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to each tutor. The combination of all of these con-
straints, coupled with the fact that the tutor availabil-
ity is variable, often makes the automatic schedule
generation infeasible. However, similar to the expert,
a robust scheduling algorithm should be able to work
around such difficulties to find a solution despite the
highly complex problem setup. In this paper, we dis-
cuss an effective strategy of creating a more robust
algorithm by integrating the notion of graceful degra-
dation and strategically relaxing the constraints and
relevant parameters.
The paper is organised as follows. Section 2 pro-
vides a literature review of real world applications of
the employee scheduling problem. Section 3 defines
the problem where all of the constraints and the main
objectives are stated. Section 4 outlines the mathe-
matical formulation, i.e. the variables, constraints and
objective function. Section 5 introduces the heuris-
tics to modify the scheduling algorithm and overcome
the problem of conflicting constraints. Section 6 dis-
cusses the performance of the algorithm in generat-
ing schedules using both quantitative and qualitative
metrics. Finally, section 7 presents a summary of the
paper and highlights future experiments.
2 PREVIOUS WORK
Employee scheduling is of utmost importance in
many industries. The research community has mainly
focused on the Nurse Scheduling Problem (NSP),
which tries to schedule hospital employees to vari-
ous shifts for different days depending on the demand.
Some examples of scheduling in the context of emer-
gency services can be found in (Beaulieu et al., 2000)
and (Camiat et al., 2019). Though each setting is
unique, they share a common objective of finding a
trade off between satisfactory coverage of the service
demand, labor regulations and personnel satisfaction.
The NSP has been studied extensively, as shown in
(Burke et al., 2004) and (den Bergh et al., 2013), so
that a consistent, automated generation of schedules
is possible, while ensuring adequate demand cover-
age and employee well-being.
Even though the problem models are easily trans-
ferable amongst different industries, many specific
examples of employee scheduling are described since
the constraints, the objective function and the heuris-
tics are variable. The most well studied domains are
transportation, supply chain, call centers, airlines and
health care. More examples are described in (Ernst
et al., 2004). It can also be applied in niche fields, as
shown in (Albornoz et al., 2015) (meat packing indus-
try), (Leiva and Albornoz, 2016) (soft drink industry),
or in (Lampoudi et al., 2015) (telescope industry). All
these examples show that specialized knowledge is re-
quired to come up with an automated solution that can
be adopted by an organization. Consequently, having
a domain expert is essential to the success of an auto-
mated scheduler.
Two papers, (A
˘
gralı et al., 2017) and (Hojati and
Patil, 2011) hold our attention since they both have
a similar setup as us. For example, they all have
part-time workers with heterogeneous skills, flexible
availability and variable demand to satisfy, and use
heuristics to overcome constraint conflicts. (Hojati
and Patil, 2011) showcases a 2-step method: the first
one is to find the optimal shifts (shift duration, place-
ment, and corresponding employees), and the second
one is to generate a schedule considering those good
shifts. Furthermore, heuristics are used to come up
with a feasible solution. Though both problem setups
are similar to ours, we have to deal with many more
constraints related to employee satisfaction.
The large number of constraints and variables cre-
ate a lot of constraint conflicts. Over-constrained
problems are difficult to satisfy or optimize. One way
to resolve this issue is to apply constraint relaxation.
In (Junker, 2004), a divide-and-conquer method is de-
scribed to explain which constraints are responsible
for the conflicts. This form of constraint relaxation is
a powerful way to make a problem feasible, although
the method is aggressive since it removes some con-
straints. In our case, we want to avoid the complete
removal of a constraint to ensure employee satisfac-
tion and sufficient demand coverage, both of which
are necessary for a successful adoption of the system.
(Burke et al., 2004) concludes that there has been
a lot of work on finding and tuning scheduling algo-
rithms. However, the applications that are highlighted
are often toy problems or problems with low dimen-
sions. In (De Causmaecker et al., 2004), several real
world scheduling problems are discussed. Yet, not
many studies demonstrate how to find solutions in real
world scheduling issues with an over-constrained en-
vironment, where optimization methods coupled with
heuristics are used to find a viable solution.
The main contribution of this paper is to provide
an exhaustive view of automated scheduling in online
tutoring, including a mathematical formulation of the
problem, the creation of heuristics with the help of a
domain expert, and the implementation of a graceful
degradation protocol.
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