Fleet sizing for transporters with seasonal demands

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.