Invite Your Friend and You’ll Move Up in Line: Optimal Design of Referral Priority Programs

Abstract

Problem definition: This paper studies the optimal design of referral priority programs, in which customers on a waiting list can jump the line by inviting their friends to also join the waiting list. Academic/practical relevance: Recent years have witnessed a growing presence of referral priority programs as a novel customer-acquisition strategy for firms that maintain a waiting list. Different variations of this scheme are seen in practice, raising the question of what should be the optimal referral priority mechanism. Methodology: I build an analytical model that integrates queuing theory into a mechanism design framework in which the objective of the firm is to maximize the system throughput, that is, accelerate customer acquisition as much as possible. Results: My analysis shows that the optimal mechanism has one of the following structures: full priority; partial priority; first in, first out (FIFO); and strategic delay. A full-priority (partial-priority) scheme enables referring customers to get ahead of all (only some) nonreferring ones. A FIFO scheme does not provide any priority-based referral incentive. A strategic-delay scheme grants full priority to referring customers but artificially inflates the delay of nonreferring ones. I show that FIFO is optimal if either the base-market size or the referral cost is large. Otherwise, partial priority is optimal if the base-market size is above a certain threshold; full priority is optimal at the threshold base-market size; strategic delay is optimal if the base-market size is below the threshold. I also find that referrals motivate the firm to maintain a larger capacity and therefore can surprisingly shorten the average delay, even though more customers sign up and strategic delay is sometimes inserted. Managerial implications: My paper provides prescriptive guidance for launching an optimal referral priority program and rationalizes common referral schemes seen in practice.

Design of Covid‐19 testing queues

“…While we propose one implementation, various other means can also achieve partial priority. For example, Coffman and Mitrani (1980) suggest a scheme that probabilistically determines in each busy period which type to receive full priority; Hassin and Haviv (2006) propose a relative priority scheme that probabilistically determines which type to serve next; Erlichman and Hassin (2015) put forward a scheme where those who receive partial priority can only overtake some nonpriority customers, rather than all of them (a similar scheme is also mooted in Yang 2021); Yang et al. (2021) consider a scheme in which placeholders in the queue are reserved for future priority customers.…”

“…Yang (2021) establishes that giving partial priority to referring customers in referral priority programs can maximize the rate of customer acquisition. Similar to Yang (2021), we also find in our setting that partial priority can be optimal (better than FIFO and full priority) because it can strike a delicate balance between the joining incentives of the two customer classes. However, in contrast to all the papers above, where the ordering of customer classes is fixed, in our paper, whether the symptomatic or the asymptomatic receives (partial) priority depends on the testing demand, that is, the ordering of patient classes in the optimal policy can change with the model environment.…”

“…Yang et al (2021) examine queue-scalping, a form of decentralized partial priority. Yang (2021) establishes that giving partial priority to referring customers in referral priority programs can maximize the rate of customer acquisition. Similar to Yang (2021), we also find in our setting that partial priority can be optimal (better than FIFO and full priority) because it can strike a delicate balance between the joining incentives of the two customer classes.…”

Implications of vaccine shopping during pandemic

“…Admittedly, in many countries, more than two vaccines are available to choose from, suggesting that a general n server approach may be more suitable. Moreover, we assume that there is a single server at each queue with exponentially distributed service times, as commonly assumed in prior work (Cui et al., 2020; Sunar et al., 2021; Yang, 2021) and consistent with the queueing game literature as noted by Cui et al. (2020).…”

Management model based on Relational Marketing to increase customer satisfaction through the implementation of the Knowledge Creation Model.

“…The design of the priority referral program consists of a technique applied to initial customers. They are guaranteed to be moved up in the waiting queue, resulting in reduced waiting time, on the condition that they refer the service to their contacts and generate new customers [13]. In recent years, technologies such as artificial intelligence and data analysis have been implemented.…”