New algorithms for minimizing the weighted number of tardy jobs on a single machine

In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or is taken as a parameter in the sense of parameterized comp...

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Bibliographic Details
Published in:Annals of operations research Vol. 298; no. 1-2; pp. 271 - 287
Main Authors: Hermelin, Danny, Karhi, Shlomo, Pinedo, Michael, Shabtay, Dvir
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2021
Springer
Springer Nature B.V
Subjects:
Algorithms
Business and Management
Case studies
Combinatorics
Complexity theory
Context switching
Dynamic programming
Intelligent devices
Job shops
Knapsack problem
Management
Moving averages
Operations research
Operations Research/Decision Theory
Parameters
Polynomials
Production scheduling
S.I.: CoDIT2017-Combinatorial Optimization
Scheduling
Simulated annealing (Mathematics)
Studies
Theory of Computation
Israel
New York
United States > US
Weighted number of tardy jobs
NP-hard
Fixed parametrized tractability
Single machine scheduling
Polynomial time algorithms
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:In this paper we study the classical single machine scheduling problem where the objective is to minimize the weighted number of tardy jobs. Our analysis focuses on the case where one or more of three natural parameters is either constant or is taken as a parameter in the sense of parameterized complexity. These three parameters are the number of different due dates, processing times, and weights in our set of input jobs. We show that the problem belongs to the class of fixed parameter tractable (FPT) problems when combining any two of these three parameters. We also show that the problem is polynomial-time solvable when either one of the latter two parameters are constant, complementing Karp’s result who showed that the problem is NP-hard already for a single due date.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-018-2852-9