The problem of constructing a feasible schedule with maximum startup time and minimum total earliness

Abstract

We considered a problem of scheduling a single device performing independent tasks with different durations and due terms on the criteria of maximizing the startup time of the task and minimizing the total earliness, in which all the tasks are not delayed. For the specified launch time, the algorithm is presented to build a feasible schedule with the minimum total earliness. The proof is provided that the problem of constructing an optimal feasible schedule according to the criteria of maximizing the startup time of the task and simultaneously minimizing the total earliness specified in the lexicographical order is P-solvable. We propose an exact polynomial algorithm for finding the optimal schedule on the criteria of minimizing the total earliness for a given startup time of the tasks.