Recharge and consolidation decisions for stored value cards with an application to Beijing public transit

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.