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Sue’s Market Optimization

Sue’s Market Optimization . Julian Archer Shannon Cummings Ashley Green David Ong. Overview . Introduction Problem Statement Initial Data One Queue Model Multiple Queue Model Overall Results Conclusion. Introduction .

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Sue’s Market Optimization

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  1. Sue’s Market Optimization Julian Archer Shannon Cummings Ashley Green David Ong

  2. Overview • Introduction • Problem Statement • Initial Data • One Queue Model • Multiple Queue Model • Overall Results • Conclusion

  3. Introduction • 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

  4. Problem • 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

  5. Initial Data Number of Items Per Customer 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

  6. Initial Data Interarrival Times (Monday-Thursday) 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.

  7. Initial Data

  8. Initial Data • Payment Methods

  9. Initial Data: Model Flowchart

  10. One Queue Model: Arena Model

  11. One Queue Model: Features • 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

  12. One Queue Model: Results • 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*#Cashiers] • Goal to Reduce: • Wait times and lengths • Cost • Runtime

  13. One Queue Model: Results Optimal Result: 12 Cashiers & 4 Baggers

  14. One Queue Model: Results • 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

  15. One Queue Model: Results Optimum 8 Hour Cashier Schedule: Max = 15 Cashiers Min = 5 Cashiers

  16. One Queue Model: Results • Third Stage Data Collection • Action: • Keep optimized cashier schedule • Vary bagger schedule • Main Focus: • Cost • Wait time and length • Same parameters

  17. One Queue Model: Results Optimal 8 Hour Bagger Schedule: Max = 5 Baggers Min = 1 Bagger

  18. One Queue Model: Results • 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

  19. Optimal Cashier Schedule Optimal Bagger Schedule

  20. One Queue Model: Optimal Conditon • 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

  21. Multiple Queue Model: Arena Model

  22. Multiple Queue Model: Overview • Single Entry • Assign Attributes and Variables • Decide Shopping Time Delay • Decide 1 of 20 Counters • Seize Cashier

  23. Multiple Queue Model: Sub Model

  24. Multiple Queue Model: Schedule Method

  25. Multiple Queue Sub Model • 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

  26. Multiple Queue Model: Bagging Process • Decide bagging type • Decrement customers • Dispose Customers from system

  27. Overall Results • 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 Benefits of One Large Queue Benefits of Multiple Small Queues

  28. Conclusion • 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

  29. Questions? Thanks for listening……

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