1. Simulation Study of a Call Center Gaurav Chhabra & Sachin Jayaswal

2. 2 Motivation  Rapid growth in Call Center industry in the last decade  Call center targets a specific level of service to its customers  Staff level – a major decision

3. 3 Problem Definition  Customer Classes  Regular  Priority  Service levels  Maximum time on hold  Maximum abandonment rate  Objective: To determine the optimum staffing level

4. 4 Input Data  Pattern of call arrivals  Pattern of call service  Call mix  Balk probability, renege probability  Target service levels

5. 5 Output Measures  Percentage of customers served who spent less than the target time on hold  Percentage of customers who hung up without being served (abandonment rate)

6. 6 Data Collection  Call arrivals - Number of calls made every 15 minutes (converted to IAT)  Service times - Number of seconds needed to serve a call

7. 7 Distribution of Inter-Arrivals Times

8. 8 Distribution of Service Times

9. 9  Different scenarios considered:  Priority Calls – 50%, 40%, 30%, 20%, 10% Call Mix

10. 10  Balk – 5% of the customers balk when they find line busy  Renege Distribution  Literature Review:  Parkan 1987  Harris, Hoffman, and Saunders 1987  Our Model:  CONT(0.0,1,0.25, 2, 0.40, 3,0.50,4,0.70,5,1.0,6) Balk and Renege Distributions

11. 11 Renege Distributions

12. 12 Target Service Levels  Priority Calls  Calls attended within 1 minute >= 90%  Abandonment rate <= 5%  Regular Calls  Calls attended within 5 minutes >= 80%  Abandonment rate <= 10%

13. 13 Simulation Model

14. 14

15. 15 Results % of priority Calls Performance Measures # of Agents 121314 50% Service Level - Priority[80.61,83.63][86.35,89.37][92.74,94.30] Service Level - Regular[98.30,98.70][98.78,98.98][98.82,99.06] Abandonment Rate - Priority[5.08,6.18][3.98,4.82][2.36,3.00] Abandonment Rate - Regular[18.64,21.40][10.74,13.34][4.74,5.98] Avg. wait time - Rapid[0.46,0.52][0.33,0.39][0.18,0.22] Avg. wait time - Regular[0.91,1.03][0.56,0.68][0.30,0.38] Agent Utilization[0.980.0.980][0.962,0.962][0.931,0.931]

16. 16 % of priority Calls Performance Measures # of Agents 121314 40% Service Level - Priority[81.04,84.14][87.27,89.67][93.12,94.84] Service Level - Regular[98.48,98.82][98.82,99.02][98.86,99.08] Abandonment Rate - Priority[5.40,6.96][3.70,4.86][2.12,3.10] Abandonment Rate - Regular[16.99,19.51][9.59,11.71][4.63,6.07] Avg. wait time - Rapid[0.45,0.51][0.32,0.36][0.17,0.21] Avg. wait time - Regular[0.93,1.03][0.56,0.68][0.29,0.37] Agent Utilization[0.982,0.982][0.965,0.965][0.932,0.932]

17. 17 % of priority Calls Performance Measures # of Agents 121314 30% Service Level - Priority[82.73,85.65][90.09,92.23][93.52,94.86] Service Level - Regular[98.77,98.97][98.87,99.05][98.95,99.11] Abandonment Rate - Priority[5.01,6.51][3.42,4.70][2.18,2.98] Abandonment Rate - Regular[15.79,17.59][8.54,10.22][4.30,5.08] Avg. wait time - Rapid[0.44,0.48][0.29,0.33][0.18,0.20] Avg. wait time - Regular[0.95,1.07][0.57,0.65][0.31,0.37] Agent Utilization[0.982,0.982][0.964,0.964][0.936,0.936]

18. 18 % of priority Calls Performance Measures # of Agents 121314 20% Service Level - Priority[83.89,86.85][89.83,92.17][93.43,95.47] Service Level - Regular[98.83,99.05][98.95,99.13][98.99,99.15] Abandonment Rate - Priority[4.61,6.57][2.97,4.41][2.27,3.07] Abandonment Rate - Regular[14.69,16.31][7.68,9.28][3.78,4.84] Avg. wait time - Rapid[0.42,0.46][0.27,0.31][0.16,0.20] Avg. wait time - Regular[0.94,1.06][0.53,0.63][0.28,0.34] Agent Utilization[0.983,0.983][0.963,0.963][0.933,0.933]

19. 19 % of priority Calls Performance Measures # of Agents 121314 10% Service Level - Priority[84.06,87.46][89.36,93.00][92.37,95.09] Service Level - Regular[98.95,99.15][99.04,99.18] Abandonment Rate - Priority[3.43,6.81][3.09,4.97][1.29,3.17] Abandonment Rate - Regular[13.24,14.46][7.12,8.48][3.83,4.61] Avg. wait time - Rapid[0.38,0.42][0.25,0.31][0.17,0.21] Avg. wait time - Regular[0.90,1.00][0.54,0.64][0.29,0.37] Agent Utilization[0.983,0.983][0.966,0.966][0.937,0.937]

20. 20 Future Research Directions  Non Stationary Distribution of Call Arrivals  Staff Scheduling  Different models for Balk/Renege

21. 21 Comments/Questions