An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations
Abstract In this research study we present an advanced adaption of the economic and efficient optimized production model by integrating Weibull-distributed progressive degradation, dynamic holding costs, fluctuating demand, and strong strategies for effectively managing shortages and backlogs. The e...
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| Format: | Article |
| Language: | English |
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Springer
2025-02-01
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| Series: | Discover Applied Sciences |
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| Online Access: | https://doi.org/10.1007/s42452-024-06423-x |
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| author | Gopal Kumar Gupta Atma Nand N. S. Chauhan Shivanand |
| author_facet | Gopal Kumar Gupta Atma Nand N. S. Chauhan Shivanand |
| author_sort | Gopal Kumar Gupta |
| collection | DOAJ |
| description | Abstract In this research study we present an advanced adaption of the economic and efficient optimized production model by integrating Weibull-distributed progressive degradation, dynamic holding costs, fluctuating demand, and strong strategies for effectively managing shortages and backlogs. The economic production quantity model aims to enhance production volumes and reduce total variable costs for commodities that have a near-term expiration date yet possess a prolonged shelf life due to delayed deterioration. The model characterizes inventories with three unique demand patterns by analytically solving ordinary differential equations through Maclaurin series approximations. It specifically addresses situations when product demand varies predictably over time and accounts for the probability of defective items during production. This model has significant implications for cognitive processes in the production of consumer goods, since it provides valuable insights into efficient inventory management and production planning. The paper employs two illustrations to substantiate the utility of the established model and utilizes sensitivity analysis to propose other subjects for exploration. This work proposes an enhanced economic and efficient optimized production (EPQ) model to tackle production faults, dynamic demand patterns, Weibull-distributed deterioration-related inventory management challenges. With these components, the model tries to maximize manufacturing quantities and lower total variable costs for products with near-term expiration dates. The model analytically solves the differential equations approximating inventory levels under three different demand patterns: constant, linear, and quadratic using Maclaurin series approximations. The model also addresses the likelihood of faults in produced goods throughout the production process. |
| format | Article |
| id | doaj-art-b1a5931dfc3f430fa798105682aa46af |
| institution | Kabale University |
| issn | 3004-9261 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Springer |
| record_format | Article |
| series | Discover Applied Sciences |
| spelling | doaj-art-b1a5931dfc3f430fa798105682aa46af2025-02-02T12:36:44ZengSpringerDiscover Applied Sciences3004-92612025-02-017212210.1007/s42452-024-06423-xAn EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximationsGopal Kumar Gupta0Atma Nand1N. S. Chauhan2Shivanand3Symbiosis Institute of Technology Nagpur Campus, Symbiosis International (Deemed University)Department of Mathematics, School of Applied and Life Sciences, Uttaranchal UniversityDepartment of Mathematics, Faculty of Engineering (FOE), Teerthanker Mahaveer UniversityDepartment of Pharmacy, Shyam Sai Institute of EducationAbstract In this research study we present an advanced adaption of the economic and efficient optimized production model by integrating Weibull-distributed progressive degradation, dynamic holding costs, fluctuating demand, and strong strategies for effectively managing shortages and backlogs. The economic production quantity model aims to enhance production volumes and reduce total variable costs for commodities that have a near-term expiration date yet possess a prolonged shelf life due to delayed deterioration. The model characterizes inventories with three unique demand patterns by analytically solving ordinary differential equations through Maclaurin series approximations. It specifically addresses situations when product demand varies predictably over time and accounts for the probability of defective items during production. This model has significant implications for cognitive processes in the production of consumer goods, since it provides valuable insights into efficient inventory management and production planning. The paper employs two illustrations to substantiate the utility of the established model and utilizes sensitivity analysis to propose other subjects for exploration. This work proposes an enhanced economic and efficient optimized production (EPQ) model to tackle production faults, dynamic demand patterns, Weibull-distributed deterioration-related inventory management challenges. With these components, the model tries to maximize manufacturing quantities and lower total variable costs for products with near-term expiration dates. The model analytically solves the differential equations approximating inventory levels under three different demand patterns: constant, linear, and quadratic using Maclaurin series approximations. The model also addresses the likelihood of faults in produced goods throughout the production process.https://doi.org/10.1007/s42452-024-06423-xDeterministic time-varying demandDynamic holding costsNon-instantaneous Weibull-distributed deteriorationManufacturing flaws |
| spellingShingle | Gopal Kumar Gupta Atma Nand N. S. Chauhan Shivanand An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations Discover Applied Sciences Deterministic time-varying demand Dynamic holding costs Non-instantaneous Weibull-distributed deterioration Manufacturing flaws |
| title | An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations |
| title_full | An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations |
| title_fullStr | An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations |
| title_full_unstemmed | An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations |
| title_short | An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations |
| title_sort | epq inventory model with weibull distribution dynamic time dependent holding cost under various demand pattern using maclaurin series approximations |
| topic | Deterministic time-varying demand Dynamic holding costs Non-instantaneous Weibull-distributed deterioration Manufacturing flaws |
| url | https://doi.org/10.1007/s42452-024-06423-x |
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