Improved Bounds for Open Online Dial-a-Ride on the Line

We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is the first bound that strictly separates online Dial-a-Ride on the line from online TSP on the line in terms of competitive analysis, and is the best currently known lower bound even for general metric spaces. On the other hand, we present an algorithm that improves the best known upper bound from 2.9377 to 2.6662. The analysis of our algorithm is tight

Fast infeasibility detection algorithms for dial-a-ride transit problems

"(Revised February 14, 1998.)"--T.p. -- "February 1998"--Cover.Includes bibliographical references (p. 18).Supported by a grant from the United Parcel Service and a contract from the Office of Naval Research. ONR N00014-96-1-0051by Ravindra K. Ahuja, Robert Dial, James B. Orlin

Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line

The online Dial-a-Ride problem is a fundamental online problem in a metric space, where transportation requests appear over time and may be served in any order by a single server with unit speed. Restricted to the real line, online Dial-a-Ride captures natural problems like controlling a personal elevator. Tight results in terms of competitive ratios are known for the general setting and for online TSP on the line (where source and target of each request coincide). In contrast, online Dial-a-Ride on the line has resisted tight analysis so far, even though it is a very natural online problem. We conduct a tight competitive analysis of the Smartstart algorithm that gave the best known results for the general, metric case. In particular, our analysis yields a new upper bound of 2.94 for open, non-preemptive online Dial-a-Ride on the line, which improves the previous bound of 3.41 [Krumke\u2700]. The best known lower bound remains 2.04 [SODA\u2717]. We also show that the known upper bound of 2 [STACS\u2700] regarding Smartstart\u27s competitive ratio for closed, non-preemptive online Dial-a-Ride is tight on the line

Anticipation in the Dial-a-Ride Problem: an introduction to the robustness

International audienceThe Dial-a-Ride Problem (DARP) models an operation research problem related to the on demand transport. This paper introduces one of the fundamental features of this type of transport: the robustness. This paper solves the Dial-a-Ride Problem by integrating a measure of insertion capacity called Insertability. The technique used is a greedy insertion algorithm based on time constraint propagation (time windows, maximum ride time and maximum route time). In the present work, we integrate a new way to measure the impact of each insertion on the other not inserted demands. We propose its calculation, study its behavior, discuss the transition to dynamic context and present a way to make the system more robust

Transfers in the on-demand transportation: the DARPT Dial-a-Ride Problem with transfers allowed

International audienceToday, the on-demand transportation is used for elderly and disabled people for short distances. Each user provides a specific demand: a particular ride from an origin to a destination with hard time constraints like time windows, maximum user ride time, maximum route duration limits and precedence. This paper deals with the resolution of these problems (Dial-a-Ride Problems - DARP), including the possibility of one transshipment from a transfer point by request. We propose an algorithm based on insertion techniques and constraints propagation

Constraint Propagation for the Dial-a-Ride Problem with Split Loads

International audienceAbstract. This paper deals with a new problem: the Dial and Ride Problem with Split Loads (DARPSL), while using randomized greedy insertion techniques together with constraint propagation techniques. Though it focuses here on the static versions of Dial and Ride, it takes into account the fact that practical DARP has to be handled according to a dynamical point of view, and even, in some case, in real time contexts. So, the kind of algorithmic solution which is proposed here, aim at making easier to bridge both points of view. First, we propose the general framework of the model and discuss the link with dynamical DARP, second, we describe the two algorithms (DARP and DARPSL), and lastly, show numerical experiments for both

A ride time-oriented scheduling algorithm for dial-a-ride problems

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theory, aims at finding minimal user ride time schedules in polynomial time. The algorithm can either return optimal feasible routes or it can return incorrect infeasibility declarations, on which feasibility can be recovered through a specifically-designed heuristic. The algorithm is furthermore supplemented by a battery management algorithm that can be used to determine charging decisions for electric and autonomous vehicle fleets. Timing solutions from the proposed scheduling algorithm are obtained on millions of routes extracted from DARP and e-ADARP benchmark instances. They are compared to those obtained from a linear program, as well as to popular scheduling procedures from the DARP literature. Results show that the proposed procedure outperforms state-of-the-art scheduling algorithms, both in terms of compute-efficiency and solution quality.Comment: 12 pages, 1 figur