1 Department of Business Studies, Aarhus School of Business, Aarhus BSS, Aarhus University2 CORAL - Centre for Operations Research Applications in Logistics, Aarhus School of Business, Aarhus BSS, Aarhus University3 Department of Economics and Business Economics, Aarhus BSS, Aarhus University4 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
We consider a single-server queueing system designed to serve homogeneous jobs. The jobs arrive to the system after a Poisson process and all processing times are deterministic. There is a set-up cost for starting up production and a holding cost rate is incurred for each job present. Also, there is a service cost per job, which is a convex function of the service time. The control policy specifies when the server is on or off. It also specifies the state-dependent processing times. In order to avoid a very detailed control policy (which could be hard to implement) we will only allow the server to use n different processing times. Hence, we must subdivide the infinite state space into n disjoint sets and for each set decide which processing time to use. We show how to derive a mathematical expression for the long-run average cost per time unit. We also present an algorithm to find the optimal control policy. Finally some numerical results are presented.
Control; Service; Markov processes; Queueing
Main Research Area:
The European Operational Research conference, Rotterdam, The Netherlands, 2001