Mathematical programs with equilibrium constraints (MPECs) in process systems engineering

Mathematical programming methods have proven extremely valuable for the design and operation of chemical processes. This has been made possible by more flexible modeling constructs, increased computing power, and a better fundamental understanding of solution algorithms and problem formulations. Related optimization models have a number of options to represent discrete decisions. Many of these situations naturally lend themselves to equilibrium constraints. This thesis studies Mathematical Programs with Equilibrium Constraints in Process Systems Engineering.;MPEC properties, including concepts of stationarity and linear independence that are essential for well-defined NLP formulations are discussed. Nonlinear programming based solution strategies for MPECs are then reviewed.;Nonlinear programming based solution strategies for MPECs are numerically compared. A systematic strategy for the formulation of well-posed complementarity constraints in proposed. This strategy is used to make complementarity formulations for commonly used nonsmooth functions and applied to a number of widely-used examples in process engineering. This combination of well-posed formulations and MPCC solutions strategies is demonstrated on two large-scale case studies with as many as 8000 discrete decisions.;An MPEC formulation for the optimization of a class of hybrid dynamic models, where the differential states remain continuous over time is proposed. This class of hybrid system include differential inclusions of the Filippov type. Here, particular care is required in the formulation in order to preserve smoothness properties of the dynamic system. Results on three case studies, including process control examples, illustrate the effectiveness and accuracy of the proposed MPEC optimization methodology for a class of hybrid dynamic systems.;A mathematical program with equilibrium constraints (MPEC) approach is developed for efficient operation of gas pipelines. The resulting model handles time dependent operations in order to determine minimum energy consumption and operating cost over a given time horizon. The MPEC structure also allows flow reversals, flow transitions and other nonsmooth elements to be incorporated within the approach. Applied to industrial gas pipelines, this approach can also deal with customer demand satisfaction in the presence of compressor outages and minimize recovery time for systems that are unable to meet customer demands at all times. A large-scale oxygen pipeline case study is considered to demonstrate this approach and complex energy pricing schemes are also applied to this problem. These schemes include time of day electricity pricing, along with extensions to real time pricing and day ahead pricing. Compared to flat rate and minimum energy optimizations, respectively, we observe operating cost savings up to 5.13% for time of day electricity pricing and up to 12.85% for real time pricing.