Analysis of strategies for substitutable and complementary products in a two-levels fuzzy supply chain system

In this paper, the pricing competition models have been studied between two substitutable and one complementary products in a two-echelon fuzzy supply chain system. Here, three manufacturers separately (one each) produce and sell their products through a common retailer in the cooperative and non-cooperative markets. The demand for each product depends linearly on the products’ prices. Here, manufacturing costs, base demands and price elasticity are characterized as fuzzy parameters. The closed-form expressions of optimal wholesale and retail pricing decisions have been derived for four different market situations under game theory to maximize the expected profit function of each participant of the supply chain. Sharing of profits under co-operation mechanism amongst the manufacturers and retailer in different proportions are presented numerically for the fuzzy model. As particular cases, the optimal pricing decisions have been derived for two substitutable products or two complementary products separately and the results of previous investigators are presented. In addition, the traditional deterministic version of the fuzzy problem is numerically solved. The results of fuzzy and crisp models are presented and compared. Finally, the problem is illustrated with some numerical data for four market situations, sensitivity analyses are performed and management decisions are explored. The products’ demands and supply chain profits are graphically presented for different price elasticity of the substitutable and complementary products.