# Scheduling Problem in Call Centers with Uncertain Arrival Rates Forecasts - A Distributionally Robust Approach

### Mathilde Excoffier, Céline Gicquel, Oualid Jouini, Abdel Lisser

#### Abstract

We focus on the staffing and shift-scheduling problem in call centers. We consider that the call arrival rates are subject to uncertainty and are following unknown continuous probability distributions. We assume that we only know the first and second moments of the distribution. We propose to model this stochastic optimization problem as a distributionally robust program with joint chance constraints. We consider a dynamic sharing out of the risk throughout the entire scheduling horizon. We propose a deterministic equivalent of the problem and solve linear approximations of the program to provide upper and lower bounds of the optimal solution. We applied our approach on a real-life instance and give numerical results.

#### References

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- with p 2 [0; 1[. Function f is C¥, so we can compute the second
- ln2(p)(1 + 2py)
- ln2(p)(1 + 2py)

#### Paper Citation

#### in Harvard Style

Excoffier M., Gicquel C., Jouini O. and Lisser A. (2015). **Scheduling Problem in Call Centers with Uncertain Arrival Rates Forecasts - A Distributionally Robust Approach** . In *Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-075-8, pages 5-13. DOI: 10.5220/0005203800050013

#### in Bibtex Style

@conference{icores15,

author={Mathilde Excoffier and Céline Gicquel and Oualid Jouini and Abdel Lisser},

title={Scheduling Problem in Call Centers with Uncertain Arrival Rates Forecasts - A Distributionally Robust Approach},

booktitle={Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2015},

pages={5-13},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005203800050013},

isbn={978-989-758-075-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Scheduling Problem in Call Centers with Uncertain Arrival Rates Forecasts - A Distributionally Robust Approach

SN - 978-989-758-075-8

AU - Excoffier M.

AU - Gicquel C.

AU - Jouini O.

AU - Lisser A.

PY - 2015

SP - 5

EP - 13

DO - 10.5220/0005203800050013