On a Fleet Sizing and Allocation Problem

This paper deals with a practical application of queueing theory. In particular, an approximate but quick method is developed for solving a fleet sizing and allocation problem. The problem concerns an optimal allocation of the total available transport vehicle units to many fleets in such a way that all fleets provide (as nearly as possible) a uniform level of service. The level of service is measured in terms of the fraction of arriving orders for shipment delayed due to the lack of immediate availability of a transport vehicle unit. The method employs some new results in queueing theory for approximating the delay probability and the service facility size in multi-server systems. An illustrative example is included to demonstrate a way of applying the method.