Advanced Methods and Models for Employee Timetabling Problems
Type of document
disertační práceAuthor
Bäumelt, Zdeněk
Supervisor
Hanzálek. Zdeněk
Šůcha, Přemysl
Field of study
Řídicí technika a robotikaStudy program
Elektrotechnika a informatikaInstitutions assigning rank
České vysoké učení technické v Praze. Fakulta elektrotechnická. Katedra řídicí techniky.Metadata
Show full item recordAbstract
This thesis is focused on the design of efficient models and algorithms for
employee timetabling problems (ETPs). From our point of view, there are two
significant gaps in the current state of the art.
The first one, also important in practice, concerns the ETP with strongly
varying workforce demand. Unlike the classical Nurse Rostering Problem
(NRP) this problem considers dozens of shift types that can cover the demand
more precisely than early, late and night shift type used in NRP. In
this work we call this problem the Employee Timetabling Problem with a High
Diversity of shifts (ETPHD). It comes as no surprise that the exact methods
like Integer Linear Programming are not able to find its solution in reasonable
time. Therefore, a transformation of ETPHD based on mapping of shift
types to shift kinds was proposed. The transformation allows one to design a
multistage approach (MSA). The aim of the first two stages is to find an initial
ETPHD solution, where a rough position of assigned shifts is determined.
This proved to be substantial for the last stage of MSA, where the solution
is consequently improved in terms of its quality. In order to verify the MSA
performance, a cross evaluation methodology was proposed. It is based on the
comparison of the performance provided by more approaches on more combinatorial
problems. Therefore, real life ETPHD instances from an airport ground
company and also standard benchmark NRP instances were considered. The
experiments confirmed the better or equal performance of our approach in the
most of the cases.
The second gap in the literature is an absence of parallel algorithms for
ETPs. We focused on the Nurse Rerostering Problem (NRRP) that appears
when a disruption in the roster occurs, e.g., when one of the employees becomes
sick. For this purpose, the parallel algorithm solving NRRP was proposed in
order to shorten needed computational time. This algorithm was designed for a
Graphics Processing Unit (GPU) offering a massive parallelization. To the best
of our knowledge, this is the first usage of GPU for ETPs. The performance
of the GPU parallel algorithm was tested on the real life NRRP benchmark
instances and evaluated from two points of view. Firstly, the quality of the
results was compared to the known results from the state of the art. Secondly,
the speedup achieved by the parallel algorithm related to the sequential one
was verified. In average, the parallel algorithm is able to provide the results of
the same quality 15 times faster than the sequential one.
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