Throughput Analysis of an Amazon Go Retail under the COVID-19-related Capacity Constraints

The throughput of a finite-capacity queueing system is the mean number of clients served during a time interval. The COVID-19 outbreak has posed a serious challenge for many commercial establishments, including the retails, which have struggled to adapt to new working dynamics. Retails have been forced to adjust their service guidelines to comply with biosecurity protocols, ensuring to observe governmental and public health policies. A significant change for the retail market has been the capacity restrictions to ensure social distancing, i.e., a limitation on the number of customers simultaneously shopping in the store. Such a constraint has an impact on the throughput that can be achieved by a retail. This article assesses the impact of the capacity restriction measures on an Amazon Go-like retail performance through a throughput analysis under COVID-19-related capacity restrictions. For the assessment, we first retrieved real data from a retail located in Cartagena, Colombia. Two scenarios were considered: i) low demand and ii) high demand. Further, we built an Amazon Go-like, two-queue, M/M/c/K retail model with a CONWIP (Constant Work-In-Process) approach, considering biosecurity-based capacity restrictions due to the COVID-19 pandemic. The R package 'queueing' was used to set up the model, and an algorithm was created to go over each sampling period and find the hourly optimum capacity and throughput under the dynamic conditions of both scenarios (low and high demand). Results from the performance analysis show that, for some operational conditions, the optimum maximum throughput is achieved with capacities below the biosecurity-based capacity, while for some other operational conditions the maximum throughput cannot be achieved with the restrictions, as the optimum capacity lies beyond the biosecurity-based capacity. These results suggest that the maximum capacity definition should not be static. Instead, it should be done considering the retail's dimensions, the biosecurity policies, and the dynamic retail's operational conditions such as the demand and service capacity.