Counting and enumerating feasible rotating schedules by means of Gröbner bases

This paper deals with the problem of designing and analyzing rotating schedules with an algebraic computational approach. Specifically, we determine a set of Boolean polynomials whose zeros can be uniquely identified with the set of rotating schedules related to a given workload matrix subject to st...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2016-07, Vol.125, p.139-151
Main Authors: Falcón, Raúl, Barrena, Eva, Canca, David, Laporte, Gilbert
Format: Article
Language:English
Subjects:
Boolean ideal
Gröbner basis
Rotating schedule
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Summary:This paper deals with the problem of designing and analyzing rotating schedules with an algebraic computational approach. Specifically, we determine a set of Boolean polynomials whose zeros can be uniquely identified with the set of rotating schedules related to a given workload matrix subject to standard constraints. These polynomials constitute zero-dimensional radical ideals, whose reduced Gröbner bases can be computed to count and even enumerate the set of rotating schedules that satisfy the desired set of constraints. Thereby, it enables to analyze the influence of each constraint in the same.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2014.12.002