Abstract
Stored value cards (SVCs) are ubiquitous, but little investigation has been undertaken into actual and desired replenishment behaviour, or the economic impact of card consolidation on consumers and service providers (such as retailers and public transit authorities). We develop classic and joint replenishment economic order quantity models for reloadable SVCs where the card value may be lost, for example, through theft or breakage. We extend the models to consider potential benefits of discounts, and providing refunds upon card loss (via external recording of card value). We also show how SVC consolidation and service expansion decisions can benefit consumers and service providers. As a case study, we utilise the Beijing subway system ‘YiKaTong’ card to demonstrate cost optimisation at the consumer and enterprise level. Direct observations of recharging and a survey suggest that commuters take the likelihood of card loss into account and are risk averse. The results of the work help to explain and predict consumer recharge behaviour, and should assist service providers evaluating decisions relating to their market scope, technology, pricing, and service capacity.
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Notes
For some breakages or malfunctions, it may be possible to restore the value stored on the card and to return the deposit, but the consumer would still incur the cost of arranging for the replacement, β.
Note that this could also apply in cases where stations require less than one cashier—as there may be other tasks that the cashier can perform while idle.
For example, as occurs in London’s Oyster system and Hong Kong’s Octopus system. The Oyster system provides a refund of the stored value (less a 10 GBP administration fee) for lost registered or personalised cards (the latter requiring a security question), which are then deactivated. In the Octopus system, the user is charged a 20 HKD handling fee and is liable for unauthorised use within 3 h of reporting the loss. The costs indicated by the model in this paper can be compared with the additional costs and time related to different read/write requirements and (potentially real-time) data transmission. We note that systems with external storage can facilitate online recharge. The model here remains pertinent, but the values of ν and u are likely to be a lot lower with no need for a physical queueing and service associated with recharge. The same is true for systems allowing cell phones with near field communication capability.
A recent paper reports that excluding construction costs, the Beijing system received 14 billion CNY in subsidies in 2010 (Cheng, 2011). For 1.84 billion rides, that amounts to a subsidy of 7.6 CNY/ride.
The 0.69 is obtained by dividing the average line length (sampled every minute) of 3.4 by the average arrival rate (from the total number of arrivals) of 4.9 and includes a service time of approximately 10 s.
A separate survey conducted by the first author, of a convenience sample of 22 people in 2010, yielded an average value of 0.4/year. With these loss rates, it is not surprising that in the first 8 years of operation 41.76 million YiKaTong cards were issued.
This is even more the case if some commuters are not aware that the value stored on each card is not stored externally, and thus cannot be recovered upon card loss.
A single-day ridership record of 10.276 million passengers was set on 8 March 2013 (anon, 2013).
At present, Beijing subway does not provide refunds of card value upon card loss, although it appears that external records are kept. A third-party payment licence is currently being sought from the government to introduce a ‘deposit account’. Whereas the current ‘wallet account’ is anonymous and stored values are not reimbursable upon card loss, the deposit account will require registration and ID verification (much like SIM card registration requires now) and card value losses will be reimbursable (anon, 2011).
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Acknowledgements
The research underlying this paper was supported by the National Natural Science Foundation of China under Research Fund 70890082. The authors are grateful for the advice of Professor Jim Bookbinder on an earlier version of the paper.
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Robb, D., Yang, Y. Recharge and consolidation decisions for stored value cards with an application to Beijing public transit. J Oper Res Soc 65, 1511–1521 (2014). https://doi.org/10.1057/jors.2013.107
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DOI: https://doi.org/10.1057/jors.2013.107