On the Dual and Inverse Problems of Scheduling Jobs to Minimize the Maximum Penalty

In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial...

Full description

Saved in:
Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 7; p. 1131
Main Authors Lazarev, Alexander A., Pravdivets, Nikolay, Werner, Frank
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2020
Subjects
Algorithms
branch and bound
dual problem
Food science
inverse problem
Inverse problems
Job shops
Lower bounds
minimization of maximum penalty
Polynomials
Release dates
Scheduling
single-machine scheduling
Online AccessGet full text

Cover

More Information
Summary:In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on the optimal objective function value of the original problem, we use the optimal function value of a sub-problem of the dual problem in a branch and bound algorithm for the original single-machine scheduling problem. We present some initial computational results for instances with up to 20 jobs.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8071131