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The closed-loop supply chain considers conceptually the possibility of reverse logistics with the use of recycling, remanufacturing and disposal centers. This study contributes for the first time a green closed-loop supply chain framework for the ventilators, which are highly important in the case of the COVID-19 pandemic. The proposed model simulates a case study of Iranian medical ventilator production. The proposed model includes environmental sustainability to limit the carbon emissions as a constraint. A novel stochastic optimization model with strategic and tactical decision making is presented for this closed-loop supply chain network design problem. To make the proposed ventilator logistics network design more realistic, most of the parameters are considered to be uncertain, along with the normal probability distribution. Finally, to show the managerial dimensions under the COVID-19 pandemic for our proposed model, some sensitivity analyses are performed. Results confirm the high impact of carbon emissions and demand variations on the optimal solution in the case of COVID-19.

The recent advances in manufacturing systems motivate several studies to focus on Economic Production Quantity (EPQ) problem. Althuogh there are several extentions to the EPQ, this paper provides a new extension by considering some of the real world parameters like: (a) shortages in the form of partial backordering, (b) inventory can deteriorate stochastically, (c) machine can break down stochastically, and (d) machine repair time may change stochastically based on the failure status of machine. As far as we know, there is no study treated all these suppositions in an EPQ framework. In addition to this development, two forms of uniformly-and exponentially-distributed repair times are formulated and necessary convexity conditions are discussed. Then, the corresponding optimality conditions are written that lead to finding the roots of two equations. Due to difficulty of achieving a closed-form solution, the solution is obtained numerically by means of Newton-Raphson method. Finally, some sensitivity analyses are provided to explain the models' applicability. The practicality and efficiency of the proposed method in this context lends weight to development of proposed EPQ with more complex elements and its application more broadly.

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