Linear Programming is an optimization technique to attain the most effective outcome or optimize the objective function (like maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships called the constraints. In this paper, we have discussed fundamental and detailed techniques of formulating LPs models in various real-life decision problems, decisions, works, etc. In the human body, an unhealthy diet can cause a lot of nutrition-related diseases. Sometimes, having a proper diet costs beyond one’s limit and it affects us to develop a diet based budget-friendly nutrition model. Our goal is to minimize the total cost considering the required amount of nutrition values required. To construct the study we took some standard values of nutrition ingredients to compute the budget-friendly values. It's quite hard to resolve most of the real-life models with a large number of decision variables & constraints by hand calculations implies the use of AMPL (A Mathematical Programming Language) coding to get the optimal result. The number of variables & constraints isn't mattered in any respect for the computer techniques used in this study. This study results in some standard values of diet plan for optimizing the nutrition for a particular person with limited costs.
Published in | Science Journal of Applied Mathematics and Statistics (Volume 8, Issue 5) |
DOI | 10.11648/j.sjams.20200805.12 |
Page(s) | 59-66 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2020. Published by Science Publishing Group |
Optimization, Linear Programming Diet, Optimization Model, Real-Life Application, AMPL, Computer-Based Program
[1] | Hillier, Frederick S. Introduction to operations research. Tata McGraw-Hill Education, 2012. |
[2] | Kantorovich, L. V. "On one effective method of solving some classes of extreme problems." Reports from the Academy of Sciences. Vol. 28. No. 3. Federal State Unitary Enterprise Academic Science, Publishing, Printing and Book Distribution Center Science, 1940. |
[3] | Stapel, Elizabeth. "Linear Programming: Introduction." Purple math. Available from https://www.purplemath.com/modules/linprog.htm |
[4] | Noyes, James, and Weisstein, Eric W. "Linear Programming." From MathWorld-A Wolfram Web Resource. https://mathworld.wolfram.com/LinearProgramming.html. |
[5] | Rezaul Karim, et. al. “Linear Programming”. |
[6] | Topcu, Y. İlker. "Operations Research II Lecture Notes." (2016). |
[7] | Saigal, Romesh. "Linear programming: a modern integrated analysis." Journal of the Operational Research Society 48.7 (1997): 762-762. |
[8] | Dantzig, George B., and Mukund N. Thapa. Linear Programming. 1, Introduction {Springer Series in Operations Research}. Springer-Verlag New York Incorporated, 1997. |
[9] | Dent, John Barry, and Harold Casey. "Linear programming and animal nutrition." Linear programming and animal nutrition. (1967). |
[10] | Ferguson, Elaine L., et al. "Food-based dietary guidelines can be developed and tested using linear programming analysis." The Journal of Nutrition 134.4 (2004): 951-957. |
[11] | Darmon, Nicole, Elaine L. Ferguson, and André Briend. "A cost constraint alone has adverse effects on food selection and nutrient density: an analysis of human diets by linear programming." The Journal of Nutrition 132.12 (2002): 3764-3771. |
[12] | Santika, Otte, Umi Fahmida, and Elaine L. Ferguson. "Development of food-based complementary feeding recommendations for 9-to 11-month-old peri-urban Indonesian infants using linear programming." The Journal of Nutrition 139.1 (2009): 135-141. |
[13] | Calkins, Peter H. "Nutritional adaptations of linear programming for planning rural development." American Journal of Agricultural Economics 63.2 (1981): 247-254. |
[14] | Fletcher, L. R., P. M. Soden, and A. S. I. Zinober. "Linear programming techniques for the construction of palatable human diets." Journal of the Operational Research Society 45.5 (1994): 489-496. |
[15] | Foytik, Jerry. "Very low-cost nutritious diet plans designed by linear programming." Journal of Nutrition Education 13.2 (1981): 63-66. |
[16] | Eghbali, Hossein. "Implement a Proper Nutrition Model for Athletes Using the Linear Optimization Model." Available at SSRN 3568367 (2020). |
[17] | Ibrahim, Nur Fadhilah, Thurga Dewi Arunasalan, and Nurul Akmal Mohamed. "Cheap vs healthy: Analyzing McDonald’s menu using linear programming." Bulletin of Electrical Engineering and Informatics 9.2 (2020): 771-776. |
[18] | Mallick, Priyaranjan, et al. "Broiler Poultry Feed Cost Optimization Using Linear Programming Technique." Journal of Operations and Strategic Planning (2020): 2516600X19896910. |
[19] | Very-Jr, Eliseu, et al. "Planning dietary improvements without additional costs for low-income individuals in Brazil: linear programming optimization as a tool for public policy in nutrition and health." Nutrition Journal 18.1 (2019): 40. |
[20] | Alaini, Reham, Roslee Rajikan, and Siti Masitah Elias. "Diet optimization using linear programming to develop low-cost cancer prevention food plan for selected adults in Kuala Lumpur, Malaysia." BMC public health 19.4 (2019): 546. |
[21] | Henson, Spencer. "Linear programming analysis of constraints upon human diets." Journal of Agricultural Economics 42.3 (1991): 380-393. |
[22] | Mansini, Renata, Wlodzimierz Ogryczak, and M. Grazia Speranza. "Twenty years of linear programming based portfolio optimization." European Journal of Operational Research 234.2 (2014): 518-535. |
[23] | Kabak, Özgür, and Füsun Ülengin. "Possibilistic linear-programming approach for supply chain networking decisions." European Journal of Operational Research 209.3 (2011): 253-264. |
[24] | Chretienne, Philippe, et al. "Scheduling theory and its applications." Journal of the Operational Research Society 48.7 (1997): 764-765. |
[25] | Ben-Tal, Aharon, and Arkadi Nemirovski. "Robust solutions of uncertain linear programs." Operations research letters 25.1 (1999): 1-13. |
[26] | Bhuiyan, Md Anwarul Islam, and Shek Ahmed. "A new computer-oriented technique for solving a linear programming problem using bender’s decomposition method." |
[27] | Nilu, Tanzila Yeasmin, Shek Ahmed, and M. A. I. Bhuiyan. "A study of sensitivity analysis in linear programming problem and its implementation in real life." |
[28] | Fourer, Robert, David M. Gay, and Brian W. Kernighan. AMPL: A mathematical programming language. Murray Hill, NJ: AT & T Bell Laboratories, 1987. |
[29] | Ahmed, Hashnayne, and Shek Ahmed. "A Comparative Study on Harvesting Plan Predicting Insurance with Two-Stage Stochastic Analysis." International Journal on Data Science and Technology 5.4 (2019): 73. |
[30] | Fourer, Robert. "AMPL models for not linear optimization using linear solvers." Proc. EURO-INFORMS Joint Int. Meeting, Rome, Italy. 2013. |
[31] | Hsu, Chien-Ning, et al. "The interplay between a maternal and post-weaning high-fat diet and gut microbiota in the developmental programming of hypertension." Nutrients 11.9 (2019): 1982. |
[32] | Gay, David M. "The AMPL modeling language: An aid to formulating and solving optimization problems." Numerical analysis and optimization. Springer, Cham, 2015. 95-116. |
APA Style
Tanzila Yeasmin Nilu, Shek Ahmed, Hashnayne Ahmed. (2020). Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming. Science Journal of Applied Mathematics and Statistics, 8(5), 59-66. https://doi.org/10.11648/j.sjams.20200805.12
ACS Style
Tanzila Yeasmin Nilu; Shek Ahmed; Hashnayne Ahmed. Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming. Sci. J. Appl. Math. Stat. 2020, 8(5), 59-66. doi: 10.11648/j.sjams.20200805.12
AMA Style
Tanzila Yeasmin Nilu, Shek Ahmed, Hashnayne Ahmed. Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming. Sci J Appl Math Stat. 2020;8(5):59-66. doi: 10.11648/j.sjams.20200805.12
@article{10.11648/j.sjams.20200805.12, author = {Tanzila Yeasmin Nilu and Shek Ahmed and Hashnayne Ahmed}, title = {Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming}, journal = {Science Journal of Applied Mathematics and Statistics}, volume = {8}, number = {5}, pages = {59-66}, doi = {10.11648/j.sjams.20200805.12}, url = {https://doi.org/10.11648/j.sjams.20200805.12}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20200805.12}, abstract = {Linear Programming is an optimization technique to attain the most effective outcome or optimize the objective function (like maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships called the constraints. In this paper, we have discussed fundamental and detailed techniques of formulating LPs models in various real-life decision problems, decisions, works, etc. In the human body, an unhealthy diet can cause a lot of nutrition-related diseases. Sometimes, having a proper diet costs beyond one’s limit and it affects us to develop a diet based budget-friendly nutrition model. Our goal is to minimize the total cost considering the required amount of nutrition values required. To construct the study we took some standard values of nutrition ingredients to compute the budget-friendly values. It's quite hard to resolve most of the real-life models with a large number of decision variables & constraints by hand calculations implies the use of AMPL (A Mathematical Programming Language) coding to get the optimal result. The number of variables & constraints isn't mattered in any respect for the computer techniques used in this study. This study results in some standard values of diet plan for optimizing the nutrition for a particular person with limited costs.}, year = {2020} }
TY - JOUR T1 - Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming AU - Tanzila Yeasmin Nilu AU - Shek Ahmed AU - Hashnayne Ahmed Y1 - 2020/09/21 PY - 2020 N1 - https://doi.org/10.11648/j.sjams.20200805.12 DO - 10.11648/j.sjams.20200805.12 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 59 EP - 66 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20200805.12 AB - Linear Programming is an optimization technique to attain the most effective outcome or optimize the objective function (like maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships called the constraints. In this paper, we have discussed fundamental and detailed techniques of formulating LPs models in various real-life decision problems, decisions, works, etc. In the human body, an unhealthy diet can cause a lot of nutrition-related diseases. Sometimes, having a proper diet costs beyond one’s limit and it affects us to develop a diet based budget-friendly nutrition model. Our goal is to minimize the total cost considering the required amount of nutrition values required. To construct the study we took some standard values of nutrition ingredients to compute the budget-friendly values. It's quite hard to resolve most of the real-life models with a large number of decision variables & constraints by hand calculations implies the use of AMPL (A Mathematical Programming Language) coding to get the optimal result. The number of variables & constraints isn't mattered in any respect for the computer techniques used in this study. This study results in some standard values of diet plan for optimizing the nutrition for a particular person with limited costs. VL - 8 IS - 5 ER -