Optimal supply chain design and operations under multi-scale uncertainties: Nested stochastic robust optimization modeling framework and solution algorithm

Although strategic and operational uncertainties differ in their significance of impact, a “one-size-fits-all” approach has been typically used to tackle all types of uncertainty in the optimal design and operations of supply chains. In this work, we propose a stochastic robust optimization model that handles multi-scale uncertainties in a holistic framework, aiming to optimize the expected economic performance while ensuring the robustness of operations. Stochastic programming and robust optimization approaches are integrated in a nested manner to reflect the decision maker's different levels of conservativeness toward strategic and operational uncertainties. The resulting multi-level mixed-integer linear programming model is solved by a decomposition-based column-and-constraint generation algorithm. To illustrate the application, a county-level case study on optimal design and operations of a spatially-explicit biofuel supply chain in Illinois is presented, which demonstrates the advantages and flexibility of the proposed modeling framework and efficiency of the solution algorithm.