Planning time-management as sequencing given jobs with interval processing times

Abstract

An automated system for planning and controlling working hours for a person (time-management) is considered. The main stage in planning of the working hours is the construction of an optimal schedule of the jobs given for an employee. We propose to use algorithms for an optimal processing of a set of jobs with uncertain (interval) processing times on a single machine. The optimality criterion under consideration is the minimization of the total weighted completion times of the given jobs. This criterion may be interpreted as a measure of the effectiveness of the employee to fulfill the given set of jobs. Due to the nature of the planning process of the jobs for a person, it is assumed that the time needed for processing any given job may be undetermined (unknown) until the completion time of the job. Therefore, in the construction of an optimal schedule in time-management, only an upper bound and a lower bound on the factual processing time are assumed to be known for each job to be processed by a person.