Applying a CVaR Measure for a Stochastic Competitive Closed-Loop Supply Chain Network under Disruption

This paper addresses a closed-loop supply chain network design problem, in which two different supply chains compete on retail prices by defining a price-dependent demand function. So, the model is formulated in a bi-level stochastic form to demonstrate the Stackelberg competition and associated uncertainties more precisely. Moreover, it is capable of considering random disruptions in the leader supply chain while incorporating the inventory, pricing, location and allocation decisions. Afterwards, having a contract with reliable suppliers is examined to resist the consequent results of disruption in the supply process. Additionally, the sharing strategy with new resilient distribution centers is used for tackling disruption risks at distribution centers. Furthermore, after integrating the proposed bi-level model into an integrated equivalent form by using the Karush–Kuhn–Tucker (KKT) transformation method, the conditional value at risk (CVaR) measure is used to handle the considered uncertainties. Finally, a real industrial case of a filter company is applied to obtain numerical results and the performance of the stochastic model is investigated by several test problems to arrive in helpful managerial insights.