This paper considers the closed-loop supply chain design problem by examining financial criteria and uncertainty in the parameters. A robust multiobjective optimization methodology is proposed by considering financial measures such as maximizing the net present value (NPV) and minimizing the financial risk (FR). The proposed methodology integrates various multiobjective optimization elements based on epsilon constraints and robustness measurements through the FePIA (named after the four steps of the procedure: Feature–Perturbation–Impact–Analysis) methodology. Similarly, an analysis of the parameter variability using scenarios was considered. The proposed method's efficiency was tested with real information from a multinational company operating in Colombia. The results show the effectiveness of the methodology in addressing real problems associated with supply chain design.

The product-mix planning and the lot size decisions are some of the most fundamental research themes for the operations research community. The fact that markets have become more unpredictable has increaed the importance of these issues, rapidly. Currently, directors need to work with product-mix planning and lot size decision models by introducing stochastic variables related to the demands, lead times, etc. However, some real mathematical models involving stochastic variables are not capable of obtaining good solutions within short commuting times. Several heuristics and metaheuristics have been developed to deal with lot decisions problems, in order to obtain high quality results within short commuting times. Nevertheless, the search for an efficient model by considering product mix and deal size with stochastic demand is a prominent research area. This paper aims to develop a general model for the product-mix, and lot size decision within a stochastic demand environment, by introducing the Economic Value Added (EVA) as the objective function of a product portfolio selection. The proposed stochastic model has been solved by using a Sample Average Approximation (SAA) scheme. The proposed model obtains high quality results within acceptable computing times.