Estimates of the absolute error and a scheme for an approximate solution to scheduling problems

• Published in: Computational mathematics and mathematical physics Vol. 49; no. 2; pp. 373 - 386
• Main Author: Lazarev, A. A.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.02.2009; Springer Nature B.V
• Subjects: Algorithms; Computational mathematics; Computational Mathematics and Numerical Analysis; Error analysis; Estimates; Job shops; Linear programming; Mathematics; Mathematics and Statistics; Schedules; Scheduling; Studies; approximate solution; scheduling theory; absolute error estimate; minimization of maximum lateness
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542509020158

An approach is proposed for estimating absolute errors and finding approximate solutions to classical NP-hard scheduling problems of minimizing the maximum lateness for one or many machines and makespan is minimized. The concept of a metric (distance) between instances of the problem is introduced. The idea behind the approach is, given the problem instance, to construct another instance for which an optimal or approximate solution can be found at the minimum distance from the initial instance in the metric introduced. Instead of solving the original problem (instance), a set of approximating polynomially/pseudopolynomially solvable problems (instances) are considered, an instance at the minimum distance from the given one is chosen, and the resulting schedule is then applied to the original instance.