The Dial-a-Ride Problem with Split Requests and Profits

Abstract

I n this paper we introduce the dial-a-ride problem with split requests and profits (DARPSRP). Users place transportation requests, specifying a pickup location, a delivery location, and a time window for either of the two. Based on maximum user ride time considerations, the second time window is generated. A given fleet of vehicles, each with a certain capacity, is available to serve these requests, and maximum route duration constraints have to be respected. Each request is associated with a revenue and the objective is to maximize the total profit, that is, the total revenue minus the total costs. Transportation requests involving several persons may be split if it is beneficial to do so. We formulate the DARPSRP as a mixed-integer program using position variables and in terms of a path-based formulation. For the solution of the latter, we design a branch-and-price algorithm. The largest instance solved to optimality, when applied to available instances from the literature, has 40 requests; when applied to newly generated instances, the largest instance solved to optimality consists of 24 requests. To solve larger instances a variable neighborhood search algorithm is developed. We investigate the impact of request splitting under different geographical settings, assuming favorable settings for request splitting in terms of the number of people per request. The largest benefits from request splitting are obtained for problem settings exhibiting clustered customer locations.

Designing a New Shuttle Service to Meet Large-Scale Instantaneous Peak Demands for Passenger Transportation in a Metropolitan Context: A Green, Low-Cost Mass Transport Option

“…The outer loop (denoted by B) applies a branching scheme to avoid noninteger solutions. It is composed of loop A and modules (10)- (15). Modules (1)-(3) are the initialization modules for the two loops.…”

“…Many researchers have focused on studying corresponding solution techniques. CG algorithms [45,46], branch-and-price algorithms [15], branch-and-cut algorithms [47], branch-and-cut-and-price algorithms [48], tabu search algorithms [49], and dynamic-programming-based metaheuristics [14] can be used to solve problems of this type. The proposed LIPDRS problem can be regarded as an offline multivehicle routing problem because all the requests are assumed to be known beforehand.…”

Typology and literature review for dial-a-ride problems

“…Beaudry et al [7], Braekers et al [12], Detti et al [32], Hanne et al [55], Liu et al [76], Parragh [96], Parragh et al [97], Qu and Bard [106], Wong and Bell [129], Xiang et al [130], Zhang et al [134] 3.2.2 Routing properties Beaudry et al [7], Braekers et al [12], Braekers and Kovacs [13], Detti et al [32], Espinoza et al [37], Häll et al [49], Hanne et al [55], Karabuk [69], Liu et al [76], Masmoudi et al [81], Masson et al [83], Molenbruch et al [87], Parragh et al [97], Parragh et al [102], Reinhardt et al [109], Zhang et al [134] 3.2.3 Quality specifications Diana and Dessouky [33], Jaw et al [67], Jørgensen et al [68], Melachrinoudis et al [85], Paquette et al [94], Toth and Vigo [127] 3.3 Alternative objectives…”

“…Attanasio et al [5], Berbeglia et al [9], Diana et al [34], Feuerstein and Stougie [39], Garaix et al [45], Krumke et al [71], Parragh et al [102], Rekiek et al [110], Ritzinger et al [111], Yi and Tian [132] 3.3.2 Multiple objectives Diana and Dessouky [33], Guerriero et al [48], Jørgensen et al [68], Lehuédé et al [72], Mauri and Lorena [84], Melachrinoudis et al [85], Paquette et al [95], Parragh et al [101], Schilde et al [119], Schilde et al [120], Wong and Bell [129], Xiang et al [130] 3.4 Stochastic or dynamic…”

“…Groups of users formulating a single multiple-load request are normally transported together. However, on the one hand, Parragh et al [102] notice that splitting group requests among multiple rides may be more efficient from an operational point of view, even if the size of the group does not exceed vehicle capacity. Some typical split-delivery properties do not hold in the presence of precedence constraints [91].…”