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Waiting Time Management

Waiting Time Management. Chapter 11. Why?? Pervasiveness of Problem Retail staffing Back-office staffing Example: Call Centers (US economy) number: 20,000 – 350,000 people: 4 million – 6.5 million expenses: $100B - $300B (50-75% labor). Importance

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Waiting Time Management

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  1. Waiting Time Management Chapter 11

  2. Why?? • Pervasiveness of Problem • Retail staffing • Back-office staffing • Example: • Call Centers (US economy) • number: 20,000 – 350,000 • people: 4 million – 6.5 million • expenses: $100B - $300B (50-75% labor) • Importance • THE customer service standard • “Halo” “Pitchfork” effect • Lack of Managerial Intuition • Difficulty - Linear thinkers need not apply Chapter 11 - Waiting Time Management 1

  3. Waiting Line Pop Quiz! How long is the waiting line if a customer arrives exactly every 15 seconds and can be served in exactly 14 seconds? • How long is the waiting line if those times are not exact, but only averages? Chapter 11 - Waiting Time Management 3

  4. CASE STUDY (fictional): FeeHappy Savings & Loan • Target Market: • Professionals, High net worth individuals, Small/medium businesses • Operational Focus: High Service • Question to Answer: • Given work load, how many reps? Chapter 11 - Waiting Time Management 4

  5. Work Content at FeeHappy • How many customer service reps are needed? • average work content per customer x • average number of customers/day = average work per day Chapter 11 - Waiting Time Management 5

  6. Work content for the average customer Transaction Ave. Time Percentage Cashiers' check 10 5% Open checking account 25 5% Deposit/cash back 2 25% Straight deposit 1 10% Corporate deposit 8 10% Balance inquiry 1 5% Dispute 15 5% Other 3 35% Average transaction: 5 minutes Transactions performed in an hour by one worker: 60/5=12 Chapter 11 - Waiting Time Management 6

  7. Customer Arrivals at FeeHappy Average Time May 1 May 8 May 15 # 0f Transactions 08:00-09:00 6 12 9 9 09:00-10:00 4 11 12 9 10:00-11:00 18 24 39 27 11:00-12:00 52 28 28 36 12:00-13:00 40 60 35 45 13:00-14:00 31 25 25 27 14:00-15:00 25 10 19 18 15:00-16:00 5 7 15 9 Total: 181 177 182 180 180 transactions x 5 minutes/transaction x 1 hour/60 minutes = 15 hours of work/day 15 hours of work = 1.875 workers(2 workers) Chapter 11 - Waiting Time Management 7

  8. Effect of Variance: Variance of Customer Arrivals During the Day Workers handle 12 transactions per hour Time Number of Transactions Workers Needed 08:00-09:00 9 1 09:00-10:00 9 1 10:00-11:00 27 3 11:00-12:00 36 3 12:00-13:00 45 4 13:00-14:00 27 3 14:00-15:00 18 2 15:00-16:00 9 1 Chapter 11 - Waiting Time Management 8

  9. Effect of Variance: • Variance of Transaction Times and Number of Customers • Average day, 11:00-12:00: 36 transactions x 5 minutes/transaction = 180 minutes of work • 180 minutes of work = 3 workers • Heavy day, May 1, 11:00-12:00 • 52 transactions: 6 accounts opened, 4 disputes... (higher than average transaction time) • 52 transactions x 7 minutes/transaction = 364 minutes of work • 364 minutes of work = 6 workers Chapter 11 - Waiting Time Management 9

  10. Waiting Line Math ECONOMICS OF WAITING LINES Waiting $ Capacity None A lot Service Facility Capacity Chapter 11 - Waiting Time Management 10

  11. Waiting Line Math 12 Conventional “Wisdom” Line Length Actual Relationship 1 Excess Tight Capacity Chapter 11 - Waiting Time Management 11

  12. A TALE OF TWO TELLERS One teller scenario Arrival Transaction Waiting Leaves Time Transaction Time Time Teller 08:00 Balance Inquiry 1 0 8:01 08:04 Deposit/cash back 2 0 8:06 08:08 Open account 25 0 8:33 08:19 Cashier’s check 10 14 8:43 08:25 Other 3 18 8:46 08:29 Deposit/cash back 2 17 8:48 08:46 Straight deposit 1 2 8:49 08:52 Other 3 0 8:55 08:54 Other 3 1 8:58 Total 50 52 Chapter 11 - Waiting Time Management 12

  13. Two teller scenario Arrival Transaction Waiting Leaves Leaves Time Transaction Time Time Teller 1 Teller 2 08:00 Balance Inquiry 1 0 8:01 08:04 Deposit/cash back 2 0 8:06 08:08 Open account 25 0 8:33 08:19 Cashier’s check 10 0 8:29 08:25 Other 3 4 8:32 08:29 Deposit/cash back 2 3 8:34 08:46 Straight deposit 1 0 8:47 08:52 Other 3 0 8:55 08:54 Other 30 8:57 Total 50 7 Chapter 11 - Waiting Time Management 13

  14. Waiting Line Math • λ (Arrival Rate - People/hour) • μ (Service Rate - People/hour) • Average time in line=arrival rate/[service rate(service rate-arrival rate)] • λ /[μ(μ-λ)] • 1/λ = Average Time Between Arrivals = minutes per person • 1/μ = Average Service Time = minutes per person Chapter 11 - Waiting Time Management 14

  15. Waiting Line Math ρ = Utilization = λ/μ nL = Average Number in Line = λ2/[μ(μ-λ)] nS = Average Number in the System = λ/(μ-λ) tL = Average Time in Line = λ/[μ(μ-λ)] tS = Average Time in the System = 1/(μ-λ) Pn = Probability of n People in the System = (1-λ/μ)(λ/μ)n Chapter 11 - Waiting Time Management 15

  16. Waiting Line Math • Basics: • if λ (Arrival Rate) > μ (Service Rate) then people are arriving faster than they can be served • infinite line if steady state condition. • if λ < μ, but close, big lines can still form Chapter 11 - Waiting Time Management 16

  17. Customer Arrivals at FeeHappy • FeeHappy 12:00-13:00 • λ (Arrival Rate) = 45 • μ (Service Rate) = 12 • Server 4x as fast: Time = 45/[48(48-45)]=19 minutes • Utilization = 94% • Server 5x as fast: Time = 3 minutes • Utilization = 75% • Server 6x as fast:Time = 1.4 minutes • Utilization = 63% Chapter 11 - Waiting Time Management 17

  18. Customer Service and Waiting Lines • Work content of an average day: 15 hours • If inventory allowed, 1.875 workers • Service level of 1.5 minute average wait: 6 workers • Worker utilization: 31% • Scheduling complications?? Chapter 11 - Waiting Time Management 18

  19. Multiple Servers • Two servers sharing same line: • Arrival rate = 40/hour • Service rate/server = 25/hour • Number in line = 2.92 • Two servers with separate lines: • Arrival rate for both = 20/hour; • Service rate = 25/hour • Number in line = 3.20 • Arrival rate for (1)= 24/hour; for (2) = 16/hour • Service rate = 25/hour • Number in line = (1) >18 (2) 1.2 Chapter 11 - Waiting Time Management 19

  20. Table 11.11: Multiple Servers, Ave. Number in Line Separate lines Sharing lines

  21. Centralization of Waiting Lines • Example: • Telephone call center • Average handle time per call = 3 minutes • Service level desired: Average seconds to answer = 10 • Call volume = 4,000 calls per hour • Call Volume Workload hours Staff Required Total Staff • Facilities per Facility per Facility per Facility Required • 20 200 10 14 280 •  8 500 25 30 240 •  4 1,000 50 56 224 •  2 2,000 100 107 214 •  1 4,000 200 209 209 Chapter 11 - Waiting Time Management 20

  22. Solutions • Recognize speed of service/efficiency trade-off • Reduce randomness of arrivals - appointment systems - pricing incentives • Reduce randomness of service time • System changes - pooling resources - reducing handoffs Chapter 11 - Waiting Time Management 21

  23. Psychology of Queuing"Perception is Essence" • Perception more important than reality  • Unoccupied time feels longer than occupied time • Operational Action: distract and entertain with related or unrelated activity • Preprocess waits feel longer than in-process waits • Anxiety makes waits feel longer • Operational Action: communicate as soon as possible, get customers "in-process" Chapter 11 - Waiting Time Management 22

  24. Psychology of Queuing • Uncertain waits feel longer than known waits • Unexplained waits feel longer • Operational Action: communicate frequently • Unfair waits feel longer • Operational Action: physically segment different markets Chapter 11 - Waiting Time Management 23

  25. Waiting Line Lessons • Intuition is poor • Matching service rate to customer arrival rate is a disaster • Waiting line decisions should be in synch with strategy Chapter 11 - Waiting Time Management 24

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