Abstract: A computer and method use at least an index of a last item in a new partial schedule and an ending time of the last item to identify a set of one or more stored partial schedules. The computer and method determine whether the new partial schedule dominates any stored partial schedule in the set, based on comparison of at least new lower bound(s) and new upper bound(s) on attribute(s) of a complete schedule that comprises the new partial schedule, with corresponding lower bound and upper bound of each complete schedule to be built using each stored partial schedule. Any stored partial schedule in the set is removed, when the new partial schedule is determined to dominate said any stored partial schedule. When no stored partial schedule in the set dominates the new partial schedule, the new partial schedule is added to the set, followed by repeating the process.

Abstract: A computer and method generate a new sequence of assignments of activities of work (e.g. cleaning, sales, accounting) to be performed by an employee, in a particular time period in a day in an organization. An attribute of the new sequence (e.g. number of transitions between activity assignments) has a specific value that is then used to identify a stored sequence from a matrix. Then, costs of these two sequences are compared to determine one of the new sequence or the stored sequence to be an optimal sequence, for the specific value of the attribute and the particular time period. The optimal sequence is then stored in the matrix. In this manner multiple optimal sequences are obtained for several values of the attribute and for numerous time periods in the day. The optimal sequences may be combined with periods of breaks to form a daily schedule.

Abstract: A computer and method formulate, for inclusion in a constraint to be used in scheduling employees to perform an activity a within a time slot s, a sum of a sequence of variables that are defined based on new workload levels, created to model a gap between: a number of employees needed to perform activity a in time slot s, and the number of employees to be scheduled to perform activity a in time slot s. The computer and method further prepare, for inclusion in a function to be optimized during scheduling, a scalar product of the sequence of variables and a sequence of values. Each value in the sequence of values depends on a distance between: the number of employees needed to perform activity a in the time slot s and a new workload level indicated by the corresponding variable with which the value is multiplied.