Solution of the Dial-a-Ride Problem with multi-dimensional capacity constraints

Abstract

The Dial‐a‐Ride Problem (DARP) consists of planning routes and schedules for picking up and delivering users within user‐specified time windows. Vehicles of a given fleet with limited capacity depart from and end at a common depot. The travel time of passengers cannot exceed a given multiple of the minimum ride time. Other constraints include vehicle capacity and vehicle route duration. In practice, scheduling is made more complicated by special user requirements and an inhomogeneous vehicle fleet. The transportation of elderly and handicapped people is an important example, as space for wheelchairs is limited and a lift is required. In this study, we present a modified insertion heuristic to solve the DARP with multi‐dimensional capacity constraints, and the performance of the proposed algorithm is tested in simulation. We show that the proposed methodology is effective when compared with the classic algorithms.

Quality of service in dial-a-ride operations

“…The different operational rules studied concern reservation policies and the composition of the vehicle fleet. Two types of reservation policies were considered: either a customer calls the company and obtains a reservation immediately (no call-back), or the company calls the customer back several Roy et al (1985) Coslovich et al (2006 Sexton and Bodin (1985) Dessouky et al (2003) Jaw (1984) Teodorovic and Radivojevic (2000) Sexton and Bodin (1980) Toth and Vigo (1997) Wilson and Miller (1977) Wong and Bell (2006) Sexton and Bodin (1985) Diana and Dessouky (2004) Sexton and Bodin (1980) Aldaihani and Dessouky (2003) Total ride time Diana (2004) Wilson and Miller (1977) Psaraftis (1980) Wilson et al (1976) Psaraftis et al (1979 Total time (between the call and the delivery time) Wilson et al (1976) Maximum number of stops while a user is on board Armstrong and Garfinkel (1982) hours later to confirm the reservation (call-back). The operational rules concerning the vehicle fleet are linked to its composition: either the fleet is composed of only minibuses, or it is primarily composed of taxis.…”

The dial-a-ride problem: models and algorithms

“…Instances containing between 50 and 2000 requests were solved. The objective considered by Wong and Bell (2006) is the minimization of a linear combination of total operating time, passenger ride time and taxi cost for unassigned requests. The authors work with several vehicle types and maximum route durations.…”

A pickup and delivery problem for ridesharing considering congestion

“…Xiang, Chu and Chen (2006) proposed a fast heuristic for solving a large-scale static dial-a-ride problem under complex constraints by applying insertions, inter-route exchanges, and secondary objective to provide diversification. Wong and Bell (2006) proposed a heuristic including parallel insertions, reinsertions, and exchanges. Some heuristics solve the problem by clustering the users first according to a proximity relation.…”