Evaluation and optimization of process systems with discrete and continuous uncertainties

This thesis addresses the problem of developing a quantitative measure for the flexibility of a design to withstand uncertainties in the continuous parameters and discrete states. The metric is denoted as the expected stochastic flexibility, E(SF). Given a joint probability distribution for the parameters and probabilities of failure for the discrete states, the E(SF) predicts the probability of feasible operation of a design. The basic element of the E(SF) is the SF, a statistical metric that measures the probability of feasible operation for the case when the system only contains continuous uncertainties.; To determine the SF for the special case of linear models, a novel inequality reduction scheme is proposed in which numeric integration through Gaussian quadrature is performed over the feasible region in the space of the continuous uncertainties. For the determination of the E(SF), a bounding scheme is proposed to avoid the evaluation of the SF for each state of the discrete uncertainties. For problems with nonlinear constraints a sequence of optimization problems that mimics the inequality reduction scheme is used to evaluate the SF. This sequence of optimization problems can be formulated as a single nonlinear programming model which can easily be extended to design optimization problems for maximizing the SF subject to a cost constraint. For large models a solution method based on Generalized Benders Decomposition is proposed to effectively solve these problems. The use of alternative metrics is also described; specifically the use of a quadratic penalty (i.e. the Taguchi approach). The similarities and differences between the SF and the metric based on this approach are discussed.; The special case of multiproduct batch plants with uncertain demands and equipment availability is also considered. By taking advantage of the special structure of the model, efficient evaluation and optimization methods for both the SF and E(SF) are presented for the design of these plants.; Extensive numerical results are presented throughout the thesis. The results show not only that the proposed methods are computationally efficient, but that they provide useful information regarding tradeoffs between cost and flexibility. Furthermore, the proposed approach allows the integration of flexibility and reliability under a common metric.