Essays in Simulation-based Stochastic Programming
Open AccessIn this dissertation, our objective is to develop the augmented probability simulation as an alternate method to solve particular stochastic programming problems with expectation functions. In the first essay, we propose evolutionary Markov chain Monte Carlo (MCMC) methods to solve one stage stochastic programming problems with constraints and consider certain MCMC methods in constrained domains. We illustrate the implementation of our approach for different settings, including simple deterministic problems with linear/quadratic objective functions, stochastic problems with uncertainty in the objective function or/and the constraint. Overall, the first essay serves as the introduction to the proposed approach, namely, augmented simulation methodology, in solving stochastic problems. In the second essay, we modify our simulation-based approach in order to solve particular two-stage stochastic problems with recourse and demonstrate its implementation using different illustrative examples. A particular setting of a linear production planning problem with uncertainty in constraints is solved by using the proposed algorithm. A version of the same problem with quadratic cost functions is also demonstrated. In the third essay, we adapt our approach to solve the two-stage stochastic recourse problems with decision dependent (endogenous) uncertainty and illustrate the implementation via a production planning problem. In so doing, we consider problems with continuous first stage decision variables under continuous source of uncertainty. A brief discussion of the potential extension of the proposed method to solve two-stage stochastic dynamic problems is also included. Overall, this dissertation aims to make a contribution to the literature by developing an implementation of this approach for certain two-stage problems with continuous uncertainties. Our limited experience suggests that the proposed approach may provide potential benefits in solving two stage problems and specifically problems with decision dependent uncertainty.
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