1. On the interaction between resource flexibility and flexibility structures Fikri Karaesmen, Zeynep Aksin, Lerzan Ormeci Ko ç University Istanbul, Turkey Sponsored by a KUMPEM research grant FIFTH INTERNATIONAL CONFERENCE ON "Analysis of Manufacturing Systems –Production Management" May 20-25, 2005 - Zakynthos Island, Greece

2. Outline Motivation The methodology Some structural results Numerical examples Work-in-Progress

3. Resource flexibility in practice: multilingual call (contact) centers Compaq’s call centers in Ireland: supports nine European languages Toshiba call center in Istanbul: eight European languages Similar centers for Dell, Gateway, IBM, DHL, Intel, etc. Language and cultural know-how mix. Language and technical skills mix. Excellent example of multi-skill service structure

4. Resource flexibility Part of a general framework that encompasses manufacturing and services –Flexible manufacturing capacity: assigning demand types to flexible plants –FMS: routing parts to the right flexible machine –Human resources: cross-training of workers or service representatives

5. Emerging questions What is the value of cross-training? What can be expected out of a good dynamic routing system? What is the right scale of flexibility? –is everyone x-trained? –if only some, how many? What is the right scope of flexibility? –can x-trained personnel deal with all calls? –if not, what is the right skills mix?

6. Related literature Process Flexibility –Jordan and Graves (1995): manufacturing flexibility, demand-plant assignments (motivated by a GM case) –Graves and Tomlin (2003) –Iravani, Van Oyen and Sims (2005) –Aksin and Karaesmen (2004) Flexible servers in queueing systems –Van Oyen, Senturk-Gel, Hopp (2001) –Pinker and Shumsky (2000) –Chevalier, Shumsky, Tabordon (2004) –Aksin and Karaesmen (2002) –Hopp, Tekin, Van Oyen (2004) Review papers –Sethi and Sethi (1990) –Hopp, Van Oyen (2004)

7. Methodological issues Static –Network flow problem with random demand –Framework of Jordan and Graves (1995) –Simplistic but captures basic characteristic of problem –Enables structural properties Dynamic –Can take into account queueing, abandonments, blocking –Difficult to decouple staffing question from call routing –Stochastic dynamic optimization problem –Very difficult problem in general

8. The Network Flow Model The system is represented by a graph. An arc between demand i and resource j implies that demand i can be treated by resource j. Without loss of generality, each demand type has a main corresponding department. demandscapacities 1 2 3 C1C1 C2C2 C3C3 No resource flexibility demandscapacities 1 2 3 C1C1 C2C2 C3C3 Partial resource flexibility

9. Definitions and Assumptions Demand =( 1, 2,.. n ) is a random vector. Capacities and flexibility structure are given. The allocation (routing) takes place after the realization of the demand. Plausible objective: maximization of expected throughput (flow) Solve max-flow problem for each possible realization and take expectations (over the random demand vector). Easy to simulate, difficult to establish structural results.

10. Some useful properties E[T 1 ]E[T 2 ]E[T 3 ] Obviously: And less obviously: More flexibility is better! Diminishing returns to flexibility!

11. Some useful properties E[T 1 ] E[T 4 ] E[T 3 ]E[T 2 ] Expected throughput is submodular in any two parallel arcs. Parallel arcs are substitutes!

12. Some useful properties E[T 1 ]E[T 2 ] If capacity is symmetric, then: Balanced flexibility is better!

13. The right scale of flexibility Not all service representatives / workers have multiple skills. Let  be the proportion of service representatives with multiple skills What is the right level of  ? What happens to the preceding properties as  changes?

14. The right scale of flexibility With the additional constraint: For any realization the following LP must be solved:

15. The right scale of flexibility E[T|  =0] E[T|  =0.2]E[T|  =0.4] Expected throughput is concave in . Diminishing returns to scale!

16. Examples: effects of scale E[T 1 ]E[T 2 ] E[T 3 ] E[T 4 ]

17. Examples: effects of scale E[T 1 ]E[T 2 ] E[T 3 ] E[T 4 ]

18. Example: scale, and variability of demand E[T 1 ]E[T 2 ] E[T 3 ] E[T 4 ]

19. Robustness of the results: comparison with a call center model A call center with N customer classes and departments Arrivals occur according to Poisson processes with rates i Processing times (talk times) are exponentially distributed with rate . Limited number of waiting spaces. Impatient customers abandon the queue: abandonment times are exponentially distributed with rate . C servers per department.

20. Methodology Call routing policies have an effect on the performance. Difficult stochastic dynamic control problem in multiple dimensions We extend a bound/approximation by Kelly by reducing the problem to N single dimensional Markov Decision Processes Combine the solutions of the MDPs in a concave optimization problem (an LP). Solve the LP: the result is a bound on the expected throughput per unit time which is fairly tight.

21. A numerical example: the symmetric case A three class call center All parameters symmetric (call volumes, service rates, abandonment parameters) Five servers, twenty five phone lines for each class Vary scale: 0-5 x-trained servers Vary flexibility structure

22. Results  Expected Throughput E[T 1 ]E[T 2 ] E[T 3 ] E[T 4 ]

23. Flexibility Insights Obvious result: more flexibility is better Balanced skill sets are better –spread out flexibility rather than exclusive flexibility High scale is desireable but.. –diminishing returns to scale –marginal value of scale increases with better scope for low levels of scale –scale and scope decisions interact –good skill-set design is essential for optimal cross- training practice

24. Managerial Implications Start with skill-set design; determining the right scale should follow this design decision: what type of flexibility followed by how much If the call center deals with calls that share similar parameters (symmetric) prefer a low scope strategy at high scale to a high scope strategy at low scale. For large call centers, even low scope and low scale should be sufficient (20% flexible capacity?) For smaller call centers higher scope is desirable.

25. Future and ongoing work On network flow models –More structural results on scale effects –A complete numerical study –Flexibility/capacity interactions On queueing models –Call routing policies –Capacity design Some information available at: http://call.ku.edu.tr