In supply chain optimization multiple objectives are considered simultaneously, for example to increase resilience and reduce costs. In this paper we discuss the corresponding bicriteria problems to find a good balance between these two objectives. We give a general model for supply chain resilience that integrates strategic decisions with the operational level. This modular model allows the flexible combination of various constraints, objectives and different types of uncertainties. We treat uncertainties with a scenario-based approach. The resulting models have continuous and discrete decision variables. The computation of the Pareto frontier for these large-scale bicriteria mixed-integer problems creates a computational challenge. We illustrate and use the novel Adaptive Patch Approximation algorithm to efficiently compute approximations of the Pareto frontier. After presenting the theoretical advantages of the algorithm we compute the Pareto frontier of several supply chain problems. Our analysis of the different shapes of Pareto frontiers illustrates the characteristics of different types of bicriteria problems as well as the relevant impact on decision makers.
Preprint, Fraunhofer ITWM Institute for Industrial Mathematics, Kaiserslautern, Germany, 9/2020