Operations Research — Simulation to decrease wait time
Grocery store operation is stressed with the high demand and social distancing. A simulation can be used to make decisions which decrease wait times for customers waiting to check-out. The simulation is written in R and has a user interface in Rshiny.
Simulation Basics
3 independent variables are considered: Maximum number of customers arriving per minute, Maximum time at counter, and Number of Cashier lines. The customer arrival pattern is based on a variable number of customers arriving each minute with the maximum number of customers arriving per minute set to a fixed limit. A uniform distribution in number of customers is used, although other possible distributions could be the normal distribution and Poisson distribution. The checkout time at counter varies for each customer. The maximum time for checkout is set to a fixed limit. Again a uniform distribution of times is used. Other types of distributions for checkout time can also be considered.
Simulation Algorithm
Create a distribution representing number of customers which arrive to check out at each time increment
Create a distribution representing number of minutes each customer spends at the check-out counter
Create a customer table
Create a list of counters, 0 indicates counter is empty, x indicates counter is occupied for x minutes
Create a for loop to run through each time step
Assign each incoming customer an ID
Add rows to the customer table based on number of incoming customers
Fill each row in customer table
Number of customers waiting to check out are customers waiting at time, t-1, and new arrivals
The first timestep has no customers waiting at check out lines
Create a for loop to run through each customer waiting to check out
Find the customer id for a waiting customer
Find an empty counter
Choose amount of time, x, customer takes at check out counter by sampling from a distribution of times
Release counter after x minutes
If no empty counter is found, add customer to number of waiting customers
Go to the next time increment
Return customer table
The customer table will be similar to this:
Simulation Results
Different Scenarios
Depending on the interplay of the independently controlled variables, Maximum number of customers arriving per minute, Maximum time at counter, and Number of Cashier lines, scenarios with short and long wait times can result.
Evaluating resource and process requirements for different solutions
If the scenario is long wait times, two solutions can be considered.
Solution 1: Opening another cashier line for 10 minutes
Solution 2: Process change to decrease time at counter by 1 minute per transaction
Simulations provide us a way to examine the expected results for different solutions prior to implementation, serving as guidelines for decision-making.
I didn’t get around to posting the code.
