Novel formulation and decomposition-based optimization for strategic supply chain management under uncertainty

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McLean, Kyle
Optimization , Supply chain management
This thesis proposes a novel synergy of the classical scenario and robust approaches used for strategic supply chain optimization under uncertainty. Two novel formulations, namely the naïve robust scenario formulation and the affinely adjustable robust scenario formulation, are developed, which can be reformulated into tractable deterministic optimization problems if the uncertainty is bounded by the infinity-norm. The two formulations are applied to a classical farm planning problem and an energy and bioproduct supply chain problem. The case study results demonstrate that, compared to the scenario formulation, the proposed formulations can achieve the optimal expected economic performance with smaller number of scenarios, and they can correctly indicate the feasibility of a problem. The results also show that the affinely adjustable robust scenario formulation can better address uncertainties than the naïve robust scenario formulation. Next, a strategic optimization problem for an industrial chemical supply chain from DuPont was studied. The supply chain involves one materials warehouse, five manufacturing plants, five regional product warehouses and five market locations. Each manufacturing plant produces up to 23 grades of final products from 55 grades of primary raw materials. The goal of the strategic optimization is to determine the capacities of the five plants to maximize the total profits of the supply chain system while satisfying uncertain customer demands at the different market locations. A mathematical model is developed to relate the material and product flows in the supply chain, based on which the classical scenario approach and the affinely adjustable robust scenario formulation were developed to address the uncertainty in the demands. The case study results show the advantages of the affinely robust scenario formulation over the scenario formulation. Using the affinely adjustable robust scenario formulation often results in problems with very large sizes, which cannot be solved by regular optimization solvers efficiently. In order to exploit the decomposable structure of the formulation, Dantzig-Wolfe decomposition is studied in the thesis. Two approaches to implement Dantzig-Wolfe decomposition are developed, and both approaches involve the solution of a sequence of linear programming (LP) and mixed-integer linear programming (MILP) subproblems. The computational study of the industrial chemical supply chain shows that a combination of the two Dantzig-Wolfe approaches can achieve an optimal or a near-optimal solution much more quickly than a state-of-the-art commercial LP/MILP solver, and the computational advantage increases with the increase of number of scenarios involved in the problem.
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