2. Khudyakov Polina Designing a Call Center with an IVR MSc. Seminar Advisor: Professor Avishai Mandelbaum

3. Call centers around the world Call center operators represent: 4% of the workforce in USA 1.8% of the workforce in Israel 1.5% of the workforce in Great Britain 0.5% of the workforce in France All Fortune 500 companies haves at least one call center, which employs on average 4,500 agents More than $300 billion is spent annually on call centers around the world

4. Quality of service 92% of U.S. consumers form their image of a company based on their experience using the company’s call center 63% of the consumers stop using a company’s products based on a negative call center experience almost 100% of the consumers between ages 18 and 25 stop using a company’s products based on a negative call center experience

5. Future of call centers

6. Self-services Interactive Voice Response (IVR) Outbound Voice Messaging (OVM) The Web Outbound Email Speech Recognition

7. Three sound reasons for using IVR Improved customer satisfaction reduce queue times extended service hours offer privacy Increased revenue extended business hours unload trained agents from routine requests and simple service Reduced cost typical service phone call involving a real person costs 7$ an Internet transaction, with a person responding, costs 2.5$ a “self-service” phone call with no human interaction costs 50 cent

8. Halfin and Whitt (1981) (M/M/S) Massey and Wallace (2004) (M/M/S/N) Garnet, Mandelbaum and Reiman (2002) (M/M/S+M) Srinivasan, Talim and Wang (2002) (Call center with an IVR) Background

9. Customer interaction with a call center with an IVR Customer joining the system … End of Service Waiting in queue IVR

10. Schematic model 1 2 3 N...... 1-p 1 2 S...... … N-S p “ IVR ” N servers “ Agents ” S servers λ θ μ

11. Model description N – number of trunk lines Poisson(λ) - arrival process exp(θ) - IVR service time p – probability to request agent’s service S – number of agents exp(μ) - agent’s service time No abandonment

12. Closed Jackson network … 1 2 p 1-p N servers S servers exp(θ) exp(μ) … 3 1 server exp(λ)

13. Stationary probabilities Stationary distribution of closed Jackson network (product form) Stationary probabilities of having i calls at the IVR and j calls at the agents pool where

14. Probability to find the system busy Srinivasan, Talim and Wang (2002) Probability (busy signal)= P (N call in the system( PASTA ))=

15. waiting time Srinivasan, Talim and Wang (2002) Probability that the system is in state (i,j), when a call is about to finish its IVR process: Distribution function of the waiting time Expected waiting time

16. Other performance measures Expected queue length Agents’ utilization Offered load

17. Operational regimes Quality - Driven Few busy signal Short waiting time for agents Agents over IVR Efficiency - Driven High utilization of agents IVR over Agents Quality&Efficiency – Driven (QED) Careful balance between service quality and resources efficiency

18. The domain for asymptotic analysis: QED M/M/S/N queue (Massey A.W. and Wallace B.R.) Our system (intuition)

19. The domain for asymptotic analysis: QED (continuation) Theorem. Let λ, S and N tend to simultaneously. Then the conditions are equivalent to the conditions where QED

20. Approximation of P(W>0) Theorem. where Let λ, S and N tend to simultaneously and satisfy the QED conditions, where μ, p, θ are fixed. Then

21. Exact formula for P(W>0) Exact Approximate

22. Illustration of the P(W>0) approximation A smal-size call center 0 0.2 0.4 0.6 0.8 1 1.2 13579 11131517192123 252729 S, agents exact approx A mid-size call center 0 0.2 0.4 0.6 0.8 1 1.2 303234363840424446485052545658606264666870 S, agents exact approx 0 0.2 0.4 0.6 0.8 1 1.2 6062646668707274767880828486889092949698 100 S, agents exact approx A large call center - 0 0.2 0.4 0.6 0.8 1 1.2 450455460465470475480485490495500505510515520525530535540545550 S, agents approx A mid-size call center

23. Approximation of P(busy) Theorem. where Let λ, S and N tend to simultaneously and satisfy the QED conditions, where μ, p, θ are fixed. Then

24. Approximation of E[W] where Theorem. Let λ, S and N tend to simultaneously and satisfy the QED conditions, where μ, p, θ are fixed. Then

25. Approximation of waiting time density Theorem. where Let λ, S and N tend to simultaneously and satisfy the QED conditions, where μ, p, θ are fixed. Then

26. Illustration of the waiting time density

27. QED Performance :characterization :Quality - Driven :Efficiency - Driven

28. Special cases M/G/N/N loss system (Jagerman)

29. Special cases M/M/S system (Halfin and Whitt)

30. Theorem. Special cases (M/M/S/N system) Let λ, S and N tend to simultaneously and satisfy the following conditions: where is fixed. Then

31. Costs of call center Salaries – 63% Hiring and training costs – 6% Costs for office space – 5% Trunk costs – 5% IT and telecommunication equipment – 10% Others – 11%

32. Costs of call center Salaries – 63% Hiring and training costs – 6% Costs for office space – 5% Trunk costs – 5% IT and telecommunication equipment – 10% Others – 11%

33. Optimization problem - cost of an agent per time unit - telephone cost per trunk and time unit - number of staffed agents - number of telephone trunks - expected trunk utilization

34. IVR vs. Agents

36. Add abandonment and retrials to the model Mixed customer population Dimensioning: finding the parameters and for given cost of an agent and cost of customer’s delay Possible future research