Designing Closed-Loop Supply Chains with Nonlinear Dimensioning Factors Using Ant Colony Optimization

Closed-loop supply chain (CLSC) design implies themodelling of the forward and the reverse flows of products in an integrated way. This paper introduces nonlinear dimensioning factors in the design of CLSC and uses ant colony optimization to optimize the design of the supply chain. The proposed algorithm is called SCAnt-NLDesign. The modelled nonlinear dimensioning factors are: cost variations in transportation distances between facilities (tapering principle), scale economies related to transported quantities, and scale economies regarding the facilities' capacity. Results show that the proposed SCAnt-NLDesign algorithm reduced the total cost in 44%, when compared to a linear formulation of a CLSC. Note also that a mixed integer linear programming implementation of the nonlinear CLSC was not able to get closed to the optimal solution, given worse results than the linear CLSC.