On-Line Dial-a-Ride Problems Under a Restricted Information Model

Abstract

In on-line dial-a-ride problems servers are traveling in some metric space to serve requests for rides which are presented over time. Each ride is characterized by two points in the metric space, a source, the starting point of the ride, and a destination, the endpoint of the ride. Usually it is assumed that at the release of a request, complete information about the ride is known. We diverge from this by assuming that at the release of a ride, only information about the source is given. At visiting the source, the information about the destination will be made available to the servers. For many practical problems, our model is closer to reality. However, we feel that the lack of information is often a choice, rather than inherent to the problem: additional information can be obtained, but this requires investments in information systems. In this paper we give mathematical evidence that for the problem under study it pays to invest. Prelude.In dial-a-ride problems servers are traveling in some metric space to serve requests for rides. Each ride is characterized by two points in the metric space, a source, the starting point of the ride, and a destination, the endpoint of the ride. The problem is to design routes for the servers through the metric space, such that all requested rides are made and some optimality criterion is met.Dial-a-ride problems have been studied extensively in the literature of operations research, management science, and combinatorial optimization. Traditionally, such combinatorial optimization problems are studied under the assumption that the input of the problem is known completely to the optimizer.In a natural setting of dial-a-ride problems requests for rides are presented over time while the servers are enroute serving other rides, making the problem an on-line optimization problem. Examples in practice are taxi and minibus services, courier services, and elevators. In their on-line setting dial-a-ride problems have been studied in [1] and [4], where single-server versions of the problem are studied, as we will do here. These papers study the problem in which rides are specified completely upon presentation, i.e., both source and destination of the ride become known at the same time. We diverge from this setting here.

Zone pAth Construction (ZAC) based Approaches for Effective Real-Time Ridesharing

“…The ridesharing problem is related to the Online Multi-Vehicle Pick-up and Delivery problems which typically represent problems where there are multi-capacity vehicles that transport multiple resources/loads from their origins to destinations. When vehicles are used to move people instead of resources, the problem is referred to as dial-a-ride problem (Feuerstein & Stougie, 2001;Lipmann et al, 2002;Bonifaci et al, 2006) and when all the origins or all the destinations are located at a depot, the problem is referred to as vehicle routing problem (Ritzinger et al, 2016). The general representation of the dial-a-ride problems is ideally suited to represent problems faced by companies such as Super Shuttle (transports people from an airport to different locations in the city), Uber Pooling (transports customers from near by start locations to near by destination locations).…”

Typology and literature review for dial-a-ride problems

“…Minimizing the time interval needed to complete all available requests, Feuerstein and Stougie [39] and Ascheuer et al [3] compute lower bounds on this competitive ratio. Lipmann et al [75] include incomplete ride information, meaning that destinations only become known when their corresponding origin is visited. Feuerstein and Stougie [39] also find lower bounds on the competitive ratio for a minimization of the average completion time.…”

A Decentralised Approach for the Transportation On Demand Problem

“…This problem is known as the Dynamic Dial-A-Ride Problem (DDARP) with several places of pickup and delivery. In [11], the DARP problem was treated online by considering a homogeneous fleet of vehicles with unit capacities, i.e. a vehicle having a passenger on board, cannot serve another one except if it reached the first passenger destination.…”