Waiting Time ManagementChapter 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)

Chapter 11 - Waiting Time Management 1

– Importance

• THE customer service standard

• “Halo” “Pitchfork” effect

– Lack of Managerial Intuition

• Difficulty - Linear thinkers need not apply

• How long is the waiting line if a customer arrives exactly every 15 seconds and can be served in exactly 14 seconds?

Waiting Line Pop Quiz!

Chapter 11 - Waiting Time Management 3

• How long is the waiting line if those times are not exact, but only averages?

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

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

5Chapter 11 - Waiting Time Management

Transactions performed in an hour by one worker: 60/5=12

Transaction Ave. Time PercentageCashiers' 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

Work content for the average customer

Chapter 11 - Waiting Time Management 6

AverageTime May 1 May 8 May 15 # 0f Transactions08:00-09:00 6 12 9 909:00-10:00 4 11 12 910:00-11:00 18 24 39 2711:00-12:00 52 28 28 3612:00-13:00 40 60 35 4513:00-14:00 31 25 25 2714:00-15:00 25 10 19 1815:00-16:00 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)

Customer Arrivals at FeeHappy

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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 27 314:00-15:00 18 215:00-16:00 9 1

Effect of Variance:

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Variance of Transaction Times and Number of Customers– Average day, 11:00-12:00: : 36 transactions x 5

minutes/transaction = 180 minutes of work180 minutes of work = 3 workers

– Heavy day, May 1, 11:00-12:0052 transactions: 6 accounts opened, 4 disputes... (higher than average transaction time)52 transactions x 7 minutes/transaction = 364 minutes of work364 minutes of work = 6 workers

Effect of Variance:

Chapter 11 - Waiting Time Management 9

Capacity

Waiting

10

Waiting Line MathECONOMICS OF WAITING LINES

$

None A lot

Service Facility Capacity

Chapter 11 - Waiting Time Management

12

1

Conventional “Wisdom”

Actual Relationship

Waiting Line Math

Lin

e

Le

ngt

h

Excess TightCapacity  

11Chapter 11 - Waiting Time Management

A TALE OF TWO TELLERS

One teller scenario

Arrival Transaction Waiting LeavesTime Transaction Time Time Teller08:00 Balance Inquiry 1 0 8:0108:04 Deposit/cash back 2 0 8:0608:08 Open account 25 0 8:3308:19 Cashier’s check 10 14 8:4308:25 Other 3 18 8:4608:29 Deposit/cash back 2 17 8:4808:46 Straight deposit 1 2 8:4908:52 Other 3 0 8:5508:54 Other 3 1 8:58

Total 50 52

Chapter 11 - Waiting Time Management 12

Two teller scenario Arrival Transaction Waiting Leaves

LeavesTime Transaction Time Time Teller 1

Teller 208:00 Balance Inquiry 1 0 8:0108:04 Deposit/cash back 2 0 8:0608:08 Open account 25 0 8:3308:19 Cashier’s check 10 0 8:2908:25 Other 3 4 8:3208:29 Deposit/cash back 2 3 8:3408:46 Straight deposit 1 0 8:4708:52 Other 3 0 8:5508:54 Other 3 0 8:57

Total 50 7

13Chapter 11 - Waiting Time Management

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 personChapter 11 - Waiting Time Management 14

ρ = Utilization = λ/μnL = 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

Waiting Line Math

Chapter 11 - Waiting Time Management 15

• 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

Waiting Line Math

Chapter 11 - Waiting Time Management 16

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 minutesUtilization = 75%

– Server 6x as fast:Time = 1.4 minutesUtilization = 63%

Customer Arrivals at FeeHappy

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• 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??

Customer Service and Waiting Lines

Chapter 11 - Waiting Time Management 18

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

Table 11.11: Multiple Servers, Ave. Number in Line

Sharing lines

Separate 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

Centralization of Waiting Lines

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Solutions1. Recognize speed of service/efficiency

trade-off

2. Reduce randomness of arrivals

- appointment systems

- pricing incentives

3. Reduce randomness of service time

4. System changes

- pooling resources

- reducing handoffs

Chapter 11 - Waiting Time Management 21

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

• 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

Psychology of Queuing

Chapter 11 - Waiting Time Management 23

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