One-Shot Coordination of First and Last Mode Service in Multi-Modal Transportation

Abstract

In this thesis, we propose a coordination of the rst and last mode connectivity in a multi- modal transportation system. In particular, we consider a one-shot problem wherein the passengers must be transported to or from a common location before a fixed deadline. We consider a macroscopic model, wherein we model a region of interest by a graph and consider flows of vehicles and volumes of passenger demand and vehicle supply. We then consider the problem of operator's profit maximization through optimal pricing and allocations of feeder vehicles given the knowledge of demand and supply distributions. Due to the speci c nature of the problem, we can first determine the optimal prices, subsequent to which the overall problem becomes a linear program. We first study the problem of one-shot feed-in". Given the large scale or scope of the problem and the need for a near real-time implementation, we rst seek to reduce the problem size. We propose an o -line route elimination algorithm that given a route- set returns another reduced" route-set by eliminating the routes that would never be used in an optimal solution irrespective of the demand and supply distributions. In simulations on a 24 node graph, our proposed route reduction algorithm reduced the number of optimization variables to nearly one third of the original number. Such a reduced route-set could then be utilized for faster computation of the optimal solutions of the feed-in problem when the demand and supply distributions are revealed. We then analyse the supply optimization problem for one-shot feed-in for a given demand distribution. In this problem, given a total supply, we are interested in optimally distributing the supply so as to maximize the operator's pro ts. With this formulation, we give the closed form expression of the \absolute maximum pro ts" of the operator over all supply distributions given the demand distribution. Next, we go on to show that the one-shot feed-out" problem is equivalent to the supply optimization problem for one-shot feed-in" and that similar results can be drawn using the equivalence analysis. Finally, we propose a simple framework for determining the prices. With this framework, we are able to analyse the cost of a rst or last mode feeder service relative to the best alternative transportation at which the feeder service becomes pro table. We demonstrate our analytical results with a suite of simulations, including a com- parative study of our model with respect to a macroscopic single-depot single-window routing problem.