On optimal decision models for supply chain and financial management

Abstract

Deriving and obtaining an optimal decision is a very complicated and difficult task in practice, but it is essential for decision makers in the industries. In this thesis, efforts are devoted to formulate, structure and analyze some optimal decision models by using mathematical tools for the problems in supply chain and financial management.

In a supply chain system, activities include the planning and management of manufacturing operations, the inventory control of products and the selling of a product or service from supplier to customer. All participants including manufacturers, suppliers, retailers, third-party service providers and customers can be seemed as independent or cooperating organizations aiming to optimize their profits. Products such as food and metal parts may deteriorate while in storage and hence they become unfit to use with time. This thesis investigates the effects of inspection policies on optimal decisions for a deteriorating inventory system under the situation that deteriorated items are sold to customers together with serviceable items. An algorithm is provided to obtain the optimal inspection time which aims to maximize the net profit of an inventory holder. Then when uncertainty exists, the actual market demand of some products may turn out to severely deviate from the initial order amount. To make up for the deficiency arising from this situation, a reorder option is introduced which renders a second manufacturing chance available shortly before the selling season. Furthermore, in order to describe the retail price competition behavior of n retailers, a model using a game theoretic approach is proposed. In the model, suppliers and retailers would try to optimize their own profit functions by improving their services and/or product quality with a view to establishing brand loyalty and competing with each other in the market.

Problems in financial management, such as derivative pricing, risk management and portfolio selection problem, have always been concerned by experts and investors. Due to some specific features in high tech industry including high-risk, multi-stage and technology life cycle, how to evaluate the investment opportunity in such a high risk industry is an important and practical issue. In this thesis, an irreversible regime-switching Markov chain is employed to model the project in the high-tech industry, and then real option theory and modern capital budgeting are applied to evaluate an investment opportunity. Further, the problem of pricing and hedging of basket credit derivatives is discussed. The key advantage of the hedging method in this thesis is that smaller numbers of single-name credit default swaps are chose as hedging instruments. An optimal portfolio selection under a hidden Markov regime-switching model is also studied. In order to control the risk of portfolio allocation in n risky assets, the maximum Value-at-Risk (MVaR) is imposed as a constraint. The separation principle and the dynamic programming technique are employed to investigate the optimal portfolio problem.