A robust optimization approach in a multi-objective closed-loop supply chain model under imperfect quality production

The closed-loop supply chain model with an assumption of perfect produced items is used commonly in the literature. We consider the imperfect quality production to provide meaningful solutions to practical problems. In this novel model, we assume that the screening is not always perfect, and inspection errors are more likely to take place in practice. The model considers multiple periods, echelons, and uncertainties. Moreover, the proposed robust multi-objective mixed integer linear programming model considers the optimization of three objectives simultaneously. The first objective function is optimized to minimize the total cost of the supply chain. The second objective function seeks to minimize the environmental influence, and the third objective function is optimized to maximize the social benefits. The augmented weighted Tchebycheff method is used to aggregate the objective functions into one objective and produce the set of efficient solutions. Robust optimization, based on the extended Mulvey et al. (1995) approach, is used to obtain a set of solutions that are robust against the future fluctuation of parameters. Finally, numerical examples have been presented to test and analyze the tradeoff between solution robustness and model robustness.