Control policies for queueing and production/inventory systems.

Abstract

In this dissertation, control policy for the M/G/1 queueing system with batch arrivals and its application to production/inventory systems and shuttle dispatch systems, are studied. These systems are closely related with each other and the results obtained in the study for the development of models in the production/inventory systems and shuttle systems. (1) The following control policy for the M/G/1 queueing system with batch arrivals is considered: At the end of a busy period, the server takes a sequence of vacations, each for a r and om amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length exceeds a prespecified value m at this time, the server begins to serve the queue until it is empty. For this system we develop an efficient procedure to find the optimal policy under a linear cost structure. (2) The (s,S) inventory policy is also considered, for production/inventory systems where the inventory can be replenished only on an item-by-item basis. The processing time required to produce an item is assumed to follow an arbitrary distribution. In our (s,S) policy, the production of items stops at the instant the inventory level is raised to S and production begins again at the instant the inventory level reaches or drops below s, s $<$ S, for the first time. The following two problems are analyzed: (i) the continuous review (s,S) policy with Poisson dem and s (ii) the (s,S) policy with compound Poisson dem and s and irregular inspection intervals. For each problem, under the linear cost structure, we develop an efficient procedure to find the optimal (s,S) policy. (3) A new control limit policy is presented for the shuttle dispatching problem with two terminals. Under the assumptions that control actions are taken at both terminals and that the number of passengers is known only when the shuttle is present at that terminal, a procedure to calculate the mean waiting time for an arbitrary passenger at each terminal is developed for given control values.