Optimal control of a distributed service system with moving resources: Application to the fleet sizing and allocation problem

Usually two control problems are considered for a service system: Firstly, how to decide whether to accept or to reject an arriving client, and secondly, how many resource units to install. Today's renting firms offer the possibility to return a rented unit to an arbitrary location of the firm. Thus, a third control problem arises: How to organise transhipments of resource units between the locations of the firm. In our paper we pursue two aims. At first, we develop a queueing network model for the movement of units through the locations without any control. Such a model is helpful to find out the main streams of units as well as the locations with a significant imbalance between the inflow of units and the demand. Then, we give some answers to the second and third control problem under a given cost and gain structure. Our approach combines simulation with Genetic Algorithms (simulation optimisation). Some examples demonstrate the applicability of the proposed approach.