A coordinated location-inventory problem in closed-loop supply chain

• We solve a coordinated inventory location problem in a closed loop supply chain.
• A conic integer programing formulation is provided.
• An outer approximation based solution algorithm is provided.
• Coordination leads to slight increase in long run average costs.
• Outer approximation is efficient for retailer demand with higher coefficient of variations.

This paper considers a coordinated location-inventory model under uncertain demands for a closed loop supply chain comprising of one plant, forward and reverse distribution centers, and retailers. The inventory of new and returned products is managed at forward and reverse distribution centers respectively through a periodic review policy. The proposed model determines the location of forward and reverse distribution centers and the associated capacities, the review intervals of the inventory policy at distribution centers, and the assignments of retailers to the distribution centers. We model six different coordination strategies. All the models are formulated as nonlinear integer programs with chance constraints and transformed to conic quadratic mixed-integer programs that can be efficiently solved by CPLEX. An outer approximation based solution algorithm is developed to solve the conic quadratic mixed-integer program. The benefit of different types of coordination strategies is shown through extensive computational testing.