A new approach to solving the problem: "Minimization of total weighted tardiness when fulfilling independent tasks in due times at one machine"

Abstract

Based on the problem properties research, a new approach to its solution is offered and an effective approximate algorithm based upon it is developed. Conditions for optimal solution to be found in polynomial time are formulated. When these conditions are not satisfied, the truncation rules that allow to decrease the time for solving the task essentially are offered. This algorithm allowed to get exact solutions for a series of problems with a number of variables essentially more than 50. Optimal values of the criterion function got by this algorithm for test examples were congruent with criterion function values got by known methods.