Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties

Abstract

This dissertation addresses the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs). Since the reduced model is often still intractable, we discuss two special solution approaches. The first is a sequential scenario decomposition heuristic in which we sequentially solve endogenous MILP subproblems to determine the binary investment decisions, fix these decisions to satisfy the first-period and exogenous NACs, and then solve the resulting model to obtain a feasible solution. The second approach is Lagrangean decomposition. We present numerical results for a process network planning problem and an oilfield development planning problem. The results clearly demonstrate the efficiency of the special solution methods over solving the reduced model directly. To further generalize this work, we also propose a graph-theory algorithm for non-anticipativity constraint reduction in problems with arbitrary scenario sets. Finally, in a break from the rest of the thesis, we present the basics of stochastic programming for non-expert users.

Multistage Stochastic Programming Models for Pharmaceutical Clinical Trial Planning

“…At termination, all decisions are fixed in original MSSPs yielding a feasible solution. For the oilfield development planning problem [15], the SSD solution was within 0.2% of the optimum.…”

“…Although the algorithm required considerable time to converge, it reduced the memory requirements considerably. Apap and Grossmann [15] proposed a sequential scenario decomposition (SSD) approach for solving MSSPs with endogenous and exogenous uncertainties. The algorithm starts at the initial time period and selects one scenario from each exogenous scenario group.…”

Decision-dependent probabilities in stochastic programs with recourse

“…The application is the same as in Goel and Grossmann (2006). Apap and Grossmann (2017) discuss formulations and solution approaches for stochastic programs with Decision-Dependent Information Structure.…”

Recent Advances in Mathematical Programming Techniques for the Optimization of Process Systems under Uncertainty

“…As shown in Figure 5, we use a superstructure form of the alternative tree in order to capture all possible outcomes (Apap and Grossmann, 2015). A simplified, compact form of the updated model (Apap and Grossmann, 2015) is given in Eq. In other words, the set of scenarios in the exogenous scenario tree corresponds to a Cartesian product over the sets of realizations for the exogenous parameters (denoted by ), and, similarly, the set of scenarios in the endogenous scenario tree corresponds to a Cartesian product over the sets of realizations for the endogenous parameters (denoted by ).…”

“…In order to eliminate redundant NACs, a number of theoretical properties have been proposed by Goel and Grossmann (2006), Gupta and Grossmann (2011), and Apap and Grossmann (2015) based on the concepts of symmetry, adjacency, transitivity, and scenario grouping. In order to eliminate redundant NACs, a number of theoretical properties have been proposed by Goel and Grossmann (2006), Gupta and Grossmann (2011), and Apap and Grossmann (2015) based on the concepts of symmetry, adjacency, transitivity, and scenario grouping.…”