Chapter 8 Variability and Waiting Time Problems A Call Center - PDF document

2015/3/29 Chapter 8 Variability and Waiting Time Problems A Call Center Example  Arrival Process and Service Variability  Predicting Waiting Times  Waiting Line Management  8.1 The Operation of a Typical Call Center Call center Answered Incoming Calls Sales reps calls Calls processing calls on Hold  At peak, 80% of calls dialed received a busy signal.  Customers getting through had to wait on average 10 min.  Extra telephone Blocked calls Abandoned calls expense per day for (busy signal) (tired of waiting) waiting was $25,000. Holding cost Cost of capacity Lost throughput $$$ Revenue $$$ Lost goodwill Cost per customer Lost throughput (abandoned) 3 1

2015/3/29 A “Perfect or Somewhat Odd” Call Center Arrival Service Patient Time Time 1 0 4 2 5 4 3 10 4 4 15 4 5 20 4 6 25 4 7 30 4 8 35 4 9 40 4 10 45 4 11 50 4 12 55 4 7:00 7:10 7:20 7:30 7:40 7:50 8:00 4 A More Realistic Service Process Patient 1 Patient 3 Patient 5 Patient 7 Patient 9 Patient 11 Patient Arrival Service Time Time Patient 2 Patient 4 Patient 6 Patient 8 Patient 10 Patient 12 1 0 5 2 7 6 Time 3 9 7 7:00 7:10 7:20 7:30 7:40 7:50 8:00 4 12 6 5 18 5 3 6 22 2 Number of cases 7 25 4 2 8 30 3 9 36 4 1 10 45 2 11 51 2 0 2 min. 3 min. 4 min. 5 min. 6 min. 7 min. 12 55 3 Service times 5 2

2015/3/29 Variability Leads to Waiting Time Patient Arrival Service Time Time 1 0 5 Service time 2 7 6 3 9 7 4 12 6 5 18 5 Wait time 6 22 2 7 25 4 8 30 3 9 36 4 7:00 7:10 7:20 7:30 7:40 7:50 8:00 10 45 2 5 11 51 2 12 55 3 4 3 Inventory (Patients at 2 lab) 1 0 7:00 7:10 7:20 7:30 7:40 7:50 8:00 6 Observations Most customers have to wait, although, on average, there is plenty of capacity in the call center. The call canter is unable to provide consistent service quality. If customer abandon calls after long waits, the call center loses customer goodwill and revenue. 7 3

2015/3/29 8.2 Variability: Where does it come from? Tasks • Inherent variation • Lack of SOPs • Quality (scrap / rework) Processing Buffer Input • Unpredicted Volume swings Resources • Random arrivals • Breakdowns / Maintenance (randomness is the rule, • Operator absence not the exception) • Set ‐ up times Routes • Incoming quality • Variable routing • Product Mix • Dedicated machines 8 Ignoring Variability Leads to Problems Random arrivals and varying demands are common in services. In the presence of variability, one cannot estimate the process performance based on averages. Q: Why does variability not average out over time? A: You cannot inventory services — Capacity can never run ahead of demand. 9 4

2015/3/29 8.3 Analyzing an Arrival Process Arrival Interarrival Call Time, AT i Call 1 Call 2 Call 3 Call 4 Call 5 Call 6 Call 7 Time IA i =AT i+1 ‐ AT i 1 6:00:29 00:23 2 6:00:52 01:24 3 6:02:16 00:34 4 6:02:50 6:00 6:01 6:02 6:03 6:04 6:05 6:06 Time 02:24 5 6:05:14 00:36 6 6:05:50 IA 1 IA 2 IA 3 IA 4 IA 5 IA 6 00:38 7 6:06:28 Standard Deviation  Coefficien t of Variation Mean 10 Seasonality over the Course of a Day An arrival process is not stationary if the average number of arrivals in any given time interval is not fixed over the entire time period. no. of customers per 15 minutes 160 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0 0:15 0:15 2:00 2:00 3:45 3:45 5:30 5:30 7:15 7:15 9:00 9:00 10:45 10:45 12:30 12:30 14:15 14:15 16:00 16:00 17:45 17:45 19:30 19:30 21:15 21:15 23:00 23:00 Time 11 5

2015/3/29 Exponential Distribution Customers arriving independently from each other follow exponential inter ‐ arrival times.  Random (Poisson) arrivals 100 90 Number of calls with given duration t 80 70 60 t   1 f ( t ) e a 50 a 40 30 a = average inter ‐ arrival time 20 10 0 Duration t 12 How to Analyze a Demand/Arrival Process Stationary Arrivals? YES NO Random Arrivals? Break arrival process up into smaller time intervals YES NO • Compute a : average interarrival time • Compute a : average interarrival time • CV a = St.dev. of interarrival times/ a • CV a =1 • All results of chapter 8 apply • All results of chapters 8 and 9 apply • Results of chapter 9 do not apply, require simulation or more advanced tools Standard deviation of interarriv al time   mean a CV a Average interarriv al time 13 6

2015/3/29 8.4 Service Times in Call Center 800 Frequency 600 400 Std. Dev = 141.46 Mean = 127.2 N = 2061.00 200 Call durations 0 [seconds] Standard deviation of activity t ime   mean p CV p Average activity t ime 14 8.5 Predicting Average Waiting Time: One Server Inventory Inventory waiting I q in service I p Inflow Outflow Entry to Begin Departure system Service Waiting Time T q Service Time p Flow Time T=T q +p 15 7

2015/3/29 The Waiting Time Formula flow rate 1 / a p     utilizatio n 100 % capacity 1 / p a      2 2 CV CV utilizatio n        a p Time in queue Activity Time      1 utilizatio n  2  Variability factor Average flow time T Utilization factor Service time factor Increasing Variability Utilization 100% 16 Reducing average waiting time does not guarantee customer satisfaction. A small percentage of customers may experience long waits and complain bitterly. Solution: service guarantee and/or service recovery 17 8

2015/3/29 8.6 Multiple, Parallel Resources with One Queue Inventory in service I p Inventory waiting I q Outflow Inflow Flow rate Entry to system Begin Service Departure Time in queue T q Service Time p Flow Time T=T q +p 18 Waiting Time for Multiple, Parallel Resources Under the assumption that Flow rate 1 / interarriv al time 1 / a p      Utilizatio n 1   Capacity m ( 1 / activity t ime) m / p a m we approximate the average waiting time as        2 2   2 ( m 1 ) 1 CV CV Activity time utilizatio n          a p Time in queue        m 1 utilizatio n 2     19 9

2015/3/29 The Power of Pooling Independent Resources 70.00 2x(m=1) m=1 60.00 Waiting Time T q 50.00 40.00 m=2 30.00 20.00 m=5 10.00 m=10 0.00 60% 65% 70% 75% 80% 85% 90% 95% Utilization u Pooling benefits are lower if queues are not truly independent Pooled Resources (m=2) 20 8.7 Service Levels in Waiting Systems 1 90% of calls had Fraction of to wait 25 Waiting times for those customers who 0.8 seconds or less customers who do not get served immediately have to wait x 0.6 seconds or less Fraction of customers who get 0.4 served without waiting at all 0.2 Waiting time [seconds] 0 TWT 0 50 100 150 200 Target Wait Time (TWT) depends on your market position and the importance of incoming calls for your business Service Level = Probability{Waiting Time  TWT} 21 10

2015/3/29 Staffing & Incoming Calls over the Course of a Day Number of customers Number of Per 15 minutes CSRs 160 160 17 16 140 140 15 14 120 120 13 12 100 100 11 10 9 80 80 8 7 60 60 6 5 40 40 4 3 2 20 20 1 0 0 Time 0:15 0:15 2:00 2:00 3:45 3:45 5:30 5:30 7:15 7:15 9:00 9:00 10:45 10:45 12:30 12:30 14:15 14:15 16:00 16:00 17:45 17:45 19:30 19:30 21:15 21:15 23:00 23:00 22 8.10 Priority Rules in Waiting Time Systems  First ‐ Come ‐ First ‐ Serve: easy to implement + perceived fairness  Shortest Processing Time Rule: Minimizes average waiting time  Sequence based on importance: emergency or profitable customers A: 9 minutes B: 10 minutes C: 4 minutes D: 8 minutes A C B D 9 min. 4 min. C 13 min. A 19 min. D B 23 min. 21 min. Total wait time: 4+13+21=38 min Total wait time: 9+19+23=51min 23 11

2015/3/29 8.11 Reducing Variability Reduce Arrival Variability  appointment/reservation: how to handle late arrivals or no ‐ shows  encourage customers to avoid peak hours. Reduce Service Time Variability  training and technology  limit service selection  reduce customer involvement 24 Actual Wait Time vs. Perceived Wait Time Perceived Wait Time Satisfaction  Amount of time customers 1 believe they have waited sensitivity 0.8 prior to receiving service. 0.6  Has a greater effect on 0.4 customer satisfaction than 0.2 actual waiting time 0 t* Perceived Wait threshold 25 12

2015/3/29 Factors Affecting Perceived Wait Times Customer ‐ Related Factors Server ‐ Related Factors  Solo versus group waits  Passive vs. active waits  Waits for more valuable  Unfair vs. fair waits versus less valuable  Uncomfortable vs. services comfortable waits  Customer’s own tolerance  Unexplained vs. explained waits  Unproductive vs. Productive waits 26 Suggestions for Managing Queues 1. Determine an acceptable waiting time for your customers 2. Try to divert your customer’s attention when waiting 3. Inform your customers of what to expect 4. Keep employees not serving the customers out of sight 5. Segment customers 6. Train your servers to be friendly 7. Encourage customers to come during the slack periods 8. Take a long ‐ term perspective (and redesign the system) 27 13