Restaurants operate in a tough and competitive environment where each customer visit and customer experience count towards profits and long-term business sustainability. Managing restaurant revenues is a complex activity because of the mismatch that can occur between demand (highly volatile customer arrival pattern characterized by the day and time of arrival, number and size of customer groups, and uncertain customer dining times) and supply (such as the number of tables and their seating capacities, number of chefs and order takers). Long customer queues and waiting times result when demand exceeds the restaurant�s capacity during a particular dining slot.

Restaurant queues typically provide two-sided cues to a customer. While some may perceive the queues as a reflection of a restaurant�s popularity in terms of cuisine or ambience, others may perceive them as an outcome of the restaurant�s poor operational design principles. While the former group may visit a restaurant after interpreting long queues as a symbol of popularity, the latter group may be demotivated after seeing a large number of waiting customers and skip the queue. Today, with easy access to customer feedback scores and reviews on websites such as Yelp or Zomato, managing long customer wait times at restaurants is crucial. When customers have a choice, this waiting may influence their service experience, total time spent at the restaurant, and ultimately spending, reneging, and return behaviour. Not much is known however, about the system-wide impact of waiting on customer behaviour and resulting revenue. In particular, we would like to ask the question � �How does customer waiting time affect the long-term revenues of a restaurant?�

There are analytical models that analyse the effect of customer waiting times on the service times in a general service system setting; however, few studies study the long term impact of customer waiting times on restaurant�s revenue. Further, the assumptions present in the analytical queuing models may make application of these models to restaurant waiting time problematic. While restaurant tables may resemble other perishable assets such as airline seats, the revenue management problem for an airline may not be directly applicable to a restaurant. Prolonged waiting times (boarding delays) may have a minimal long-term consequence for an airline because the customer has few travel options. On the other hand, there may be multiple restaurants in the same location that offer similar cuisines. Further, the table capacity of a restaurant is sometime more flexible (additional chairs can be accommodated on demand) than airline seating.

We adopt a multi-method approach (empirical and simulation) to answer the research question. We obtain customer-level data from a popular Indian restaurant and develop empirical models to study the customer reneging and return behaviour. To find out the impact of the consequences of waiting time and other restaurant operating parameters on the long-term restaurant revenue, we embed the empirical models in a detailed discrete-time simulation model. Our experiment shows that, without waiting, the total revenue generated by the restaurant would increase by nearly 15% compared to the current situation. Stimulating customers to reserve could enable restaurants to reap part of this benefit. Furthermore, the results of simulation experiments suggest that, within the boundaries of the current capacity, revenue could be increased by a maximum of 7.5% if more flexible rules were used to allocate customers to tables. Alternatively, by increasing the existing seating capacity by 20%, revenue could be boosted by 7.7% without the need to attract additional customers. Our findings extend the knowledge on the consequences of customer waiting, and enable service providers to better understand the financial and operational impact of waiting-related decisions in service settings.

Our integrated approach enabled us to combine exogenous and endogenous arrivals, to handle effects that are non-linear and non-stationary, and incorporate (higher-order) time-varying interactions. In the empirical study we established that customers who are subject to longer waiting times are more likely to renege. If they do not renege, customers who experienced a longer waiting time dine shorter, and the time until they return to the restaurant increases. This finding suggests that even though a restaurant manager could be satisfied by seeing a queue of customers waiting for a seat on a particular night, the long-term implications for the restaurant might be less positive. After all, the customer has to decide whether the (expected) service provided is worth the wait.

The generalizable relevance of the effects partly depends on the extent to which the restaurant depends on repeating customers, table categories and the number of tables per category, the availability of alternative dining options, the reservation policy, etc. A restaurant at a touristic location might not expect any returns anyway and might in fact benefit from the signalling value of a queue. However, at such locations a queue can be risky as well, as customers facing a long wait might balk or renege. For a restaurant in a local neighbourhood, returning customers may be vital for its survival, but reneging might be a smaller problem because alternative options could be unavailable. For both types of restaurants, effectively managing queues and waiting time is essential, but the impact of specific policies can be totally different between cases. Furthermore, it should be noted that in the investigated restaurant waiting is relatively pleasant, because customers do not physically have to stand in line. This means they can engage in other activities while waiting. As a consequence, the identified negative effect of waiting time on reneging and return behaviour could very well be larger in contexts where customers are expected to stand in a physical line. Our results demonstrate that ignoring the effect of waiting time on customer reneging, returns, and the subsequent impact on arrival rates can lead to highly unrealistic results in estimating operational performance.

In our future work, we plan to understand which customer segment should be prioritized for table allocation in the reservation system during busy dining slots. Today, customers use different modes of reservation such as app and call centre to register their table request. Some customer segments may be more serious with their reservation and may have low cancellation and no-show chances, while another segment may be less serious about their reservation and may not show up for dine in. We intend to show if reservation mechanisms can be developed that leverage the features of the customer segments to allocable tables and maximize restaurant revenues.

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¹Â This paper, published in Journal of Operations Management (Volume 63, 2018, pp 59-78), was a finalist for the Jack Meredith Best Paper Award in Journal of Operations Management 2019 and received honorable mention. The co-authors of this paper are Jelle de Vries and Rene de Koster.