| This thesis explores the application of mixed integer optimization techniques to planning and scheduling problems of significant importance to the chemical process industries. The goal is to develop novel models for these problems, as well as effective algorithms for their solution.;The problem of selecting processes and capacity expansion policies for a chemical complex is addressed first. The objective is to maximize the net present value given predictions for prices and demands during a long range time horizon. This planning problem is modelled as a multiperiod mixed integer linear program (MILP), and a computational study is carried out to evaluate the performance of several solution strategies. Based on a variable disaggregation technique that exploits the presence of lot sizing substructures, an alternative formulation is also given. This includes more variables and constraints but exhibits a tighter linear programming relaxation, and it requires an order of magnitude less computational time than the original one.;We then propose a strategy for reformulating a large class of multiperiod MILP models for planning and scheduling. The strategy is illustrated with an MILP model that can handle a wide variety of scheduling problems in multiproduct/multipurpose batch chemical plants.;Subsequently, we consider the problem of multiproduct scheduling on continuous parallel production lines. A large-scale mixed integer nonlinear program (MINLP) is developed and solved by using the generalized Benders decomposition. The proposed technique is applied to a real world problem for a polymer production plant. The corresponding MINLP, which contains 780 binary variables, 23,000 continuous variables and 3,200 constraints, predicts annual savings of several million dollars.;Last, we address theoretical and computational issues related to generalized Benders decomposition. First, it is proved that an MINLP formulation with zero nonlinear programming relaxation gap requires only one Benders cut in order to converge. Second, by exploiting the Kuhn-Tucker optimality conditions for nonlinear problems, a methodology is developed which avoids the explicit solution of large nonlinear subproblems. Finally, a theoretical analysis shows that the application of generalized Benders decomposition to nonconvex problems does not always lead to the global optimum for these problems. |
