Reducing risk of infection - The COVID-19 queueing game

Area of Science:

• Operations Research
• Epidemiology
• Business Management

Background:

• The COVID-19 pandemic necessitated capacity limits in retail environments like supermarkets and department stores to curb infection rates.
• Customer flow and interaction within stores present risks of disease transmission, requiring strategic management.

Purpose of the Study:

• To develop and analyze mathematical models for optimizing queue sizes and customer waiting times in retail settings.
• To introduce a novel method for quantifying customer infection risk during different phases of the shopping experience.
• To determine optimal strategies for authorities and businesses to balance safety, operational costs, and customer experience.

Main Methods:

• Construction and analysis of two queueing and risk-assessment models.
• Application of Stackelberg game theory for authority-led capacity management.
• Derivation of equilibrium strategies for store management regarding cashier allocation and space partitioning.

Main Results:

• A novel approach to calculate infection risk, proportional to the second factorial moment of customer density in different zones.
• Identification of optimal strategies for setting maximum customer capacity by authorities.
• Determination of optimal cashier staffing and store layout (space partitioning) for minimizing costs and risks.

Conclusions:

• The developed models provide a framework for businesses and authorities to manage in-store capacity and operations effectively.
• Findings support strategies for mitigating infection risk while optimizing operational efficiency and reducing costs.
• The research offers practical insights for enhancing public health and economic resilience in retail sectors during pandemics.