flexible and robust optimization combination for reliable forward-reverse logistic network design using benders’ decomposition method

Over the past few years, understanding sustainability issues such as cost savings and pollution reduction in the industry has led to the design of closed-loop logistics networks with hybrid facilities also, the occurrence of sudden disturbances and the damages caused by them has developed the use of reliability approaches the present study has applied the strategy of reliable support facilities in the multi-product forward-reverse logistics network and has used stochastic programming to model the disorder to face the decision-maker ambiguity in the confidence levels, the constraints, and objectives of the problem, and in continuation, to ensure the optimality of the above classes, flexible-robust combination programming has been employed, presented in the form of a mixed-integer linear mathematical programming model then benders decomposition algorithm is proposed to solve the model, which with a subset of optimization cuts and appropriate convergence rate, improved optimal solutions are produced for optimal planning path.