An Introduction to Linear Programming Problems with Some Real-Life Applications



Abstract Views
3922

Downloads
2238

Citations

Share

##plugins.themes.bootstrap3.article.sidebar##

Submitted Mar 15, 2022
Published Apr 8, 2022
10.24018/ejmath.2022.3.2.108

Abstract viewed = 3922 times

Table of Contents

##plugins.themes.bootstrap3.article.main##

Linear programming is a mathematical tool for optimizing an outcome through a mathematical model. In recent times different mathematical models are extensively used in the planning of different real-life applications such as agriculture, management, business, industry, transportation, telecommunication, engineering, and so on. It is mainly used to make the real-life situation easier, more comfortable, and more economic, and to get optimum achievement from the limited resources. This paper has tried to shed light on the basic information about linear programming problems and some real-life applications. It presents the general introduction of the linear programming problem, historical overview, meaning and definition of a linear programming problem, assumptions of a linear programming problem, component of a linear programming problem, and characteristics of a linear programming problem, and some highlights of some real-life applications.

Keywords: Constraints, decision variables, linear programming, objective function, optimization

References

  1. Dantzig G B, Thapa MN. Linear programming 1:Introduction. Springer-Verlag New York, Inc, 1997.
     Google Scholar
  2. Srinath LN. Linear Programming: Principles and applications. Second Edition. Basingstoke, England: Palgrave Macmillan, 1983.
     Google Scholar
  3. Bhattarai D. Linear programming problems: Determination of optimal value of real-life practical problems. Nuta Journal. 2018; 5(1-2): 79-86.
     Google Scholar
  4. Oliveira V, Paulo P. Evaluation in Urban Planning: Advances and Prospects. Journal of Planning Literature. 2010; 24(4): 343–361.
     Google Scholar
  5. Rao S. Engineering optimization: Theory and practice, Fifth Edition. John Wiley & Sons, Inc, 2020.
     Google Scholar
  6. Sahana SK, Khowas M, Sinha K. Budget optimization and allocation: An evolutionary computing based model. Bentham Science Publishers, 2018.
     Google Scholar
  7. Kanno Y. Exploiting lagrange duality for topology optimization with frictionless unilateral contact. Japan Journal of Industrial and Applied Mathematics. 2020; 37: 25-48.
     Google Scholar
  8. Sierksma G, Zwols Y. Linear and integer optimization theory and practice. Third Edition. Taylor & Francis Group, 2015.
     Google Scholar
  9. Thie PR, Keough GE. An Introduction to linear programming and game theory. Third Edition. John Wiley & Sons, 2008.
     Google Scholar
  10. Stanimirovic I. Advances in optimization and linear programming. First Edition. Apple Academic Press, Inc. 2022.
     Google Scholar
  11. Sharma, J. Operations research theory and applications. Sixth Edition. Laxmi Publications Pvt. Ltd, 2017.
     Google Scholar
  12. Eiselt HA C-L Sandblom. Linear programming and its applications. New York, NY: Springer, 2010.
     Google Scholar
  13. William PF, Fausto PG. Modeling and Linear Programming in Engineering Management. Intech Open Access Publisher, 2013.
     Google Scholar
  14. Yang X. Linear Programming. Optimization Techniques and Applications with Examples. Hoboken, NJ, USA: John Wiley & Sons, Inc. 2018: 125–140.
     Google Scholar
  15. Elhami A, Radi B. Optimizations and programming: linear, non-linear, dynamic, stochastic and applications with Matlab. John Wiley & Sons, Inc, 2021.
     Google Scholar
  16. Bixby, Robert E. Solving real-world linear programs: A decade and more of progress. Operations research. 2002; 50(1): 3–15.
     Google Scholar