Designing rotating schedules by using Gröbner bases

Abstract

In the current paper, we deal with the problem of designing rotating schedules from 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 and with the different constraints which are usually imposed to them.These polynomials constitute zero-dimensional radical ideals, whose reduced Gröbner bases can be computed to determine explicitly the set of rotating schedules which satisfy each constraint and hence, making possible to analyze their influence in the final pattern. Finally, we use this polynomial method to classify and characterize the set of rotating schedules related to a given number of shifts and work teams.