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This paper considers the capacity determination in a closed-loop supply chain network when a queueing system is established in the reverse flow. Since the queueing system imposes costs on the model, the decision maker faces the challenge of determining the capacity of facilities in such a way that a compromise between the queueing costs and the fixed costs of opening new facilities could be obtained. We develop a De Novo programming approach to determine the capacity of recovery facilities in the reverse flow. To this aim, a mixed integer nonlinear programming (MINLP) model is integrated with the De Novo programming and the robust counterpart of this model is proposed to cope with the uncertainty of the parameters. To solve the model, an interactive fuzzy programming approach is combined with the hard worst case robust programming. Numerical results show the performance of the developed model in determining the capacity of facilities

A De Novo programming approach for a robust closed-loop supply chain network design under uncertainty: An M/M/1 queueing model