One-Shot Coordination of Feeder Vehicles for Multi-Modal Transportation

Abstract

In this paper, we consider coordinated control of feeder vehicles for the first and last mode of a multi-modal transportation system. We adopt a macroscopic approach and model a geographical region as a graph with one of the nodes being an interchange between different modes of transportation. We model customer demands and supplies of vehicles as volumes and consider flows of vehicles. We propose one-shot problems for passenger transportation to or from the interchange within a fixed time window, under the knowledge of the demand distribution. In particular, we pose the problem of operator profit maximization through routing and allocations of the vehicles as well as pricing. With K.K.T. analysis we propose an offline method for reducing the problem size. Further, we also analyse the problem of maximizing profits by optimally locating the supply for a given total supply and present a closed form expression of the maximum profits that can be earned over all supply distributions for a given demand distribution. We also show an equivalence between optimal supply location problem and the last mode problem. Finally we present a model for determining the comparative cost of the best alternate transportation for the feeder service to be viable. We illustrate the results through simulations and also compare the proposed model with a traditional vehicle routing problem.