# Julian Archer Shannon Cummings Ashley Green David Ong.

## Presentation on theme: "Julian Archer Shannon Cummings Ashley Green David Ong."— Presentation transcript:

Julian Archer Shannon Cummings Ashley Green David Ong

 Introduction  Problem Statement  Initial Data  One Queue Model  Multiple Queue Model  Overall Results  Conclusion

 Sue of Sue’s Market has hired us a consultant firm to solve a number of issues that she has in her current store  Goal: ◦ Reduce wait time for customers ◦ Create a schedule that allows for worker limitations ◦ Save Sue money while creating a checkout areas with maximum output and efficiency. ◦ Having the least amount of baggers and cashiers working at one time to maximum profit

 Staffing of employees during peak hours ◦ 2pm-10pm ◦ Employees can only work 3-5 hours a day  Long lines ◦ Desired Queue Wait:  Optimal: 2-3 minutes  Acceptable: 10-12 minutes ◦ Desired Queue Length: 4-5 people  Minimizing Cost

After conducting a best fit analysis it was found that the number of items purchased per customer, on average, must be distributed empirically. MIN: 4 items MAX: 149 ITEMS Sample mean: 88.9 Number of Items Per Customer

From this graph we observe that the customers arrive at a lognormal distribution with a logarithmic mean of 0.00983 and a logarithmic standard deviation of 0.00308. However, the p- value is less than 15% which tells us that we have to use the empirical distribution. Initial Data Interarrival Times (Monday-Thursday)

 Payment Methods

 Basic Flow ◦ Assign customers amount of shopping items ◦ Decides to determine customer movement  Resource Usage ◦ Cashier Resources  Seized with series of delays  Based on schedule ◦ Bagger Resources  Bagging process

 Initial Data Collection: Changing Resources ◦ Focused on:  Number Out of System  Total Runtime  Queue Wait Times and Lengths  Resource Utilization and Busy  Cost  [(runtime/60)*5.5*#Baggers]+[(runtime/60)*7.25*#Cashie rs] ◦ Goal to Reduce:  Wait times and lengths  Cost  Runtime

Optimal Result: 12 Cashiers & 4 Baggers

 Second Stage Data Collection ◦ Action:  Changed Cashier Schedule  Fixed Amount of Baggers (4) ◦ Main Focus  Queue wait time and length  Still looked at same parameters as earlier

Optimum 8 Hour Cashier Schedule: Max = 15 Cashiers Min = 5 Cashiers

 Third Stage Data Collection ◦ Action:  Keep optimized cashier schedule  Vary bagger schedule ◦ Main Focus:  Cost  Wait time and length  Same parameters

Optimal 8 Hour Bagger Schedule: Max = 5 Baggers Min = 1 Bagger

 Final Stage of Data Collection ◦ Action:  Vary cashier schedule beyond 8 hours  Vary bagger schedule beyond 8 hours ◦ Main Focus  Cost  Queue Wait and Length  Runtime  Same previous parameters

Optimal Cashier ScheduleOptimal Bagger Schedule

 Total Cost: \$470.84 per day ◦ =((7.25*MR(Cashier)(TNOW/60)) + (5.50*MR(Bagger)(TNOW/60))  Total Average Queue Wait: 4.21 minutes ◦ Cashier Wait: 3.06 minutes ◦ Bagger Wait: 1.15 minutes  Average Cashier Queue Length: ∽5 People  Total Runtime: 556.66 minutes

 Single Entry  Assign Attributes and Variables  Decide Shopping Time Delay  Decide 1 of 20 Counters  Seize Cashier

 Decide Price Check Delays  Decides for Payment Type based on number of Items Purchased  Decided If Bagger available or not  Release Resources  Exit Sub model

◦ Decide bagging type ◦ Decrement customers ◦ Dispose Customers from system

Benefits of One Large Queue Benefits of Multiple Small Queues  Equal customer wait times  Avoid unnecessary time choosing a lane  Provides for more orderly checkout process  Allows for specialized lanes ◦ Express ◦ Self check out ◦ Special payment lanes  More familiar  Do not have to worry about queue placement

 Optimized Bagger and Cashier Schedules ◦ Adhered to 3-5 hour constraints ◦ Extended schedule beyond 8 hours to account for overtime  Minimize Queue Time ◦ Preferred 2-3 Minutes, Max 10-12 Minutes  Average of 6-7 Minutes ◦ Our Queue: 4.21 Minutes  Minimize Queue Length ◦ Queue length less than 5 people  Decreased Cost and Runtime ◦ Total Cost: \$470.84 ◦ Total People In and Out of System: 891 People ◦ Total Runtime: 556.66 Minutes

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