Waiting Time Management Chapter 11

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

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 Chapter 11 - Waiting Time Management 5

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

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

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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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 3 0 8:57 Total 50 7 Chapter 11 - Waiting Time Management 13

Chapter 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 person Chapter 11 - Waiting Time Management 14

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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 Number in line = (1) >18 (2) 1.2 Chapter 11 - Waiting Time Management 19

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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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

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

Chapter 11 - Waiting Time Management 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

Chapter 11 - Waiting Time Management 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