A mixed integer nonlinear programming model and heuristic solutions for location, inventory and pricing decisions in a closed loop supply chain

•Facility location, inventory and pricing decisions in a closed loop supply chain.•Mixed integer nonlinear programming models.•Effective heuristics for the solution of the model.•The heuristics give less than 5% error from an upper bound.

We analyze a network design problem for a closed-loop supply chain that integrates the collection of the used products with the distribution of the new products. We present a mixed integer nonlinear facility location-inventory-pricing model to decide on the optimal locations of the facilities, inventory amounts, prices for new products and incentive values for the collection of right amount of used products in order to maximize the total supply chain profit. We develop heuristics for the solution of this model and analyze the effectiveness of these heuristics and the effects of the parameters on this system through numerical experiments.