Self-organized carpools with meeting points

Abstract

Carpooling promises benefits to the environment and consumers alike, but research has shown that there are multiple practical challenges to realizing these benefits. One possible solution is the addition of meeting points (hubs) in the design of carpooling systems. Recent studies indicate that introducing hubs increases both carpool participation and system-wide savings. Little to no research has been conducted, however, to understand the origin of these savings, determine their utility in different carpooling models, or detailing how hubs should be introduced (i.e. as a mandate or option). Additionally, we know nothing about the impact of hubs on self-organizing carpools (the primary means of creating carpooling systems). To address these gaps, we studied the impact of meeting points on two types of carpooling models (pick-up/drop-off and to/from), using two solution paradigms (centralized and self-organized), with hubs that were either mandated or optional. Our findings show that adding the option of meeting hubs improves system-wide savings from carpooling. These findings, along with our introduction of a new efficient carpool enumeration technique, have important practical implications for the design of modern carpooling systems in the development of more effective and sustainable uses of transportation resources.

Keywords:

• Transportation
• heuristics
• carpooling

Appendix: Generating random instances

Pseudo-random numbers for our test instance were generated by the procedure originally used in Drezner, Kalczynski, and Salhi (2019), which was based on the idea of Law and Kelton (1991). We used this approach so that it can be easily replicated by others to verify the results reported in this paper.

We generate a sequence of integer numbers in the open range (0, 100,000). A starting seed r₁, which is the first number in the sequence, is selected. The sequence is generated by the following rule for $k\ge 1:$

• Set $\theta =12,219r_k.$

• Set $r_{k+1}=\theta -\lfloor \frac{\theta }{100,000}\rfloor \times 100,000,$ i.e. $r_{k+1}$ is the remainder of dividing θ by 100,000. It is also the last five digits of θ.

For the x-coordinates of the meeting points and original locations we used $r_1=97$ and for the y-coordinates we used $r_1=367.$ We divided the coordinates by 2,500, so the points are in a 40 by 40 square. The coordinates of the first five original locations are: (0.0388, 0.1468), (34.0972, 33.7492), (33.6868, 21.4748), (19.0092, 0.5812), (33.4148, 21.6828). The destination z is in the middle of the square, i.e. at (20, 20).