3 research outputs found
Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition
In this paper, we study chance constrained mixed integer program with
consideration of recourse decisions and their incurred cost, developed on a
finite discrete scenario set. Through studying a non-traditional bilinear mixed
integer formulation, we derive its linear counterparts and show that they could
be stronger than existing linear formulations. We also develop a variant of
Jensen's inequality that extends the one for stochastic program. To solve this
challenging problem, we present a variant of Benders decomposition method in
bilinear form, which actually provides an easy-to-use algorithm framework for
further improvements, along with a few enhancement strategies based on
structural properties or Jensen's inequality. Computational study shows that
the presented Benders decomposition method, jointly with appropriate
enhancement techniques, outperforms a commercial solver by an order of
magnitude on solving chance constrained program or detecting its infeasibility
Extensions of Multistage Stochastic Optimization with Applications in Energy and Healthcare
This dissertation focuses on extending solution methods in the area of stochastic optimization. Attention is focused to three specific problems in the field. First, a solution method for mixed integer programs subject to chance constraints is discussed. This class of problems serves as an effective modeling framework for a wide variety of applied problems. Unfortunately, chance constrained mixed integer programs tend to be very challenging to solve. Thus, the aim of this work is to address some of these challenges by exploiting the structure of the deterministic reformulation for the problem. Second, a stochastic program for integrating renewable energy sources into traditional energy systems is developed. As the global push for higher utilization of such green resources increases, such models will prove invaluable to energy system designers. Finally, a process for transforming clinical medical data into a model to assist decision making during the treatment planning phase for palliative chemotherapy is outlined. This work will likely provide decision support tools for oncologists. Moreover, given the new requirements for the usage electronic medical records, such techniques will have applicability to other treatment planning applications in the future
Extensions of Multistage Stochastic Optimization with Applications in Energy and Healthcare
This dissertation focuses on extending solution methods in the area of stochastic optimization. Attention is focused to three specific problems in the field. First, a solution method for mixed integer programs subject to chance constraints is discussed. This class of problems serves as an effective modeling framework for a wide variety of applied problems. Unfortunately, chance constrained mixed integer programs tend to be very challenging to solve. Thus, the aim of this work is to address some of these challenges by exploiting the structure of the deterministic reformulation for the problem. Second, a stochastic program for integrating renewable energy sources into traditional energy systems is developed. As the global push for higher utilization of such green resources increases, such models will prove invaluable to energy system designers. Finally, a process for transforming clinical medical data into a model to assist decision making during the treatment planning phase for palliative chemotherapy is outlined. This work will likely provide decision support tools for oncologists. Moreover, given the new requirements for the usage electronic medical records, such techniques will have applicability to other treatment planning applications in the future