A Duality-Based Robust Optimization Framework for Sustainable Manufacturing Decision Problems
Keywords:
Robust optimization, lagrangian duality, sustainable manufacturing, budgeted uncertainty, robust counterpart, production planning.Abstract
Sustainable manufacturing necessitates production planning decisions that are capable of reflecting the interplay among economic efficiency, energy use, environmental emissions, and uncertainty in operational parameters. In this paper, present a novel dual-based robust optimization approach for solving sustainable manufacturing decision problems under budgeted uncertainty. Study develops a mathematical production planning problem model considering cost, energy use, and environmental emissions in the objective function as well as demand, resource capacity, energy, and environmental emission constraints. Budgeted uncertainty is assumed in the objective function coefficients, the resource consumption rates, energy usage, and emission coefficients. Since the corresponding min-max problem with respect to the uncertain parameters is semi-infinite, reformulate every worst-case uncertainty term as a deterministic finite-dimensional problem using linear programming duality. Study defines independent uncertainty budgets in order to provide different levels of protection against different uncertainty sources. Through theoretical analysis, prove the convexity, robust feasibility, monotonicity with respect to the uncertainty budgets, relations between nominal and robust solutions, and global optimality under certain constraint qualifications. Numerical experiments on a multiperiod problem model considering production activation, machine capacities, energy limitations, and environmental emission constraints verify the effectiveness of the developed framework. The numerical results show the equivalence of the primal and dual formulations of the problem as well as the tradeoff between the nominal performance and protection against unfavorable parameter deviations.
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