Uncertainty modeling for bus selection and allocation in a private transportation system

This paper describes the development of a probabilistic formulation that provides global optimum selection and allocation of a fleet of buses in a private transportation system of an organization where a third party is hired to provide transportation for its employees and their dependents. In this private transportation system, a fleet of buses is to be selected and allocated to serve employees and their independents on different prescheduled trips along different routes from the organization’s headquarters and residential compound where round-trip times of scheduled trips are subject to uncertainty due to random delays. We propose a probabilistic approach based on 0-1 integer programming for the selection and allocation to determine the optimal number and size of buses assigned to a set of prescheduled trips in a particular time interval. Examples and a case study are presented to illustrate the applicability and suitability of the proposed approach