Risk Measures in a Multi-stage Stochastic Supply Chain Approach

This paper considers the optimal design and planning problem of a closed-loop supply chain (CLSC) where profit maximization is pursued while considering: adjustments in the network structure during the planning horizon providing flexibility to the network as well as uncertainty in supply and customer demands. A multi-stage stochastic framework is developed where the effects of the uncertainty are represented by means of discrete scenarios. With the objective of achieving more robust solutions, besides the expected profit, three other risk adverse objective functions are also considered: two based on the mean absolute deviation and another centered on the conditional value at risk (CVaR) concept. In contrast to other approaches, in this work the definition of CVaR is applied to both revenues and costs. The proposed framework is evaluated by means of several cases. The advantages of using risk adverse performance measures are explored. Thus, the characteristics of the solutions obtained with the stochastic approach considering the variability of the solutions are compared with the features of the solution obtained considering a risk neutral performance measure. Finally, a sensitivity study of the parameters associated with the objective function centered on the conditional value at risk concept is conducted.