On the interaction between resource flexibility and flexibility structures

1. On the interaction between resource flexibility and flexibility structures Fikri Karaesmen, Zeynep Aksin, Lerzan Ormeci Koç University Istanbul, Turkey Sponsored by a KUMPEM research grant FIFTH INTERNATIONAL CONFERENCEON"Analysis of Manufacturing Systems –ProductionManagement" 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. l1 C1 l1 C1 C2 C2 l2 l2 C3 C3 l3 l3 demands capacities demands capacities No resource flexibility Partial resource flexibility

9. Definitions and Assumptions • Demand l=(l1, l2,.. ln) 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[T1] E[T2] E[T3] Obviously: More flexibility is better! And less obviously: Diminishing returns to flexibility!

11. Some useful properties E[T4] E[T1] E[T2] E[T3] Expected throughput is submodular in any two parallel arcs. Parallel arcs are substitutes!

12. Some useful properties E[T1] E[T2] If capacity is symmetric, then: Balanced flexibility is better!

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

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

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

16. E[T4] E[T1] E[T2] E[T3] Examples: effects of scale

17. E[T4] E[T1] E[T2] E[T3] Examples: effects of scale

18. E[T4] E[T1] E[T2] E[T3] Example: scale, and variability of demand

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 li • Processing times (talk times) are exponentially distributed with rate m. • Limited number of waiting spaces. • Impatient customers abandon the queue: abandonment times are exponentially distributed with rate q. • 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. E[T4] E[T1] E[T2] E[T3] Results Expected Throughput a

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