Advances in Operations Research / 2018 / Article / Tab 7

Review Article

An Assignment Problem and Its Application in Education Domain: A Review and Potential Path

Table 7

The hard and soft constraints related to STP adopted from Cerdeira-Pena et al. [73].

Constraint typeDescriptions

Hard constraints(i) Overlaps: avoid the possibility of a class been taught by more than one teacher in the same period and avoid classes sharing resources (i.e., a classroom, lab, etc.), where classes which involved the same group could be assigned to the same period.
(ii) Simultaneity: two classes are defined as simultaneous classes if they are taught by different teachers at the same time.
(iii) Unavailability: it considers periods when a class cannot be given or when a teacher cannot teach.
(iv) Consecutiveness: this constraint checks whether a distribution of hours for a pair teacher-class is followed. For example, some practical lessons should be taught in two consecutive periods of time.

Soft constraints(i) Overuse: it refers to the number of periods per day in which a teacher gives its lessons, over its specified maximum of periods per day.
(ii) Underuse: when teachers have preferences on their minimum number of periods per day, it indicates the number of periods under such minimum.
(iii) Holes: consider the number of empty periods between two consecutive periods where a teacher is assigned a class. Breaks and free-time periods are not considered holes.
(iv) Splits: consider the number of periods between two nonconsecutive assignments to the same class in the same day.
(v) Groups: assuming a specified maximum of periods per day for an association teacher-class, it considers the number of exceeding periods in such day. This constraint is only considered if a maximum number of consecutive periods (related with consecutiveness) for the pair class-teacher are not specified.
(vi) Undesired: assuming that there are periods in which a teacher would prefer not to teach, this constraint indicates the number of such periods where that teacher is assigned a class. This constraint is the soft version of the mandatory unavailability constraint (referring to teachers).

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