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. V C 2016 American Institute of Chemical Engineers AIChE J, 00: 000-000, 2016 Keywords: multi-scale uncertainties, stochastic robust optimization model, column-and-constraint generation algorithm, supply chain optimization
IntroductionWhen hedging against uncertainties in the optimal design and operations of supply chains, only one uniform approach has been typically used to tackle all types of uncertainty. [1][2][3] This "one-size-fits-all" approach might be stochastic programming, robust optimization, fuzzy programming, or any other methods for optimization under uncertainty. 4 However, uncertainties at strategic and operational scales may differ in their significance of impact, 5 as shown in Figure 1. Strategic uncertainties have impacts over a significant duration of the project's lifetime. Once realized, strategic uncertainties would remain unchanged for a considerable period of time. Examples of strategic uncertainties include climate and weather, technology evolution, incentives and policies, and network stability. In contrast, operational uncertainties change more frequently and often lead to immediate adjustment in operational decisions. Examples of operational uncertainties include variations in raw material quality and composition, supply and demand, cost and price, as well as in lead times of production, transportation, and material handling activities. Moreover, the realizations of operational uncertainties may be associated with that of strategic uncertainties. For example, the yields of agricultural products are expected to be dependent on the climate and weather. In addition, a decision maker may hold different levels of conservativeness toward strategic and operational uncertainties. For instance, one might be less conservative toward strategic uncertainties and willing to explore the potentials of all possibilities, but be more conservative toward operational uncertainties considering factors such as demand fulfill r...