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Project 2: ATM’s & Queues

Project 2: ATM’s & Queues. ATM’s & Queues. Certain business situations require customers to wait in line for a service Examples: Waiting to use an ATM machine Paying for groceries at the supermarket A line of people or objects is called a “queue”. ATM’s & Queues.

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Project 2: ATM’s & Queues

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  1. Project 2: ATM’s & Queues

  2. ATM’s & Queues • Certain business situations require customers to wait in line for a service • Examples: • Waiting to use an ATM machine • Paying for groceries at the supermarket • A line of people or objects is called a “queue”

  3. ATM’s & Queues • Queues occur in many places: • Running multiple programs on a computer • A print queue is formed when many documents are sent to the printer • Telephone calls on a switchboard • Vehicles waiting at a traffic light

  4. ATM’s & Queues • Studying how these lines form and how to manage them is called Queuing Theory • Queuing Theory has become an important tool in business decisions regarding quality and expense of customer service • Example: Supermarket manager sees checkout lines are too long, so more cashiers are called to work the registers, but this costs more money

  5. ATM’s & Queues • Automated services make queue theory important when direct monitoring of service isn’t possible • Example: • Bank manager can’t monitor ATM machine service at mid-night. • Opening up more machines might improve customer service but may cost a lot of money

  6. ATM’s & Queues • Managing queues is a balancing act: $$$$$$$$$$$$$$$$$$ Customer Satisfaction

  7. ATM’s & Queues • Two Queue Models • Standard Queue • Serpentine Queue

  8. ATM’s & Queues • Standard Queue • Customers select what they believe to be the shortest or most rapidly moving line from individual queues at several stations. • This model is used at most supermarkets.

  9. ATM’s & Queues • Serpentine Model • Customers form a single line, and advance to the front to get their service. • Used at most airline ticket counters and in many post offices

  10. ATM’s & Queues • Analyzing how to manage queues often uses computer simulation • Two types of Simulation • Monte Carlo • Bootstrapping

  11. ATM’s & Queues • Monte Carlo Simulation • Sample data is used to estimate the actual probability distribution of some random variable. • This theoretical distribution is then used to generate new samples.

  12. ATM’s & Queuing • Bootstrapping • When the data does not indicate any known theoretical probability distribution, we can simulate new data by random sampling from the original data

  13. ATM’s & Queues • Class Project • The People’s Bank has 3 ATM’s • At least one ATM is available 24 hours a day 7 days a week • Bank manager has records of ATM usage and customer service times for 5 weeks

  14. ATM’s & Queues • Mean numbers of customers arriving for ATM usage during every hour of the week is contained in Queue Data.xls. • The complete arrival data for the 9:00 a.m. and 9:00 p.m. hours on Fridays are shown in that file as well. • These hours happen to be the bank’s busiest days of service.

  15. ATM’s & Queues • We will study the queues for the ATM’s during: • The 9:00am hour on Friday • The 9:00pm hour on Friday • The starting and ending times of ATM service were recorded for each arriving customer. • Data for these service times during the first week of record keeping are shown in Queue Data.xls.

  16. ATM’s & Queues • Bank manager wants to avoid long wait times, long queue lengths, and do this using the least number of ATM’s • The bank manager would like to know what level of service to provide for managing the queues based on: • Services Times for individual customers • The number of customers waiting to be served

  17. ATM’s & Queues • Terms: • Wait Time (in min): The period of time that a customer must wait between arrival and the start of his or her access to an ATM • Delayed: A person who must wait more than 5 minutes • Number in Queue: the number of people in line waiting before an arriving customer can reach an ATM • Irritated: queue length is more than 3 customers • Total Present: the total number of patrons present in the queue

  18. ATM’s & Queues • The bank manager is looking at three advertising claims for service times: • (Mean Wait Claim) The mean waiting time is at most 1 minute. • (Maximum Wait Claim) No one will wait more than 12 minutes. • (Percent Delayed Claim) At most 5% of the customers will be delayed (wait more than 5 minutes)

  19. ATM’s & Queues • The bank manager is also looking at three advertising claims for the number of customers waiting in line: • (Mean Queue Claim) The mean number of people in the queue will not exceed 8. • (Percent Irritated Claim) At most 2% of the customers will be irritated (find more than 3 people in line or waiting to be served). • (Maximum Present Claim) The total number present will never exceed 10.

  20. ATM’s & Queues • Project Assumptions: • No one is using an ATM or waiting for a machine at the start of the hour. • Service times for each ATM have the same distribution as sampled in Week 1 Service Times in the sheet Data of Queue Data.xls.

  21. ATM’s & Queues • Project Assumptions (cont) • The time until the first arrival and the times between arrivals of customers have the same distribution. • In the standard queuing model, if more than one ATM is open, arriving customers enter the shortest of the existing queues. If two or more queues are the same length, a customer selects a queue at random.

  22. ATM’s & Queues • Objectives: • Based only on 9 a.m. hour on Fridays, how many ATM’s should be opened and what queuing model should be used to validate each advertising claim during 9-10 a.m. period? • Based only on 9 p.m. hour on Fridays, how many ATM’s should be opened and what queuing model should be used to validate each advertising claim during 9-10 p.m. period? NOTE: We only consider the use of a serpentine model when three ATM’s are in use

  23. ATM’s & Queues • Objectives (cont) • Finding the hourly cost of a gift certificate program for 3 ATM’s Serpentine: • If a serpentine queue is used, customers don’t physically stand in a line because the bank currently uses a number dispenser and service indicator that gives customers slips of paper indicating their position in the queue.

  24. ATM’s & Queues • Objectives (cont) • Finding the cost of gift certificate program (cont) • Bank is considering updating to a system that stamps the arrival time of a customer which could be used to document a customer’s wait time • The hourly cost for such an upgrade (maintenance, purchase price, etc.) is $20

  25. ATM’s & Queues • Objectives • Finding the cost of the gift certificate program (cont) • A $25 gift to any customer who is delayed (waits more than 5 minutes). • What is the expected hourly cost of such a plan? How would this change if it is estimated that only 60% of eligible customers would decide to claim the gift?

  26. ATM’s & Queues • Team Data will be posted on class web page • Data includes • historical records of ATM service times and customer arrival times for two hours out of each week • Parameters for six potential advertising strategies. • Mean Wait Claim • Maximum Wait Claim • Percent Delayed Claim • Mean Queue Claim • Percent Irritated Claim • Maximum Present Claim

  27. ATM’s & Queues Team Data will be posted after Spring Break Team Preliminary Report • Date: Monday March 31st, 2008

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