Optimal Scheduling Works for Two Employees with Ordered Criteria

The number of users of time management in the world is increasing due to the need for remote work (at home), study, teaching, and service. This requires the improvement of time-management models, methods, and the development of new optimization algorithms and software tools that will take into account the characteristics and needs of new time-management users. This article presents the necessary and sufficient conditions for schedule optimality, algorithms, and results of computational experiments conducted on the optimal selection and planning of interrelated jobs for two performers (a supervisor and a subordinate). Such an optimization problem arises in time management for scheduling the performance of the selected jobs in conditions of the uncertainty of the selected jobs to be scheduled and then executed. We develop a scheduling algorithm and present computational results for selecting and scheduling interrelated jobs for two employees for minimizing the schedule length as the main criterion and minimizing the sum of the weighted completion times of the jobs as the second criterion.