| The increasing competitiveness in the industry necessitates the development of optimization tools for chemical process planning. The problem of selecting processes and capacity expansion policies for a chemical complex can be formulated as a multiperiod, mixed-integer linear program (MILP). This MILP can then be reformulated by exploiting lot sizing substructures. While the reformulation produces a tight linear programming relaxation, it also introduces a large number of variables and constraints.; This dissertation focuses on the development of solution approaches for the planning problem, beginning with a polyhedral approach in which the reformulation variables are projected out, giving rise to a larger constraint system. The solution of the new system is found using a strong cutting plane method that solves the separation problem in polynomial time. In addition, the effects of time horizon discretization on the quality of the MILP solution and the behavior of the linear programming relaxation gap are studied and a number of heuristics are developed. A probabilistic analysis is provided to elucidate the computational trends.; The MILP formulation is an indirect approach to process planning. This dissertation also provides a direct solution approach, concave programming (CP), equivalent to the MILP. In solving the CP model, minimizing its nonconvex objective function poses the major obstacle. This obstacle is overcome by means of a branch-and-bound global optimization algorithm that exploits the concavity and separability of the objective function and the linearity of the constraint set. Computational results show that concave programming is an attractive, viable alternative to MILP for process planning.; For dealing with dynamic uncertainty in both internal and external process parameters, this dissertation also presents two approaches that are based on fuzzy programming and stochastic programming, respectively, for solving the process planning problem under uncertainty. |
