A Fully Polynomial Approximation Scheme for the Weighted Earliness-Tardiness Problem

• Published in: Operations research Vol. 47; no. 5; pp. 757 - 761
• Main Authors: Kovalyov, Mikhail Y, Kubiak, Wieslaw
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.09.1999; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; analysis of algorithms; Approximation; Approximation algorithms; Approximation theory; approximations/heuristic; fully polynomial approximation scheme; Integers; Iterative solutions; Job analysis; Job shops; Just in time; Just in time production; Machinery; Mathematical vectors; Operations research; Optimal solutions; Polynomials; Prior learning; Problem solving; production/scheduling; Scheduling; single machine; Studies; suboptimal algorithms; weighted earliness–tardiness; Work-rest schedules
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.47.5.757

A fully polynomial approximation scheme for the problem of scheduling n jobs on a single machine to minimize total weighted earliness and tardiness is presented. A new technique is used to develop the scheme. The main feature of this technique is that it recursively computes lower and upper bounds on the value of partial optimal solutions. Therefore, the scheme does not require any prior knowledge of lower and upper bounds on the value of a complete optimal solution. This distinguishes it from all the existing approximation schemes.