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Capacity, Collision Avoidance and Shopping Rate under a Social Distancing Regime
Haitian Zhong1, David Sankoff1
1Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada.
Entropy (Basel, Switzerland)
|December 23, 2023
Summary
Retail stores can maximize spending by optimizing customer intake rates. A new model shows that the optimal rate balances shopper slowdown with increased shopping volume for maximum equilibrium spending.
Area of Science:
- Operations Research
- Statistical Mechanics
- Retail Management
Background:
- Pandemic-induced capacity restrictions became common in retail.
- Social distancing significantly slows shopping rates in crowded stores.
Purpose of the Study:
- To develop a dynamical model of shopping rates under capacity restrictions.
- To determine the optimal customer intake rate for maximum equilibrium spending.
Main Methods:
- Statistical mechanics concepts (random particle collisions).
- Dynamical modeling of shopping rate evolution.
- Analytical determination and simulation of model trajectories.
- Validation through simulation experiments with avoidance interactions.
Main Results:
- Identified the equilibrium point and the limit beyond which equilibrium is unattainable.
- Calculated the optimal intake rate that maximizes equilibrium spending.
- Demonstrated that increased shopping volume compensates for individual shopper slowdown.
Conclusions:
- The optimal intake rate is the maximum rate compatible with equilibrium.
- Macroscopic modeling accurately predicts shopping dynamics and delays caused by customer interactions.
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