Revised eight-step feasibility checking procedure with linear time complexity for the Dial-a-Ride Problem (DARP)

Abstract

In the context of Dial-a-Ride Problems (DARPs), the eight-step feasibility checking procedure is one of the most commonly used methods. The time complexity of this procedure is considered as O(n2) in the literature. In this study, a version of this procedure is proposed with O(nlogQ) time complexity. Since, in DARPs, the capacity of each vehicle is a small constant, the method introduced in this paper performs as a linear-time technique in this context. The revised scheme is just as elegant as the original one, which makes this improvement in the time complexity more noteworthy. Our proposed technique has a lower time complexity and/or is noticeably easier to comprehend and implement than the other feasibility checking methods in the literature. Considering the standard benchmark instances, experimental results show that the revised method outperforms the classic one in terms of the computational time. Moreover, it is demonstrated that the execution time of our algorithm is competitive with that of the only technique with linear time complexity in the literature.