Research interest version française
Between 2017 an 2021, I worked at Sorbonne Université (Paris), in LIP6 lab,
in the operations research team.
Supervised by Safia Kedad-Sidhoum
and Pierre Fouilhoux,
I have done my master thesis and my PhD thesis between just-in-time scheduling and linear programming fields.
To find more about my master thesis,
you can visit page "Stage"
or directly see the report (both in french),
while to find more about my PhD thesis,
you can visit page "Thèse" (in french),
directly see the report
or the slides (both in english).
We worked on some scheduling problems around a common due date.
We proposed mixed integer formulations for these NP-hard problems in order to exactly solve them.
The first formulations we proposed were based on natural variables, similar to completion time variables.
To manage this kind of variables, an exponential number of non-overlapping inequalities,
as well as extramality constraints are needed.
Therefore, we implemented these formulations using a Branch-and-Bound algorithm,
and solve them using Cplex.
-> On this topic, see our article
published in February 2021 in Discrete Applied Maths (DAM)
(or the accepted manuscript available on arXiv)
-> My last presentation on this topic (November 2020)
Then we focus on a compact formulation for the unrestrictive case of the single machine problem.
We strengthened this formulation by adding linear inequalities, called dominance inequalities.
The set of locally optimal solutions is a always a dominant set,
and in particular when the neighborhood of each solution is obtained by applying a set of operations.
Dominance inequalities translate this dominance property:
for each operation, an inequality eliminate all the solutions that can be improved by applying this operation.
Therefore, these inequalities can cut integer points, and are then different from the classical reinforcement inequalities.
Adding the proposed dominance inequalities clearly improved the performance of the compact formulation:
under a time limit of one hour, the task number of optimally solved instances have been multiplied by three.
-> On this topic, see our article
published in European Journal of Operations Research (EJOR)
(or the accepted manuscript available on arXiv)
-> My last presentation on this topic (February 2020)
Since dominance inequalities look very promising,
we are currently working on applying them on other combinatorial optimization problems.