Designing mechanisms for crowdsourced urban parcel delivery

ABSTRACT

This paper presents a mechanism design-based approach to tackle the crowdshipping problem in which a delivery service provider (DSP) solicits ordinary individuals, termed crowdsourcees, who use their limited available time to perform urban parcel delivery. The DSP collects private information from crowdsourcees while assigning shipments to minimize the cost of delivery. Given that crowdsourcees may strategically misreport private information, the assignment is devised with a payment rule to incentivize truthful reporting. . Doing so requires additional payment to crowdsourcees, whose asymptotic properties are investigated. We extend the static mechanism to a dynamic case by performing assignment periodically and examine the bounds for periodicity. Numerical results show that the proposed mechanisms will likely reduce shipping cost compared to three alternative scenarios: 1) no such mechanism is in place; 2) the DSP pays crowdsourcees at a fixed rate; and 3) truck-only delivery. Several additional insights from the mechanism implementation are further obtained.

KEYWORDS:

• willingness-to-do-crowdshipping (WTDC)
• time availability
• guaranteed delivery time
• static and dynamic mechanisms
• private information
• truthful reporting

Nomenclature

Table

Acknowledgments

This research was funded in part by the US National Science Foundation (CMMI-1663411). The support of NSF is gratefully acknowledged. Earlier versions of the paper were presented at the INFORMS annual meetings and the Institute of Transportation Studies Seminar at the University of California, Berkeley. We thank the attendees of the presentations for their constructive feedback.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Per Eq. (3(3) $p_i={\sum }_{j\in J_i}{C}_{ij}\left({\theta }_i\right)X_{ij}^{\ast }+\left[V\left(A_{-i}^{\ast }\left({\theta }_{-i}\right)\right)-V\left(A^{\ast }\left(\theta \right)\right)\right]\mathrm{\forall }i\in I$(3) ), $p_1={\sum }_{j\in J_1}{C}_{1j}\left({\theta }_1\right)X_{1j}^{\ast }+\left[V\left(A_{-1}^{\ast }\left({\theta }_{-1}\right)\right)-V\left(A^{\ast }\left(\theta \right)\right)\right]$. Because only one shipment 1 exists in period 1 and crowdsourcee 1 has a lower WTDC than crowdsourcee 2, crowdsourcee 1 is assigned to shipment 1. Consequently, ${\sum }_{j\in J_1}{C}_{1j}\left({\theta }_1\right)X_{1j}^{\ast }=r_1{t}_{u_1}$ where $t_{u_1}$ is the travel time from the DSP location to the delivery location of shipment 1. $V\left(A_{-1}^{\ast }\left({\theta }_{-1}\right)\right)$ is the optimal TSC absent crowdsourcee 1. As here are only two crowdsourcees, $V\left(A_{-1}^{\ast }\left({\theta }_{-1}\right)\right)$ is obtained by assigning crowdsourcee 2 to shipment 1: $V\left(A_{-1}^{\ast }\left({\theta }_{-1}\right)\right)=r_2{t}_{u_1}$. $V\left(A^{\ast }\left(\theta \right)\right)$ is the optimal TSC with both crowdsourcees 1 and 2, which is obtained by assigning crowdsourcee 1 (who has a lower WTDC) to shipment 1. Thus, $V\left(A^{\ast }\left(\theta \right)\right)=r_1{t}_{u_1}$. This yields $p_1=r_1{t}_{u_1}+\left[r_2{t}_{u_1}-r_1{t}_{u_1}\right]=r_2{t}_{u_1}=10\times$ $0.75=7.5$.

2. This possibility can be ignored in the special case that $a_i^0=t_0$.

3. Note that a shipping job $j$ may be infeasible for crowdsourcee $i$ for a random draw ${\theta }_i$. In this case and for the purpose of the proof here, we could consider $C_{ij}\left({\theta }_i\right)$ to take a very large value. Then later in (8.3), we no longer need to restrict $j$ to be from $J_i$.

Additional information

Funding

This work was supported by the US National Science Foundation under grant number CMMI-1663411.