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.

Energy crisis in recent decades has demonstrated strong interdependence between national security and energy security. We are also witness of sever conflicts in oil-rich zones such as Middle-East and West of Suez. This study is the first attempt to provide a flexible multi-objective mathematical model which not only mitigates catastrophic risks by filtering and taking plausible oil-supply disruption scenarios into account, but also reduces oil-supply disruption probability by considering and optimizing political, economic and financial dimensions of oil procurement. Mentioned model determines a resilient portfolio of oil suppliers under each scenario and decides which ports or pipelines must be prepared for receiving oil. Furthermore, the proposed model in the second phase enhances oil-availability in crisis time by storing strategic oil stocks in appropriate geographic points. Also regarding to complexity of the second phase model, a meta-heuristic algorithm has been provided to solve the mentioned model. Finally validity of proposed model is checked by solving it for Greece case problem; sensitivity analysis shows that provided model significantly mitigates catastrophic risks threating energy security by balancing political affairs and reinforcing infrastructural facilities with the least possible cost.

This paper presents a strategic multi segment, multi period and multi-product supply chain management to meet reliable networks for handling disruptions strike. We present a mixed-integer programming model whose objective is to minimize the expected cost composed of probability and cost of occurrence in each scenario. The proposed model of this paper considers time value of money for each operation and transportation cost. We attempt to minimize expected costs by considering the levels of inventory, back-ordering, the available machine capacity and labor levels for each source, transportation capacity at each transshipment node and available warehouse space at each destination. The problem is generalized by taking into account backup supplier with reserved capacity and backup transshipment node that, which satisfies demands at higher price without disruption facility. We use a priority-based genetic algorithms encoding to solve the proposed problem under multi period and multi product conditions. The performance of the proposed model is examined using some instances.