pricing and inventory for a supply chain with perishable and substitutable products

decentralization allows channel members to make their decisions, independently. in this decentralized channels, members may have different power to make its decisions. hence, decisions of each member may influence on the other members’ decisions. to model such situations, bi-level programming models are useful. in this study, a supply chain including one manufacturer and multiple competitive retailers are considered. the manufacturer produces several perishable and substitutable products. the problem is formulated as a multi-follower bi-level programming model. since bi-level models are often np-hard, simulated annealing algorithm is applied to solve the proposed model. the numerical results of sensitivity analysis indicate that in the larger markets, even increasing in the prices leads to increase the profit of members. also, when the consumers are price-sensitive, the manufacturer and the retailers must decrease their prices to attract the consumers and increase their profits, consequently.