A Short Literature on Linear Programming Problem

Authors

DOI:

https://doi.org/10.4108/ew.4516

Keywords:

operational research, Linear Programming Problem, simplex Method

Abstract

Researchers and scientists have developed various approaches and methodologies over time to model and analyze different types of linear programming problems, such as assignment problems and parametric programming problems. This paper provides a critical review and classification of existing modelling approaches and solution methods related to linear programming problems. Moreover, the simplex method is discussed in detail through a comprehensive literature review. The paper concludes by presenting an integrated research framework that is directly applicable to the present context, along with suggestions for future research directions.

Downloads

Download data is not yet available.

References

Sharma JK. Operation research: Theory and application, 4th edition. Macmillan Publisher India Ltd; 2009.

Quddoos A, Javaid S, Khalid MM. A new method for finding an optimal solution for transportation problems. International Journal on Computer Science and Engineering. 2012;4:1271.

Pearson M, Monks T, Gibson A, Allen M, Komashie A, Fordyce A, Harris-Golesworthy F, Pitt MA, Brailsford S, Stein K. Involving patients and the public in healthcare operational research—The challenges and opportunities. Operations Research for Health Care. 2013;2:86–89. DOI: https://doi.org/10.1016/j.orhc.2013.09.001

Ergun O, Karakus G, Keskinocak P, Swann J, Villarreal M. Operations research to improve disaster supply chain management. Encyclopedia Of Operations Research And Management Science. 2010;6:3802–3810. DOI: https://doi.org/10.1002/9780470400531.eorms0604

Mulvey JM, Rosenbaum DP, Shetty B. Strategic financial risk management and operations research. European Journal of Operational Research. 1997;97:1–16. DOI: https://doi.org/10.1016/S0377-2217(96)00222-6

Porteus EL. Optimal lot sizing, process quality improvement and setup cost reduction. Operations research. 1986;34:137–144. DOI: https://doi.org/10.1287/opre.34.1.137

Luna AC, Diaz NL, Graells M, Vasquez JC, Guerrero JM. Mixed-integer-linear-programming-based energy management system for hybrid PV-wind-battery microgrids: Modeling, design, and experimental verification. IEEE Transactions on Power Electronics. 2016;32:2769–2783. DOI: https://doi.org/10.1109/TPEL.2016.2581021

Aksin Z, Armony M, Mehrotra V. The modern call center: A multi-disciplinary perspective on operations management research. Production And Operations Management. 2007;16:665–688. DOI: https://doi.org/10.1111/j.1937-5956.2007.tb00288.x

Taha HA. Operations Research: An Introduction. Pearson Education India; 2013.

Thompson GL, Zawack DJ. A problem expanding parametric programming method for solving the job shop scheduling problem. Annals of Operations Research. 1985;4:327–342. DOI: https://doi.org/10.1007/BF02022046

Yu W, Lui R. Dual methods for nonconvex spectrum optimization of multicarrier systems. IEEE Transactions On Communications. 2006;54:1310–1322. DOI: https://doi.org/10.1109/TCOMM.2006.877962

Sulaiman NA, Hamadameen AQO. Optimal transformation technique to solve multi-objective linear programming problem (MOLPP). Kirkuk University Journal-Scientific Studies. 2008;3:96–106. DOI: https://doi.org/10.32894/kujss.2008.42459

Mohsenian-Rad AH, Wong VWS, Jatskevich J, Schober R, Leon-Garcia A. Autonomous demand-side management based on game-theoretic energy consumption scheduling for the future smart grid. IEEE transactions on Smart Grid. 2010;1:320–331. DOI: https://doi.org/10.1109/TSG.2010.2089069

Vilaplana J, Solsona F, Teixidó I, Mateo J, Abella F, Rius J. A queuing theory model for cloud computing. The Journal of Supercomputing. 2014;69:492–507. DOI: https://doi.org/10.1007/s11227-014-1177-y

McCarl BA, Apland J. Validation of linear programming models. Journal of Agricultural and Applied Economics. 1986;18:155–164. DOI: https://doi.org/10.1017/S0081305200006208

Charnes A, Cooper WW, Miller MH. Application of linear programming to financial budgeting and the costing of funds. The Journal of Business. 1959;32:20–46. DOI: https://doi.org/10.1086/294232

Delson JK, Shahidehpour SM. Linear programming applications to power system economics, planning and operations. IEEE Transactions on Power Systems. 1992;7:1155–1163. DOI: https://doi.org/10.1109/59.207329

Vignaux GA, Michalewicz Z. A genetic algorithm for the linear transportation problem. IEEE transactions on systems, man, and cybernetics. 1991;21:445–452. DOI: https://doi.org/10.1109/21.87092

Kapoor VK. Operations research techniques for management. New Delhi: Sultan Chand & Sons.; 2003.

Adlakha V, Kowalski K, Lev B. Solving transportation problems with mixed constraints. International Journal of Management Science and Engineering Management. 2006 January;1:47-52. DOI: https://doi.org/10.1080/17509653.2006.10670996

Wang G, Wan Z, Wang X, Lv Y. Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem. Computers & Mathematics with Applications. 2008;56:2550–2555. DOI: https://doi.org/10.1016/j.camwa.2008.05.006

Bedekar PP, Bhide SR, Kale VS. Optimum coordination of overcurrent relays in distribution system using dual simplex method. In: 2009 Second International Conference on Emerging Trends in Engineering & Technology; 2009. p. 555–559. DOI: https://doi.org/10.1109/ICETET.2009.164

Kim T, Dong M. An iterative Hungarian method to joint relay selection and resource allocation for D2D communications. IEEE Wireless Communications Letters. 2014;3:625–628. DOI: https://doi.org/10.1109/LWC.2014.2338318

Karimi N, Davoudpour H. A branch and bound method for solving multi-factory supply chain scheduling with batch delivery. Expert Systems with Applications. 2015;42:238–245. DOI: https://doi.org/10.1016/j.eswa.2014.07.025

Nabli H. An overview on the simplex algorithm. Applied Mathematics and Computation. 2009;210:479–489. DOI: https://doi.org/10.1016/j.amc.2009.01.013

Boonperm Aa, Sinapiromsaran K. The artificial-free technique along the objective direction for the simplex algorithm. In: Journal of Physics: Conference Series; 2014. p. 012193. DOI: https://doi.org/10.1088/1742-6596/490/1/012193

Nabli H, Chahdoura S. Algebraic simplex initialization combined with the nonfeasible basis method. European Journal of Operational Research. 2015;245:384–391. DOI: https://doi.org/10.1016/j.ejor.2015.03.040

Sangngern K, Boonperm Aa. A new initial basis for the simplex method combined with the nonfeasible basis method. In: Journal of Physics: Conference Series; 2020. p. 012002. DOI: https://doi.org/10.1088/1742-6596/1593/1/012002

Downloads

Published

30-11-2023

How to Cite

1.
Tripathi SK, Kumar R. A Short Literature on Linear Programming Problem . EAI Endorsed Trans Energy Web [Internet]. 2023 Nov. 30 [cited 2024 Dec. 22];10. Available from: https://publications.eai.eu/index.php/ew/article/view/4516

Issue

Vol. 10 (2023): EAI Endorsed Transactions on Energy Web

Section

Short communications

License

Copyright (c) 2023 EAI Endorsed Transactions on Energy Web

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.

This is an open-access article distributed under the terms of the Creative Commons Attribution CC BY 4.0 license, which permits unlimited use, distribution, and reproduction in any medium so long as the original work is properly cited.

Crossref
Scopus
Google Scholar
Europe PMC