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Ph.D de

Ph.D
Group : Graphs, ALgorithms and Combinatorics

Chance-Constrained Programming Approaches for Staffing and Shift-Scheduling Problems with Uncertain Forecasts - Application to Call Centers

Starts on 01/10/2012
Advisor : LISSER, Abdel

Funding :
Affiliation : Université Paris-Sud
Laboratory :

Defended on 30/09/2015, committee :
Directeur de thèse
M. Steven MARTIN, Professeur, Université Paris-Sud
Rapporteurs
Mme Safia KEDAD-SIDHOUM, Maître de conférences HDR, Université
Pierre et Marie Curie
M. Dominique FEILLET, Professeur, Ecole des Mines de Saint Etienne
Examinateurs
Alain DENISE, Professeur, Université Paris-Sud
Céline GICQUEL, Maître de conférences, Université Paris-Sud
Dr. Oualid JOUINI, Maître de conférence HDR, Ecole Centrale Paris
Pierre L'ECUYER, Professeur, Université de Montréal, Canada

Research activities :

Abstract :
The staffing and shift-scheduling problems in call centers consist in
deciding how many agents handling the calls should be assigned to work
during a given period in order to reach the required Quality of Service
and minimize the costs. These problems are subject to a growing
interest, both for their interesting theoritical formulation and their
possible applicative effects. This thesis aims at proposing
chance-constrained approaches considering uncertainty on demand forecasts.

First, this thesis proposes a model solving the problems in one step
through a joint chance-constrained stochastic program, providing a
cost-reducing solution. A continuous-based approach leading to an
easily-tractable optimization program is formulated with random
variables following continuous distributions, a new continuous relation
between arrival rates and theoritical real agent numbers and constraint
linearizations. The global risk level is dynamically shared among the
periods during the optimization process, providing reduced-cost
solution. The resulting solutions respect the targeted risk level while
reducing the cost compared to other approaches.

Moreover, this model is extended so that it provides a better
representation of real situations. First, the queuing system model is
improved and consider the limited patience of customers. Second, another
formulation of uncertainty is proposed so that the period correlation is
considered.

Finally, another uncertainty representation is proposed. The
distributionally robust approach provides a formulation while assuming
that the correct probability distribution is unknown and belongs to a
set of possible distributions defined by given mean and variance. The
problem is formulated with a joint chance constraint. The risk at each
period is a decision variable to be optimized. A deterministic
equivalent problem is proposed. An easily-tractable mixed-integer linear
formulation is obtained through piecewise linearizations.

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