内容提要：

Part I: Service Systems:
Motivated by Flexible Staffing of the US-Canada Border Crossings

Abstract: In the first part of this research, we study waiting line problems at the border-crossings between the U.S. and Canada. To evaluate a practical staffing policy, we develop an analytical model to compute the important performance measures. The policy is called "congestion based staffing" or CBS, because the number of open inspection booths is adjusted according to the queue length during each planning period. Our analysis is based on the matrix-geometric solution, the regeneration cycle, and the fluid approximations. With a certain cost structure, we provide a numerical search approach to determine the best CBS policy for border-crossing stations. Under certain conditions, we can obtain the close-form solution for the optimal policy parameters and prove the convexity of the average cost function.

Part II: Manufacturing Systems:
Apply the CBS model to Production/Inventory Systems

Abstract: In the second part of this research, we show that CBS model can be applied to study a fixed number of production facilities producing a specific type of items with random demand and production time. The inventory policy is a base-stock (s, S) type with continuous review. Some production facilities can be switched to producing other secondary products if the inventory level is high and switched back when the inventory level is slow. Under a cost structure which includes a set-up cost, a linear holding cost, and a possible linear backorder cost, an average cost function is developed. Using reasonable approximation methods, we obtain the closed form formulas for computing the optimal inventory and production policy. Excellent approximation with high accuracy has been illustrated by extensive numerical analysis. These easy-to-use formulas provide practitioners a useful tool in determining the best inventory and production control policy under the random demand and production time environment.