Optimal selection and scheduling of jobs with uncertain durations for two employees

The number of potential users of time-management in the world is steadily growing due to the emerging need for remote work (in a home office), distance learning, teaching, service and, in general, the organisation of professional activities and a private life with a minimum of personal contacts due to the spread of the coronavirus infection COVID-19 since 2020 and other dangerous infections. This will require the improvement of the time-management techniques and the developments of new algorithms and software for them, which will take into account the peculiarities and needs of new users of time-management. Such problems arise in time-management for optimally selecting jobs for a given time interval and for constructing optimal schedules for processing jobs under conditions of uncertain operation durations. This article presents sufficiency conditions, algorithms, and computational results for selecting and scheduling connected jobs by two employees.