Dynamic admission and dispatching control of stochastic distribution systems

In this thesis, we study several models that help improve the operation of distribution systems. In these systems, transportation requests arrive at the systems randomly and will be satisfied by transporting from their origins to their destinations by a vehicle of capacity Q. In each system, the administrator needs to make two kinds of decision: admission decision and dispatching decision. When there is a new arrival, the administrator should decide whether to admit it or not based on the associated reward of admitting and the penalty cost of rejecting the arrival as well as the state of the system. When the vehicle is available, the administrator should decide when and where to dispatch the vehicle to balance the transportation cost and the customers' waiting cost. Our objective is to find the admission and dispatching control policies that maximize the total discounted profit of operating the systems. Three different systems are investigated in this thesis: the one-terminal system, the two-terminal system, and the one-hub-two-spoke system. We begin with the one-terminal system, which can be regarded as a bulk service queue. The optimal control policy is shown to be of threshold type. The optimal admission threshold levels are non-increasing functions of the remaining service times. We also investigate the dependence of these threshold levels on the system parameters and propose some approximations of the threshold levels. The interaction between terminals makes the two-terminal system complex and interesting. The optimal decision at one terminal is highly dependent on the state of the other terminal and the vehicle location. We fully characterize the optimal control threshold policy and show that both admission and dispatching threshold levels will decrease when there are more customers waiting at the other terminal. An approximation of the threshold levels is developed as well. We finally study the one-hub-two-spoke system. Two sub-systems, the system with one-way transportation demand and the system with two-way transportation demand, are discussed. For both sub-systems, we show that the optimal policies are of threshold type. We also partially characterize the properties of the optimal threshold levels. A number of directions for future research are discussed, especially on how to find efficient heuristic policies for hub-and-spoke systems