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Ph.D de

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-Saclay
Laboratory :

Defended on 30/09/2015, committee :
Directeur de thèse
M. Steven MARTIN, Professeur, Université Paris-Sud
Mme Safia KEDAD-SIDHOUM, Maître de conférences HDR, Université
Pierre et Marie Curie
M. Dominique FEILLET, Professeur, Ecole des Mines de Saint Etienne
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

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.

Ph.D. dissertations & Faculty habilitations


The topic of this habilitation is the study of very small data visualizations, micro visualizations, in display contexts that can only dedicate minimal rendering space for data representations. For several years, together with my collaborators, I have been studying human perception, interaction, and analysis with micro visualizations in multiple contexts. In this document I bring together three of my research streams related to micro visualizations: data glyphs, where my joint research focused on studying the perception of small-multiple micro visualizations, word-scale visualizations, where my joint research focused on small visualizations embedded in text-documents, and small mobile data visualizations for smartwatches or fitness trackers. I consider these types of small visualizations together under the umbrella term ``micro visualizations.'' Micro visualizations are useful in multiple visualization contexts and I have been working towards a better understanding of the complexities involved in designing and using micro visualizations. Here, I define the term micro visualization, summarize my own and other past research and design guidelines and outline several design spaces for different types of micro visualizations based on some of the work I was involved in since my PhD.