms. Again, vertical interactions are ignored in their studies. Thus, most of the recent works fail to consider an integrated supply chain with both horizontal and vertical interactions. We study the supply chain as a whole with two competing manufacturers, one retailer and end customers. Moreover, meaningful insights are derived for the manufacturers and retailer from horizontal as well as vertical interactions. Our research integrates price, service and investment decisions in a multi-period model. Both inter-temporal as well as intra-temporal factors are incorporated into decision making. There is a parallel stream of research in economics and marketing where demand is derived from aggregated scanner data from retailers. Both price and non-price variables are included in the model. Our model follows this approach which is common in microeconomics (see Tirole, 2000 and Shy, 2000). In particular, Hotelling (1929) was the first to introduce a formal model of product differentiation through price and location. Gabszewicz and Thisse (1979) and Cohen and Whang (1997) developed models where customers' preference for products can be strictly ordered (e.g., higher quality leads to better product preference). Other studies such as Chintagunta (1993) examined the sensitivity of equilibrium profits in an advertising game in a duopolistic market. Chintagunta and Rao, (1996) considered pricing strategies in a dynamic duopoly. Fruchter and Kalish (1997) investigated dynamic competition through advertisement in a duopoly market.

Both game theory and dynamic-system concepts are used to characterize our model of learning from repeated transactions. We assume that firms use a moving two-period profit-maximizing strategy. Information on the previous period's price and service levels as well as manufacturers' investment to expand market bases can influence market size of each product in the current period. Concepts from dynamic systems along with numerical studies on a few interesting cases help deliver several important managerial insights. The main results of our study are as follows. First, when consumers are sensitive to the market investment, it is always beneficial for the manufacturers to invest some money for market expansion in this case. Second, when demand is more sensitive to the last-period service than the last-period price in the learning process, the firm with service cost advantage will be the winner over time. Third, when demand is only sensitive to price in its learning process, the company with any type of cost advantage will gain more profit and capture a larger market base than its competitor. The retailer will sell both products at the same retail price but the firm with cost advantage will be able to support more service to its customers. Fourth, if both manufacturers have the same cost structure, the two manufacturers will converge to the same market size and sell their products at the same price, while providing equal level of service to consumers. This happens even though the two products may start with different market sizes initially. Fifth, if demand is equally sensitive to both price and service level, the manufacturer with service cost advantage may earn less profit and capture a smaller market base in the beginning. However, it will finally gain more profit and capture a larger market base than its competitor with a smaller production cost. Finally, for learning demand, myopic suppliers are not capable of coping with learning consumers. Their market sizes shrink and they earn less profit over time. The primary objective of this research is to gain meaningful insights on the behavior of the manufacturer and retailer. The results reflect our simplified assumptions. We have considered a “two-period learning model” for our study. One avenue for future work would be to extend the model to more than two-periods, finite or infinite horizon. Also, we estimated parameter values from the data for the personal care product industry. It would be interesting to estimate values of the parameters from some other industries and study how results vary across industries. We have used a linear demand function in our model because of its tractability in providing analytical results. Yet we can expect some non-linearity in the demand function in many real problems. It would be interesting to see if results we derived in our work are sensitive to the demand function. We assumed an insignificant switching cost in our model. Most businesses incur switching cost of some kind. Our model could also be extended to study multi-period competition under switching costs. We realize that our assumption on constant unit production cost over time may not be realistic. Other alternatives such as economy-of-scale production cost or decreasing return-to-scale production cost can be explored in the future. These assumptions will affect the pricing behavior of both products over time. In our case, since unit production cost is constant, a firm can increase service level and keep charging a higher price without worrying much about production cost. Thus, retail price can keep increasing as long as service advantages can make up the price increase. Other assumptions on production cost are likely to yield different results.