Stochastic programming approaches for decision-dependent uncertainty and gradual uncertainty resolution

This dissertation focuses on the multistage stochastic programing approaches for decision-dependent uncertainty and gradual uncertainty resolution. The decisions affect the time at which the uncertainty resolves, and the uncertainty resolves gradually in several stages. Chapter 1 presents literature reviews on synthesis of process networks, oil and gas field development, scenario generation methodologies, and briefly introduces stochastic programming. Chapter 2 presents a multistage stochastic programming model for the synthesis of process networks with decision-dependent uncertainties in yields that resolve gradually based on the investment and operating decision. Since the full space cannot be optimized in a reasonable time frame, a Lagrangean duality-based branch and bound algorithm has been proposed for optimizing the model. Chapter 3 presents the planning of offshore oil or gas field infrastructure under uncertainty. Uncertainties in the initial maximum oil or gas flowrate, recoverable oil or gas volume, and water breakthrough time of the reservoir are represented by discrete distributions, and they are gradually resolved as a function of design and operating decisions. To take advantage of the decomposable structure, duality-based branch and bound is implemented in AIMMS. Chapter 4 provides a generic non-convex MINLP model for planning problems under consideration. To improve the solution time and gap presented in chapter 3, a solution strategy is proposed that combines global optimization and outer-approximation. The improved solution algorithm has been used for optimizing synthesis of process networks with concave expansion cost functions and oil field planning problems. Chapter 5 introduces an algorithm for generating scenario trees for multistage stochastic programs under consideration. The proposed algorithm successively optimizes a nonlinear model that combines the moment matching methods, Bayesian reasoning, and revelation distribution. The objective of the nonlinear model is to minimize the skewness and kurtosis distances between the prior and posterior distributions. The solution of these nonlinear models leads to resolution profiles that are eventually used for generating scenario trees. Chapter 6 deals with improving the dual bound during the solution of a stochastic mixed-integer linear programming model using dual decomposition. It proposes extracting relevant sensitivity information from the branch and bound tree of every scenario subproblem, and uses that information to improve the dual bound. Two numerical examples have been presented to show the efficiency of the method, and the results have been compared with the conventional subgradient method. Chapter 7 summarizes the major findings of the dissertation and suggests future work on the subject.