A revised branch‐and‐price algorithm for dial‐a‐ride problems with the consideration of time‐dependent travel cost

Abstract

SUMMARYDeveloping demand responsive transit systems are important with regard to meeting the travel needs for elderly people. Although Dial-a-ride Problems (DARP) have been discussed for several decades, most researchers have worked to develop algorithms with low computational cost under the minimal total travel costs, and fewer studies have considered how changes in travel time might affect the vehicle routes and service sequences. Ignoring such variations in travel time when design vehicle routes and schedules might lead to the production of inefficient vehicle routes, as well as incorrect actual vehicle arrival times at the related nodes. The purpose of this paper is to construct a DARP formulation with consideration of time-dependent travel times and utilizes the traffic simulation software, DynaTAIWAN, to simulate the real traffic conditions in order to obtain the time-dependent travel time matrices. The branch-and-price approach is introduced for the time-dependent DARP and tested by examining the sub-network of Kaohsiung City, Taiwan. The numerical results reveal that the length of the time window can significantly affect the vehicle routes and quantitative measurements. As the length of the time window increases, the objective value and the number of vehicles will reduce significantly. However, the CPU time, the average pickup delay time, the average delivery delay time and the average actual ride time (ART)/direct ride time (DRT) will increase significantly as the length of the time window increases. Designing the vehicle routes to reduce operating costs and satisfy the requirements of customers is a difficult task, and a trade-off must be made between these goals.

Ridesharing Problem with Flexible Pickup and Delivery Locations for App-Based Transportation Service: Mathematical Modeling and Decomposition Methods

“…Therefore, there are number of studies focusing on developing efficient solution algorithms. Studies such as Ropke and Pisinger [5], Li and Lim [6], Baldacci et al [7], Hosni et al [8], Küçükoglu andÖztürk [9], Hu and Chang [10], and Mahmoudi and Zhou [11] all consider the general PDPTW and provide customized heuristic or exact solution approach to efficiently solve certain scales of the problem. Hosni et al [8] formulated the shared-taxi problem into a mixed interprogram, in which an optimized taxi dispatching strategy is designed to assign the passengers' reservations to a fleet of taxis with optimal routing plans.…”

Taxi-sharing: Parameterized complexity and approximability of the dial-a-ride problem with money as an incentive

“…Considering the measure, one may optimize the vehicle travel cost, see for example [3,16,19], the total travel time [10] or the profit [7]. Another option is to maximize the number of satisfied requests or a combination of all those parameters [20,21,23].…”

“…Some constraints modelize the user convenience. A usual option is to search for a feasible solution considering time windows [4,10,19,23] as it has been done for the more general pickup and devivery problem [8]. This last problem is solved with a column generation scheme where columns define admissible routes.…”

“…This last problem is solved with a column generation scheme where columns define admissible routes. In [10,19], the authors develop a similar approach merging a branch-and-cut algorithm with column generation. In [4,23], the problem is solved using a Tabu search heuristic.…”

“…A recent review about the Dial-a-Ride problem and some of its generalizations may be found in [15]. We refer the reader to [5,10] for a more specific review about DARP.…”