On the global and efficient solution of stochastic batch plant design problems

The presence of uncertainty in product demands of batch plant design formulations with fixed structure and continuous equipment sizes transforms them into large-scale nonconvex nonlinear programs. This paper describes recent developments towards the efficient solution of such mathematical models. Two global optimization algorthms, a specialized GOP algorithm and a reduced space branch and bound algorithm, are presented and applied to this class of batch plant design models. It is shown that, by taking advantage of the special structure of the resulting mathematical formulations, encouraging computational results can be obtained from both algorithms for problem sizes that would otherwise be practically unsolvable with conventional global optimization techniques. An efficient, specialized Gaussian quadrature technique is also described for the case of product demands following normal probability distribution functions with which reduced model size and improved estimation of the expected profit integral are achieved. These developments are tested on example problems from the literature covering single batch plant configuration with various scheduling policies and flexible configurations with alternative production sequences.