With the trend of globalization and increasing transportation volume, the express delivery has been developed as a major branch of international shipment and supply chain management. In express delivery chains, multiple demand classes with various levels of urgency and importance as well as the demand uncertainty are two key issues to the delivery performance. In this dissertation, we consider three resource allocation problems among multiple stochastic demand classes, which are differentiated by the system scope and the distance along the delivery chain from express hubs to customers.; In the system-wide level, we perform a heavy traffic analysis to the single vehicle loop in an automated storage and retrieval system. We show that the loop configuration, which has received little research attention, has a major impact on the cargo waiting time. Analytical models are established and empirical studies are conducted. The conclusions suggest that a substantial improvement can be achieved by making proper adjustments to the loop configuration.; In the facility-wide level, we study a routing problem in integrated automated shipment handling systems, where a critical decision is the route selection linking various origins (e.g., system gate points) and destinations (e.g., storage racks). We study two versions of a routing optimization problem where multiple flow classes of various levels of importance are requested to go through the terminal equipment network. The first version is the routing problem on unrestricted paths and the second one is the routing problem on restricted paths. In the first version, we first prove the NP-hardness of the problem with the given demand arrival schedule and single flow class. With regard to the problem in a more general setting, we propose a flow allocation routing strategy which assigns the demand at each decision location with certain probabilities to its successors. Underlying mathematical models are constructed by explicitly formulating the network characteristics. In the second version we develop a flow rationing routing strategy to allocate different flow classes on corresponding path sets. A Markov Decision Process model is established to make allocation decision and the optimal structure is characterized.; In the district-wide level, we consider a type of vehicle routing problem where the vehicles are dispatched multiple times a day for product delivery and where the orders (demands) arrive randomly throughout the day. There are two types of decisions, order assignment decisions and dispatch decisions. An order assignment decision decides how the orders are assigned to vehicles but the assigned orders are not dispatched until a dispatch decision is made which gives a vehicle routing plan to fulfill the delivery. A general framework is presented and then two versions are studied. The first version is formulated as a two-stage stochastic programming and worst-case study is performed to quantify the ratio of using stochastic programming model and the deterministic solution approach. A sample-based heuristic is then developed. The second version is formulated as a multi-stage stochastic programming and in turn a capacity reservation scheme is proposed. In both versions, numerical experiments are conducted to evaluate the benefit that the stochastic approach can enjoy over the deterministic approach.
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