Joint chance-constrained staffing optimization in multi-skill call centers. (English) Zbl 1498.90185
Summary: This paper concerns the staffing optimization problem in multi-skill call centers. The objective is to find a minimal cost staffing solution while meeting a target level for the quality of service (QoS) to customers. We consider a staffing problem in which joint chance constraints are imposed on the QoS of the day. Our joint chance-constrained formulation is more rational capturing the correlation between different call types, as compared to separate chance-constrained versions considered in previous studies. We show that, in general, the probability functions in the joint-chance constraints display S-shaped curves, and the optimal solutions should belong to the concave regions of the curves. Thus, we propose an approach combining a heuristic phase to identify solutions lying in the concave part and a simulation-based cut generation phase to create outer-approximations of the probability functions. This allows us to find good staffing solutions satisfying the joint-chance constraints by simulation and linear programming. We test our formulation and algorithm using call center examples of up to 65 call types and 89 agent groups, which shows the benefits of our joint-chance constrained formulation and the advantage of our algorithm over standard ones.
Keywords:
call center; staffing optimization; joint chance constraint; cutting plane; concave-identificationReferences:
| [1] | Ahmed S, Shapiro A (2008) Solving chance-constrained stochastic programs via sampling and integer programming. In: State-of-the-art decision-making tools in the information-intensive age. Informs, pp 261-269 |
| [2] | Atlason, J.; Epelman, M.; Henderson, S., Call center staffing with simulation and cutting plane methods, Ann Oper Res, 127, 333-358 (2004) · Zbl 1116.90342 · doi:10.1023/B:ANOR.0000019095.91642.bb |
| [3] | Atlason, J.; Epelman, M.; Henderson, S., Optimizing call center staffing using simulation and analytic center cutting-plane methods, Manag Sci, 54, 295-309 (2008) · Zbl 1232.90266 · doi:10.1287/mnsc.1070.0774 |
| [4] | Avramidis A, Chan W, Gendreau M, L’Ecuyer P, Pisacane O (2010) Optimizing daily agent scheduling in a multiskill call center. Eur J Oper Res 200:822-832 · Zbl 1177.90262 |
| [5] | Bassamboo, A.; Harrison, J.; Zeevi, A., Design and control of a large call center: asymptotic analysis of an LP-based method, Oper Res, 54, 419-435 (2006) · Zbl 1167.90528 · doi:10.1287/opre.1060.0285 |
| [6] | Buist E, L’Ecuyer P (2005) A java library for simulating contact centers. In: Proceedings of the winter simulation conference, 2005, p 10 |
| [7] | Chan W, Koole G, L’Ecuyer P (2014) Dynamic call center routing policies using call waiting and agent idle times. Manuf Serv Oper Manag 16:544-560 |
| [8] | Chan W, Ta TA, L’Ecuyer P, Bastin F (2016) Two-stage chance-constrained staffing with agent recourse for multi-skill call centers. In: The 2016 winter simulation conference, IEEE Press, Piscataway, NJ, USA, pp 3189-3200 |
| [9] | Excoffier, M.; Gicquel, C.; Jouini, O., A joint chance-constrained programming approach for call center workforce scheduling under uncertain call arrival forecasts, Comput Ind Eng, 96, 16-30 (2016) · doi:10.1016/j.cie.2016.03.013 |
| [10] | Excoffier, M.; Gicquel, C.; Jouini, O.; Lisser, A.; Pinson, E.; Valente, F.; Vitoriano, B., Comparison of stochastic programming approaches for staffing and scheduling call centers with uncertain demand forecasts, Operations research and enterprise systems (2015), Cham: Springer, Cham |
| [11] | Çezik M, L’Ecuyer P (2008) Staffing multiskill call centers via linear programming and simulation. Manag Sci 54:310-323 · Zbl 1232.90301 |
| [12] | Gans, N.; Koole, G.; Mandelbaum, A., Telephone call centers: tutorial, review, and research prospects, Manuf Serv Oper Manag, 5, 79-141 (2003) · doi:10.1287/msom.5.2.79.16071 |
| [13] | Gurvich, I.; Luedtke, J.; Tezcan, T., Staffing call centers with uncertain demand forecasts: a chance-constrained optimization approach, Manag Sci, 56, 1093-1115 (2010) · Zbl 1232.90278 · doi:10.1287/mnsc.1100.1173 |
| [14] | Hoeffding W (1994) Probability inequalities for sums of bounded random variables. The collected works of Wassily Hoeffding. Springer, pp 409-426 · Zbl 0807.01034 |
| [15] | Ingolfsson, A.; Campello, F.; Wu, X.; Cabral, E., Combining integer programming and the randomization method to schedule employees, Eur J Oper Res, 202, 153-163 (2010) · Zbl 1173.90406 · doi:10.1016/j.ejor.2009.04.026 |
| [16] | Jouini, O.; Koole, G.; Roubos, A., Performance indicators for call centers with impatience, IIE Trans, 45, 01 (2012) |
| [17] | Kooley, G.; Nielsen, BF; Nielsen, T., Optimization of overflow policies in call centers, Probab Eng Inf Sci, 29, 07 (2015) · Zbl 1370.90088 |
| [18] | L’Ecuyer P, Meliani L, Vaucher J (2003) SSJ: a framework for stochastic simulation in java. vol 1, pp 234- 242 vol 1, 01. ISBN 0-7803-7614-5 |
| [19] | Nemirovski, A.; Shapiro, A., Convex approximations of chance constrained programs, SIAM J Optim, 17, 969-996 (2006) · Zbl 1126.90056 · doi:10.1137/050622328 |
| [20] | Nemirovski A, Shapiro A (2006b) Scenario approximations of chance constraints. Probabilistic and randomized methods for design under uncertainty. Springer, pp 3-47 · Zbl 1181.90248 |
| [21] | Singh, B.; Watson, J-P, Approximating two-stage chance-constrained programs with classical probability bounds, Optim Lett, 13, 9 (2019) · Zbl 1431.90103 · doi:10.1007/s11590-019-01387-z |
| [22] | Ta TA, Chan W, Bastin F, L’Ecuyer P (2019) A simulation-based decomposition approach for two-stage staffing optimization in call centers under arrival rate uncertainty. Working paper. https://www.iro.umontreal.ca/ lecuyer/myftp/papers/ssa-2stage-decomp.pdf |
| [23] | Ta TA, Mai T, Bastin F, L’Ecuyer P (2020) On a multistage discrete stochastic optimization problem with stochastic constraints and nested sampling. Math Progr 190:1-37 · Zbl 1489.65011 |
| [24] | Wallace, R.; Whitt, W., A staffing algorithm for call centers with skill-based routing, Manuf Serv Oper Manag, 7, 276-294 (2005) · doi:10.1287/msom.1050.0086 |
| [25] | Xie W, Ahmed S, Jiang R (2017) Optimized bonferroni approximations of distributionally robust joint chance constraints. Optimization Online, 02 · Zbl 1489.90096 |
| [26] | Zan, J.; Hasenbein, J.; Morton, D., Asymptotically optimal staffing of service systems with joint QoS constraints, Queueing Syst, 78, 04 (2014) · Zbl 1309.60092 · doi:10.1007/s11134-014-9406-x |
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