A Fully Polynomial Approximation Scheme for Scheduling a Single Machine to Minimize Total Weighted Late Work

• Published in: Mathematics of operations research Vol. 19; no. 1; pp. 86 - 93
• Main Authors: Kovalyov, M. Y, Potts, C. N, van Wassenhove, L. N
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.02.1994; The Institute of Management Sciences and the Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Approximation; Approximation algorithms; approximation scheme; Dynamic programming; Exact sciences and technology; Integers; Mathematical minima; Mathematical procedures; Minimum value; Operational research and scientific management; Operational research. Management science; Operations research; Polynomials; Production scheduling; Scheduling; Scheduling, sequencing; single machine; Studies; Scheduling; Approximation; Dynamic programming; Algorithm; Production
• ISSN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.19.1.86

This paper studies approximation algorithms for the problem of nonpreemptively scheduling n jobs on a single machine to minimize total weighted late work, where the late work for a job is the amount of processing of this job that is performed after its due date. A family of approximation algorithms {DP } is derived. For any > 0, DP delivers a schedule having total weighted late work which does not exceed (1 + ) times that of an optimal schedule. Since DP requires O ( n 3 log n + n 3 / ) time, the family {DP } is a fully polynomial approximation scheme.