Effects of fuzzy data on decision making in a competitive supply chain

The essence of data plays a critical role in decision making in supply chain management (SCM). When data embedded in supply chains (SCs) are fuzzy, the associated equilibrium and performance measures also become fuzzy. This paper investigates the effects of fuzzy data on decision making in a two-echelon SC with a supplier and duopolistic retailers playing a Stackelberg strategic game in both intra- and inter-echelons. In contrast to existing approaches, this paper devises an analysis method to provide a likely interval of the fuzzy maximal profit with a known possibility level (degree of certainty) rather than a singleton (crisp value). The idea is based on the extension principle to reformulate the two-level optimization problem as a pair of parametric quadratic programs in order to calculate the lower and upper bounds of the leader’s fuzzy maximal profit at each possibility level of the obtained information. The analytic results indicate that the higher the degree of uncertainty, the smaller (larger) the lower (upper) bound of the maximum profit of each SC member. Moreover, the main results obtained from eight scenarios show that when the degree of demand diversity between the two retailers is significantly high, the Stackelberg leader is most likely to obtain lower profit and the marginal contribution of the primary demand to the total profit of the duopolistic retailers will exceed that of the powerful supplier’s maximum profit.