| This thesis studies algorithms for optimization and the applications of optimization theory and algorithms in supply chain management.Among the quasi-Newton methods for solving unconstrained optimization problems, the BFGS method is regarded as one of the most efficient methods. It possesses good global and superlinear convergence properties. Nevertheless, when the objective function is non-convex, the quasi-Newton method may not be globally convergent. As a remedy, Li-Fukushima (2001) proposed a modified BFGS (MBFGS) method by making some proper modification to the standard BFGS method. Under weak conditions, they proved that the method with Wolfe-Powell type line search or Armijo type line search is still globally convergent even when the objective function is not convex.One purpose of this thesis is to investigate the convergence of matrices sequence generated by the MBFGS method. We prove that, under certain conditions, the sequence converges if the objective function is a strictly convex quadratic function.Traditionally most multi-stage inventory models in many supply chain were based on the downstream stage. In other words, the members in supply chain are the manufacturer (supplier of the product), the wholesaler and the retailer. In the upstream stage, people just consider the problem like choice of suppliers. Fewer work is concerned with inventory model involving vendor, manufacturer and retailer.Another purpose of this thesis is to apply optimization theory and algorithms to supply chain and logistics management to maximize the profit.We propose a three stage supply chain inventory model involving multi-vendor, multi-manufacturer and multi-retailer. We give an optimal coordination strategy of how to coordinate the supply chain such that the whole cost of inventory of supply chain is minimized. We consider three coordination mechanisms, i.e., equal cycle time, integer-multiplier at each stage and integer powers of two multipliers at each firm.
|
PDF Full Text Request