A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility
The mixing process of liquid products is a crucial activity in the industry of essential commodities like, medicine, pesticide, detergent, and so on. So, the mathematical study of the mixing problem is very much important to formulate a production inventory model of such type of items. In this work,...
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3166 |
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| author | Md Sadikur Rahman Subhajit Das Amalesh Kumar Manna Ali Akbar Shaikh Asoke Kumar Bhunia Leopoldo Eduardo Cárdenas-Barrón Gerardo Treviño-Garza Armando Céspedes-Mota |
| author_facet | Md Sadikur Rahman Subhajit Das Amalesh Kumar Manna Ali Akbar Shaikh Asoke Kumar Bhunia Leopoldo Eduardo Cárdenas-Barrón Gerardo Treviño-Garza Armando Céspedes-Mota |
| author_sort | Md Sadikur Rahman |
| collection | DOAJ |
| description | The mixing process of liquid products is a crucial activity in the industry of essential commodities like, medicine, pesticide, detergent, and so on. So, the mathematical study of the mixing problem is very much important to formulate a production inventory model of such type of items. In this work, the concept of the mixing problem is studied in the branch of production inventory. Here, a production model of mixed liquids with price-dependent demand and a stock-dependent production rate is formulated under preservation technology. In the formulation, first of all, the mixing process is presented mathematically with the help of simultaneous differential equations. Then, the mixed liquid produced in the mixing process is taken as a raw material of a manufacturing system. Then, all the cost components and average profit of the system are calculated. Now, the objective is to maximize the corresponding profit maximization problem along with the highly nonlinear objective function. Because of this, the mentioned maximization problem is solved numerically using MATHEMATICA software. In order to justify the validity of the model, two numerical examples are worked out. Finally, to show the impact of inventory parameters on the optimal policy, sensitivity analyses are performed and the obtained results are presented graphically. |
| first_indexed | 2024-03-10T03:38:03Z |
| format | Article |
| id | doaj.art-593d05ab5ed443dbba6938b31b6acdbd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:38:03Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-593d05ab5ed443dbba6938b31b6acdbd2023-11-23T09:25:08ZengMDPI AGMathematics2227-73902021-12-01924316610.3390/math9243166A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation FacilityMd Sadikur Rahman0Subhajit Das1Amalesh Kumar Manna2Ali Akbar Shaikh3Asoke Kumar Bhunia4Leopoldo Eduardo Cárdenas-Barrón5Gerardo Treviño-Garza6Armando Céspedes-Mota7Department of Mathematics, The University of Burdwan, Burdwan 713104, IndiaDepartment of Mathematics, The University of Burdwan, Burdwan 713104, IndiaDepartment of Mathematics, The University of Burdwan, Burdwan 713104, IndiaDepartment of Mathematics, The University of Burdwan, Burdwan 713104, IndiaDepartment of Mathematics, The University of Burdwan, Burdwan 713104, IndiaTecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, MexicoTecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, MexicoTecnologico de Monterrey, School of Engineering and Sciences, Ave. Eugenio Garza Sada 2501, Monterrey 64849, MexicoThe mixing process of liquid products is a crucial activity in the industry of essential commodities like, medicine, pesticide, detergent, and so on. So, the mathematical study of the mixing problem is very much important to formulate a production inventory model of such type of items. In this work, the concept of the mixing problem is studied in the branch of production inventory. Here, a production model of mixed liquids with price-dependent demand and a stock-dependent production rate is formulated under preservation technology. In the formulation, first of all, the mixing process is presented mathematically with the help of simultaneous differential equations. Then, the mixed liquid produced in the mixing process is taken as a raw material of a manufacturing system. Then, all the cost components and average profit of the system are calculated. Now, the objective is to maximize the corresponding profit maximization problem along with the highly nonlinear objective function. Because of this, the mentioned maximization problem is solved numerically using MATHEMATICA software. In order to justify the validity of the model, two numerical examples are worked out. Finally, to show the impact of inventory parameters on the optimal policy, sensitivity analyses are performed and the obtained results are presented graphically.https://www.mdpi.com/2227-7390/9/24/3166mixing processsimultaneous differential equationsvariable production ratesimulated annealingdifferential evolution |
| spellingShingle | Md Sadikur Rahman Subhajit Das Amalesh Kumar Manna Ali Akbar Shaikh Asoke Kumar Bhunia Leopoldo Eduardo Cárdenas-Barrón Gerardo Treviño-Garza Armando Céspedes-Mota A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility Mathematics mixing process simultaneous differential equations variable production rate simulated annealing differential evolution |
| title | A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility |
| title_full | A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility |
| title_fullStr | A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility |
| title_full_unstemmed | A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility |
| title_short | A Mathematical Model of the Production Inventory Problem for Mixing Liquid Considering Preservation Facility |
| title_sort | mathematical model of the production inventory problem for mixing liquid considering preservation facility |
| topic | mixing process simultaneous differential equations variable production rate simulated annealing differential evolution |
| url | https://www.mdpi.com/2227-7390/9/24/3166 |
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