Hospital Nurse Scheduling Optimization Using Simulated Annealing and Probabilistic Cooling Scheme

Nurse’s scheduling in hospitals becomes a complex problem, and it takes time in its making process. There are a lot of limitation and rules that have to be considered in the making process of nurse’s schedule making, so it can fulfill the need of nurse’s preference that can increase the quality of the service. The existence variety of different factors that are causing the nurse scheduling problem is so vast and different in every case. The study is aimed to develop a system used as an equipment to arrange nurse’s schedule. The working schedule obtained will be checked based on the constraints that have been required. Value check of the constraint falsification used Simulated Annealing (SA) combined with cooling method of Probabilistic Cooling Scheme (PCS). Transitional rules used cost matrix that is employed to produce a new and more efficient state. The obtained results showed that PCS cooling methods combined with the transition rules of the cost matrix generating objective function value of new solutions better and faster in processing time than the cooling method exponential and logarithmic. Work schedule generated by the application also has a better quality than the schedules created manually by the head of the room.

On existence varieties of orthodox semigroups

An existence variety of regular semigroups is a class of regular semigroups which is closed under the operations of forming all homomorphic images, all regular subsemigroups and all direct products. In this paper we generalize results on varieties of inverse semigroups to existence varieties of orthodox semigroups.

On the Lattice of Existence Varieties of Locally Inverse Semigroups

The mapping which assigns to each existence variety of locally inverse semigroups the class of all pseudosemilattices of idempotents of members of is shown to be a complete, surjective homomorphism from the lattice of existence varieties of locally inverse semigroups onto the lattice of varieties of pseudosemilattices.

On existence varieties of locally inverse semigroups

A locally inverse semigroup is a regular semigroup S with the property that eSe is inverse for each idempotent e of S. Motivated by natural examples such as inverse semigroups and completely simple semigroups, these semigroups have been the subject of deep structure-theoretic investigations. The class ℒ ℐ of locally inverse semigroups forms an existence variety (or e-variety): a class of regular semigroups closed under direct products, homomorphic images and regular subsemigroups. We consider the lattice ℒ(ℒℐ) of e-varieties of such semigroups. In particular we investigate the operations of taking meet and join with the e-variety CS of completely simple semigroups. An important consequence of our results is a determination of the join of CS with the e-variety of inverse semigroups – it comprises the E-solid locally inverse semigroups. It is shown, however, that not every e-variety of E-solid locally inverse semigroups is the join of completely simple and inverse e-varieties.

THE EXISTENCE OF E-FREE OBJECTS IN E-VARIETIES OF REGULAR SEMIGROUPS

An existence variety (or e-variety) of regular semigroups is a class of regular semigroups which is closed under [Formula: see text], and ℍ. This concept was introduced by T.E. Hall and independently for orthodox semigroups by J. Kadourek and M.B. Szendrei who called them bivarieties. In this paper we prove the existence of e-free objects in each e-variety of E-solid regular semigroups and in each e-variety of locally inverse regular semigroups. By contrast, we show that there is no e-free object in other e-varieties.

Identities for existence varieties of regular semigroups

A natural concept of variety for regular semigroups is introduced: an existence variety (or e-variety) of regular semigroups is a class of regular semigroups closed under the operations H, Se, P of taking all homomorphic images, regular subsernigroups and direct products respectively. Examples include the class of orthodox semigroups, the class of (regular) locally inverse semigroups and the class of regular E-solid semigroups. The lattice of e-varieties of regular semigroups includes the lattices of varieties of inverse semigroups and of completely regular semigroups. A Birkhoff-type theorem is proved, showing that each e-variety is determined by a set of identities: such identities are then given for many e-varieties. The concept is meaningful in universal algebra, and as for regular semigroups could give interesting results for e-varieties of regular rings.