Inverse Linear Goal Programming Problem
DOI:
https://doi.org/10.59167/tujnas.v3i3.1284Keywords:
Inverse Linear Goal Programming , Multi-objective function , Coefficient of the objective function, Programming ProblemAbstract
This paper considers the inverse linear goal programming problem of multi-objective function in case the change in coefficient of the objective function. Let denote the set of feasible solutions points of linear goal programming problem of a multi-objective function, and let be the positive and negative deviation variables of the maximum and minimum goals respectively, be a specified cost vector, be given feasible solution vector, and be given tow vectors denoted the feasible positive deviation and the feasible negative deviation points of the max or min goals, respectively. The inverse linear goal programming problem of multi-objective function is as follows: Consider the change of the cost vectors as less as possible such that the vectors feasible solution becomes an optimal solution of LGP of multi-objective function under the new cost vectors and is minimal, where is some selected -norm. In this paper, we consider the inverse version ILGP of LGMP. under the -norm where the objective is to minimize , with denoting the index set of variables . We show that the inverse version of the considered under -norm reduces to solving a problem for the same kind; that is, an inverse multi-objective assignment problem reduces to an assignment problem.
Downloads
Published
Issue
Section
Categories
License
Copyright (c) 2023 Nagib M. A. Saif, Gerhard-Wilhelm Weber
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
From July 2025 onward, all TUJNAS publications are licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. This open license allows anyone to share (copy and redistribute) and adapt (remix, transform, and build upon) the work in any medium or format, for any purpose (even commercially), as long as appropriate credit is given to the original author(s) and source. This permissive framework encourages scholarly innovation, translation, and integration into wider academic outputs by removing unnecessary legal barriers. Users of TUJNAS content must provide proper attribution and indicate if any changes were made to the original work. By enabling unrestricted reuse, the CC BY 4.0 license maximizes the reach and impact of research findings while ensuring that authors receive full recognition for their work. (For complete legal details of the CC BY 4.0 license, please refer to the official Creative Commons website.)
Submissions (from July 2025 onward): By submitting a manuscript to TUJNAS for publication (Volume 10, Issue 2, 2025 and thereafter), authors confirm the following:
- Originality: The submission is original, has not been published elsewhere, and is not under consideration by another journal.
- Copyright Retention: The author(s) retain copyright of the work, but grant TUJNAS a non-exclusive right to publish, reproduce, distribute, and archive the article.
- Open Access License: Upon acceptance, the article will be published open access under the CC BY 4.0 license.
- Repository Deposit: The author(s) agree that the full text and metadata of the article may be deposited in digital archives or repositories, to facilitate indexing and reuse under the CC BY 4.0 license.
- Indexing and Sharing: The author(s) acknowledge that TUJNAS may make the article available to third-party indexing, abstracting, and discovery services under the CC BY 4.0 license, without the need for additional permission.
These submission terms ensure that authors understand and consent to the open-access, licensed nature of TUJNAS publications from the outset.
How to Cite
