Optimal Pricing and Retail Service Decisions in an Uncertain Supply Chain

In a two-stage supply chain composed of one manufacturer and one retailer, the pricing and retail service decisions are researched in an uncertain environment. The manufacturing cost, retail cost and market demand are all characterized as uncertain variables. In consideration of the different market power of the manufacturer and the retailer, three non-cooperative games are analyzed, and their optimal strategies are also obtained by the method of uncertainty theory. Finally, a numerical example is given to compare the optimal strategies in three non-cooperative game models. It shows that the manufacturer and the retailer make the largest expected profits in the Manufacturer-Stackelberg and Retailer-Stackelberg games, respectively, and the customers obtain the highest service level and lowest retail price in the Retailer-Stackelberg game. The literature mentioned above discussed the pricing and service decisions problem with deterministic demand and known operation costs. However, in real world, especially for some new electronic products, the relevant precise dates are difficult to obtain duce to lack of historical data. In this situation, the market base and operation cost can usually be predicted by some experts. Thus, fuzzy set theory proposed by Zadeh [12], is used to deal with the pricing decisions problem of the supply chain by some scholars [13-20]. Some researches [21-22] also studied the pricing and service decisions problem in a fuzzy environment, where the demand was a fuzzy liner function of the selling price and service level. When we use fuzzy set theory to solve the expert’s prediction, there may be some problems. For example, the market demand predicted by experts may be “about 100”. If we measure “about 100” using the fuzzy set theory, we may obtain the market demand is “about 100” with belief degree 1 by possibility measure, and is “not 100” with belief degree 1 as well. That is to say, “about 100” and “not 100” have the same belief degree in possibility measure. It seems that nobody can accept this conclusion. Hence, those imprecise quantities such as “about 100” cannot be quantified by possibility measure, and should not be considered as fuzzy variables. To deal with these problems, Liu [23-24] proposed an uncertainty theory. Later, Ding [25-26] applied the uncertainty theory to solve the inventory problems of the supply chain.