Green closed-loop supply chain network design: a novel bi-objective chance-constraint approach

In this paper, a novel chance-constrained programming model has been proposed for handling uncertainties in green closed loop supply chain network design. In addition to locating the facilities and establishing a flow between them, the model also determines the transportation mode between facilities. The objective functions are applied to minimize the expected value and variance of the total cost CO2 released is also controlled by providing a novel chance-constraint including a stochastic upper bound of emission capacity. To solve the mathematical model using the General Algebraic Modeling System (GAMS) software, four multi-objective decision-making (MODM) methods were applied. The proposed methodology was subjected to various numerical experiments. The solutions provided by different methods were compared in terms of the expected value of cost, variance of cost, and CPU time using Pareto-based analysis and optimality-based analysis. In Pareto-based analysis, a set of preferable solutions were presented using the Pareto front; then optimality-based optimization was chosen as the best method by using a Simple Additive Weighting (SAW) method. Experimental experiments and sensitivity analysis demonstrated that the performance of the goal attainment method was 13% and 24% better that of global criteria and goal programming methods, respectively