An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint
G. Calinescu (1), F. Jaehn (2), M. Li (3), K. Wang (3) ((1), Department of Computer Science, Illinois Institute of Technology, Chicago, IL, 60616, USA, (2) Management Science, Operations Research, Helmut Schmidt, University -- University of the Federal Armed Forces Hamburg
TL;DR
This paper presents an FPTAS for a single-machine scheduling problem that minimizes total weighted completion time with a position constraint on a specific job, improving approximation efficiency.
Contribution
It introduces a fully polynomial-time approximation scheme for a constrained scheduling problem, extending existing methods with a new dynamic programming approach.
Findings
Developed a dynamic programming-based FPTAS for the problem
Achieved polynomial-time approximation with controlled error bounds
Enhanced scheduling efficiency under position constraints
Abstract
In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS).
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Taxonomy
TopicsScheduling and Optimization Algorithms · Advanced Manufacturing and Logistics Optimization · Optimization and Search Problems