Te growth of world population has fueled environmental, legal, and social concerns, making governments and companies attempt to mitigate the environmental and social implications stemming from supply chain operations. Te state-run Environmental Protection Agency has initially ofered fnancial incentives (subsidies) meant to encourage supply chain managers to use cleaner technologies in order to minimize pollution. In today’s competitive markets, using green technologies remains vital. In the present project, we have examined a class of closed-loop supply chain competitive facility location-routing problems. According to the framework of the competition, one of the players, called the Leader, opens its facilities frst. Te second player, called the Follower, makes its decision when Leader’s location is known. Afterwards, each customer chooses an open facility based on some preference huf rules before returning the benefts to one of the two companies. Te follower, under the infuence of the leader’s decisions, performs the best reaction in order to obtain the maximum capture of the market. So, a bilevel mixed-integer linear programming model is formulated. Te objective function at both levels includes market capture proft, fxed and operating costs, and fnancial incentives. A metaheuristic quantum binary particle swarm optimization (PSO) is developed via Benders decomposition algorithm to solve the proposed model. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. Te computational results indicate that the proposed method is capable of efciently solving the model
