Modeling uncertainty and analyzing bottleneck characteristics in multiperiod design optimization

Abstract

In this paper we address modeling, analysis and computational synthesis issues in multipenod design problems. We present a novel minimax approach for the formulation of the objective function, to address uncertainty in the duration of individual periods. For the analysis of these problems, we offer a formal definition of bottleneck periods and derive properties that contribute to the design process. At the level of synthesis and based on the bottleneck properties, we propose a decomposition strategy for general MINLP multiperiod problems where the MILP part does not scale with the total number of periods. As shown through the derived properties and a set of example problems, the minimax objective function yields designs with enhanced robustness properties compared to the standard multiperiod objective. The bottleneck period concepts provide an analysis framework that yields a better under—standing of multiperiod problems and provides guidelines for an improved design procedure. Finally, as predicted by the theoretical derivation and illustrated through examples, the proposed bottleneck-period based OA/BP method is computationally superior to both Outer-Approximation (OA) and Generalized Benders Decomposition (GBD).