Mixed-integer nonlinear programming models and algorithms for enterprise-wide supply chain optimization under uncertainty

This thesis deals with the development of discrete-continuous optimization models and algorithms in order to address the enterprise-wide supply chain optimization under uncertainty for the process industries.;We next focus on integrating supply chain optimization with stochastic inventory under uncertainty. A non-convex MINLP models is developed for the integration of single-stage stochastic inventory and the supply chain network design that involves the selection of distribution centers. A tailored decomposition algorithm based on model properties and Lagrangean relaxation is also developed to deal with the computational challenge for large scale instances. We also extend this work to address the optimal design of multi-echelon process supply chains and the corresponding inventory systems under demand uncertainty. The multi-echelon stochastic inventory systems are modeled with the guaranteed service approach. The steady state supply chain design and operation decisions are integrated with the dynamic stochastic inventory control by using an MINLP model. Large scale instances are solved effectively with a spatial decomposition algorithm based on Lagrangean relaxation and piecewise linear approximations. As a further extension, we developed an MINLP model for the stochastic inventory management for tactical process planning under supply and demand uncertainty. A branch-and-refine algorithm based on successive piece-wise linear approximation is proposed for the global optimization of the problems with modest computational efforts.;A general computational framework is developed for global chemical supply chain planning under demand and freight cost uncertainty. The stochastic programming model formulation, the multi-cut L-shaped method and an optimization-based simulation method are discussed. Real world applications with up to 12,000 uncertain parameters are investigated, and the economic benefits of considering uncertainties are also reported.;Furthermore, we show that Dinkelbach's algorithm can be extended to solve linear fractional programming problems with discrete variables. A comprehensive comparison for solving mixed-integer linear fractional programming problems with Dinkelbach's algorithm and with commercial MINLP solvers and global optimizers is presented. Applications in the area of cyclic scheduling are considered through a reaction-separation network and a tissue paper mill with byproduct recycling.;A bi-criterion multi-period mixed-integer nonlinear programming (MINLP) model is proposed to address the optimal design and operation of process supply chains under economic and responsiveness criteria with the presence of demand uncertainty. A unique feature of the model is that it incorporates a quantitative measure of supply chain responsiveness, for a given network superstructure with single-stage stochastic inventory and production schedules. In order to handle large problem instances where the model becomes computationally expensive to solve, a hierarchical algorithm is proposed based on the decoupling of different decision-making levels. Applications on supply chains for polystyrene are considered. Next, we extend this work to address the design of process supply chains with multi-echelon stochastic inventory. We propose a novel measure of supply chain responsiveness that is based on the multi-echelon stochastic inventory theory and equivalent to the worst case response time under demand uncertainty. This measure is incorporated into a bi-criterion MINLP model, and examples on acetic acid supply chains are presented to illustrate the application of the proposed model, and to comprehensively compare the two measures of supply chain responsiveness.;The results in the main chapters show that in all cases the proposed algorithms lead to one or more orders of magnitude decrease in the solution time. The major findings of the thesis and suggestions for future work are summarized at the end of this thesis.