Said Salim Rahal – HEC Montréal, Canada
Decision rule methods offer a rich and flexible framework for solving these classes of problems. Recent literature has shown the promise of decision rules in which uncertainty-dependent decisions are represented as functions, whose parameters are decision variables to be optimized, of the underlying uncertain parameters. We first investigate hybrid strategies using linear and piecewise linear decision rules and we empirically illustrate that it is more favorable to have higher uncertainty refinement, and equivalently better approximation quality of decisions, at the start of the decision-making process. We also demonstrate a case where, unexpectedly, a linear decision rule is superior to a more complex piecewise-linear decision rule within a simulator. This bolsters the need to assess the quality of decision rule in a simulator to obtain an impartial assessment of its solution quality. Second, we develop a systematic approach to devise a linear decision rule for unit-specific event-based continuous-time formulation via steel-making with a continuous casting problem. We illustrate the solution quality of reactive, proactive, and hybrid scheduling strategies and we emphasize the added value of the latter strategy as an attractive trade-off between solution conservatism and excessive scheduling modifications.