Authors: Debjit Roy; Joseph Sebastian; Dheeraj Sharma
Addresses: Indian Institute of Management Ahmedabad, Gujarat 380015, India ' Oracle India Pvt Ltd, Bangalore, Karnataka 560076, India ' Indian Institute of Management Ahmedabad, Gujarat 380015, India
Abstract: We develop a quick and approximate way to address the fleet sizing problem for transporters with non-stationary demands and uncertain trip times. Non-stationary demands are modelled using Markov-modulated Poisson process (MMPP) and the variable fleet size is modelled using multi-server queuing construct [MMPP(2)/M/C queue]. The customer service level is expressed by the probability that a customer on arrival waits for availability of trucks. The waiting time probabilities are estimated from the steady-state probabilities, which are obtained from the solution of the continuous-time Markov chain. We demonstrate the fleet-sizing approach for a transporter with two level of demand rates and exponentially distributed truck unavailable times.
Keywords: transport fleets; fleet sizing; Markov-modulated Poisson process; MMPP; non-stationary demand; seasonal demands; uncertain trip times; modelling; multi-server queuing; truck availability; waiting times.
International Journal of Automation and Logistics, 2013 Vol.1 No.1, pp.105 - 115
Received: 23 Nov 2012
Accepted: 07 May 2013
Published online: 04 Nov 2013 *