//9 Chapter 8 Variability and Waiting Problems A Call Center Example Arrival Process and Service Variability Predicting Waiting s Waiting Line Management 8. The Operation of a Typical Call Center Incoming calls Calls on Hold Sales reps processing calls Call center Answered Calls Blocked calls (busy signal) Lost throughput Abandoned calls (tired of waiting) Holding cost Lost goodwill Lost throughput (abandoned) Cost of capacity Cost per customer At peak, 8% of calls dialed received a busy signal. Customers getting through had to wait on average min. Extra telephone expense per day for waiting was $,. $$$ Revenue $$$
//9 A Perfect or Somewhat Odd Call Center Patient 8 9 Arrival Service : : : : : : 8: A More Realistic Service Process Patient Arrival 9 8 8 9 Service Patient Patient Patient Patient Patient 9 Patient Patient Patient Patient Patient 8 Patient Patient : : : : : : 8: Number of cases min. min. min. min. min. min. Service times
//9 Variability Leads to Waiting Patient Arrival Service 8 9 9 8 Inventory (Patients at lab) : : : : : : Wait time Service time 8: : : : : : : 8: 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.
//9 8. Variability: Where does it come from? Tasks Inherent variation Lack of SOPs Quality (scrap / rework) Input Unpredicted Volume swings Random arrivals (randomness is the rule, not the exception) Incoming quality Product Mix Buffer Processing Resources Breakdowns / Maintenance Operator absence Set up times Routes Variable routing 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
//9 8. Analyzing an Arrival Process Call Arrival, AT i ::9 :: :: :: :: :: ::8 Interarrival IA i =AT i+ AT i : : : : : :8 Call Call Call Call Call Call Call : : : : : : : IA IA IA IA IA IA Coefficient of Variation Standard Deviation Mean 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 minutes 8 : : : : : 9: : : : : : 9: : :
//9 Exponential Distribution Customers arriving independently from each other follow exponential inter arrival times. Random (Poisson) arrivals Number of calls with given duration t 9 8 f ( t) e a t a a = average inter arrival time Duration t How to Analyze a Demand/Arrival Process YES Stationary Arrivals? NO YES Random Arrivals? NO Break arrival process up into smaller time intervals Compute a: average interarrival time CV a = All results of chapters 8 and 9 apply Compute a: average interarrival time CV a = St.dev. of interarrival times/a All results of chapter 8 apply Results of chapter 9 do not apply, require simulation or more advanced tools mean a Standarddeviationof interarrival time CVa Averageinterarrival time
//9 8. Service s in Call Center Frequency 8 Std. Dev =. Mean =. N =. Call durations [seconds] mean p Standarddeviationof activity time CVp Averageactivity time 8. Predicting Average Waiting : One Server Inventory waiting I q Inventory in service I p Inflow Outflow Entry to system Waiting T q Begin Service Service p Departure Flow T=T q +p
//9 The Waiting Formula utilization flow rate capacity / a / p p a % utilization CV in queue Activity a CV p utilization Average flow time T Increasing Variability Service time factor Utilization factor Variability factor Utilization % 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 8
//9 8. Multiple, Parallel Resources with One Queue Inventory in service I p Inflow Inventory waiting I q Outflow Flow rate Entry to system Begin Service Departure in queue T q Service p Flow T=T q +p 8 Waiting for Multiple, Parallel Resources Under the assumption that Utilization Flow rate / interarrival time / a p Capacity m (/ activity time) m / p a m we approximate the average waiting time as ( m Activity time utilization in queue m utilization ) CV a CV p 9 9
//9 The Power of Pooling Independent Resources x(m=)... Waiting T q m=.. m=.. m= m=. % % % % 8% 8% 9% 9% Utilization u Pooled Resources (m=) Pooling benefits are lower if queues are not truly independent 8. Service Levels in Waiting Systems Fraction of customers who have to wait x seconds or less.8.. Waiting times for those customers who do not get served immediately Fraction of customers who get served without waiting at all. Waiting time [seconds] TWT 9% of calls had to wait seconds or less Target Wait (TWT) depends on your market position and the importance of incoming calls for your business Service Level = Probability{Waiting TWT}
//9 Staffing & Incoming Calls over the Course of a Day Number of customers Per minutes 8 : : : : : 9: : : : : : 9: : : Number of CSRs 9 8 8. Priority Rules in Waiting Systems First Come First Serve: easy to implement + perceived fairness Shortest Processing Rule: Minimizes average waiting time Sequence based on importance: emergency or profitable customers A: 9 minutes B: minutes C: minutes D: 8 minutes A C 9 min. B min. D 9 min. C min. A min. D min. B Total wait time: 9+9+=min Total wait time: ++=8 min
//9 8. Reducing Variability Reduce Arrival Variability appointment/reservation: how to handle late arrivals or no shows encourage customers to avoid peak hours. Reduce Service Variability training and technology limit service selection reduce customer involvement Actual Wait vs. Perceived Wait Perceived Wait Amount of time customers believe they have waited prior to receiving service. Has a greater effect on customer satisfaction than actual waiting time Satisfaction.8... t* threshold sensitivity Perceived Wait
//9 Factors Affecting Perceived Wait s Server Related Factors Passive vs. active waits Unfair vs. fair waits Uncomfortable vs. comfortable waits Unexplained vs. explained waits Unproductive vs. Productive waits Customer Related Factors Solo versus group waits Waits for more valuable versus less valuable services Customer s own tolerance Suggestions for Managing Queues. Determine an acceptable waiting time for your customers. Try to divert your customer s attention when waiting. Inform your customers of what to expect. Keep employees not serving the customers out of sight. Segment customers. Train your servers to be friendly. Encourage customers to come during the slack periods 8. Take a long term perspective (and redesign the system)
//9 Balancing Efficiency with Responsiveness Responsiveness High Increase staff (lower utilization) System improvement (e.g. pooling of resources) Responsive process with high costs Now Reduce staff (higher utilization) Low High per unit cost (low utilization) Low cost process with low responsiveness Frontier reflecting current process Low per unit cost (high utilization) Efficiency 9 Variability is the norm, not the exception understand where it comes from and eliminate what you can Variability leads to waiting times although utilization<% Operations benefit from flexibility in capacity Demand can exhibit seasonality varying capacity Pooling resources can reduce waiting times Managing customers perceived wait times