A New Robust Scenario Approach to Supply Chain Optimization under Bounded Uncertainty
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Supply Chain Optimization (SCO) problem under uncertainty can be modeled as two-stage optimization problem where first-stage decisions are associated with design and development of facilities and second-stage decisions are associated with operation of the supply chain network. Recently, a robust scenario approach combing the traditional scenario or robust approach has been developed to better address uncertainties in SCO problems, and it can ensure solution feasibility and better expected objective value. But this approach can only address uncertainties bounded with the infinity-norm. This thesis proposes a modified robust scenario approach, which can be used to address uncertainty region bounded with the p-norm in SCO. In this case, after the normalization of the uncertainty region, the smallest box uncertainty region, that covers the normalized uncertainty region, can be partitioned into a number of box uncertainty subregions. Following some screening criteria, two subsets of the subregions that over-estimates and under-estimates the original uncertainty region can be selected. When the number of scenarios increases, the optimal objective values of the two robust scenario formulations converge to a constant, which is a good estimate of the true optimal value. This new robust scenario approach is then extended for any bounded uncertainty regions, in the context of robust optimization. In many industrial problem, the historical realizations of uncertain parameters are known. This thesis gives a preliminary discussion on a data driven robust scenario approach, where the available data are normalized and a reference box that covers the data with a certain confidence is constructed. Then, the reference box is partitioned into box-shaped uncertainty subregions. The benefits of the proposed robust scenario approach are demonstrated through some simple examples as well as an industrial SCO problem. The approach requires the solution of large-scale optimization problems when the number of scenarios is large, and these large-scale problems have a decomposable structure that can be exploited for efficient solution via decomposition-based optimization. A computational study demonstrates that, when the large-scale optimization problem is a second-order cone programming problem, generalized Benders decomposition is much faster than a state-of-the-art optimization solver.