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Capacity, Collision Avoidance and Shopping Rate under a Social Distancing Regime.

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Summary
This summary is machine-generated.

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.

Keywords:
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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.