Inventory Model for Deteriorating Pharmaceutical Items with Linear Demand Rate
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Keywords:
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Inventory Model, Pharmaceutical Goods, Deteriorating, Linear Demand Level, Complete Backlogging
Abstract
Good management of goods is needed so that the inventory activities of a business can run smoothly as the part of supply chain management which aims to monitor the flow of stock of goods from the purchasing process, and storage to the point of sale. In terms of inventory or supplies of pharmaceutical goods, conditions such as shortages or stockouts must also be considered which are a matter of control, management, and security. In this study, an inventory model is formulated with deterioration or damage to pharmaceutical goods that occurs due to the length of time when the goods are stored with a linear demand level. In the optimal solution, the inventory time occurs when it reaches the zero point (t1) of 0.34 and the cycle length (T1) of 0.83 with an average minimum total cost (TC) of $445.25 per cycle which is completed by WolframAlpha software. Sensitivity analysis changes the value results in the value of (TC) which that increases for all parameters. In increasing the linear function variables (a and b), it produces t1 and T1 stable values. An increase in the cost of each item damage (DC) and constant damage rate (theta) produces a t1 stable value, but the value of T1 increases. The increase in storage costs (h) results in a decrease in the value of t1 and T1. An increase in the cost of shortages (s) results in an increase in the value of t1 and a decrease in the value of T1.
References
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Savadkoohi, E., M. Mousazadeh, and S. A. Torabi (2018). A Possibilistic Location-Inventory Model for Multi-Period Perishable Pharmaceutical Supply Chain Network Design. Chemical Engineering Research and Design, 138; 490–505
Shah, N. H., D. G. Patel, D. B. Shah, and N. M. Prajapati (2023). A Sustainable Production Inventory Model with Green Technology Investment for Perishable Products. Decision Analytics Journal, 8; 100309
Silbermayr, L. and M. Waitz (2024). Omni-Channel Inventory Management of Perishable Products under Transshipment and Substitution. International Journal of Production Economics, 267; 109089
Soraya, I. (2016). Model Persediaan Economic Production Quantity (EPQ) Dengan Mempertimbangkan Deteriorasi. Jurnal Matematika UNAND, 3(3); 50–58 (in Indonesia)
Stechlinski, P., J. Jäschke, and P. I. Barton (2019). Generalized Sensitivity Analysis of Nonlinear Programs Using a Sequence of Quadratic Programs. Optimization, 68(2-3); 485–508
Susanti, E., F. M. Puspita, S. S. Supadi, E. Yuliza, and A. F. Ramadhan (2023). Improve Fuzzy Inventory Model of Fractal Interpolation with Vertical Scaling Factor. Science and Technology Indonesia, 8(4); 654–659
Tarigan, D. P., A. Wantoro, and S. Setiawansyah (2020). Sistem Pendukung Keputusan Pemberian Kredit Mobil Dengan Fuzzy Tsukamoto (Studi Kasus: Pt Clipan Finance). TELEFORTECH: Journal of Telematics and Information Technology, 1(1); 32–37 (in Indonesia)
Tiwari, S., L. E. Cárdenas-Barrón, M. Goh, and A. A. Shaikh (2018). Joint Pricing and Inventory Model for Deteriorating Items with Expiration Dates and Partial Backlogging under Two-Level Partial Trade Credits in Supply Chain. International Journal of Production Economics, 200; 16–36
Uthayakumar, R. and S. Karuppasamy (2016). A Pharmaceutical Inventory Model for Healthcare Industries with Quadratic Demand, Linear Holding Cost and Shortages. International Journal of Pure and Applied Mathematics, 106(8); 73–83
Uthayakumar, R. and S. Tharani (2018). An Inventory Model for Deteriorating Pharmaceutical Items with Time Dependent Demand under Complete Backlogging. Communications in Applied Analysis, 22(4); 511–530
Zhou, H., K. Chen, and S. Wang (2023). Two-Period Pricing and Inventory Decisions of Perishable Products with Partial Lost Sales. European Journal of Operational Research, 310(2); 611–626
Ahmadi, E., H. Mosadegh, R. Maihami, I. Ghalehkhondabi, M. Sun, and G. A. Süer (2022). Intelligent Inventory Management Approaches for Perishable Pharmaceutical Products in a Healthcare Supply Chain. Computers & Operations Research, 147; 105968
Alimuddin, N. H. M., Q. N. Izzuddin, M. A. Amat, and Z. A. Zaharudin (2023). A Multi-Period Model for Optimal Changi Airport Check-In Counter Operations. Science and Technology Indonesia, 8(1); 116–122
Andiraja, N. and D. Agustina (2020). Aplikasi Kendali Optimal Untuk Model Persediaan yang Mengalami Kerusakan pada Persediaan dan Perubahan Tingkat Permintaan. Jurnal Sains Matematika dan Statistika, 6(2); 12
Braglia, M., D. Castellano, L. Marrazzini, and D. Song (2019). A Continuous Review,(Q, r) Inventory Model for a Deteriorating Item with Random Demand and Positive Lead Time. Computers & Operations Research, 109; 102–121
Çömez-Dolgan, N., L. Moussawi-Haidar, B. Esmer, and M. Y. Jaber (2020). Temporary Price Increase during Replenishment Lead Time. Applied Mathematical Modelling, 78; 217–231
de Paula Vidal, G. H., R. G. G. Caiado, L. F. Scavarda, P. Ivson, and J. A. Garza-Reyes (2022). Decision Support Framework for Inventory Management Combining Fuzzy Multicriteria Methods, Genetic Algorithm, and Artificial Neural Network. Computers & Industrial Engineering, 174; 108777
Duary, A., S. Das, M. G. Arif, K. M. Abualnaja, M. A.-A. Khan, M. Zakarya, and A. A. Shaikh (2022). Advance and Delay in Payments with the Price-Discount Inventory Model for Deteriorating Items under Capacity Constraint and Partially Backlogged Shortages. Alexandria Engineering Journal, 61(2); 1735–1745
Fan, J. and J. Ou (2023). On Dynamic Lot Sizing with Bounded Inventory for a Perishable Product. Omega, 119; 102895
Gioia, D. G. and S. Minner (2023). On the Value of MultiEchelon Inventory Management Strategies for Perishable Items with On-/off-Line Channels. Transportation Research Part E: Logistics and Transportation Review, 180; 103354
He, X., X. Xu, and Y. Shen (2023). How Climate Change Affects Enterprise Inventory Management——from the Perspective of Regional Traffic. Journal of Business Research, 162; 113864
Karthick, B. and R. Uthayakumar (2021). A Single-Consignor Multi-Consignee Multi-Item Model with Permissible Payment Delay, Delayed Shipment and Variable Lead Time under Consignment Stock Policy. RAIRO-Operations Research, 55(4); 2439–2468
Kumar, S., S. Sami, S. Agarwal, and D. Yadav (2023). Sustainable Fuzzy Inventory Model for Deteriorating Item with Partial Backordering along with Social and Environmental Responsibility under the Effect of Learning. Alexandria Engineering Journal, 69; 221–241
Lee, S. M., P. Jiraporn, and H. Song (2020). Customer Concentration and Stock Price Crash Risk. Journal of Business Research, 110; 327–346
Limansyah, T., D. Lesmono, and I. Sandy (2020). Economic Order Quantity Model with Deterioration Factor and All Units Discount. In Journal of Physics: Conference Series, volume 1490. IOP Publishing, page 012052
Lin, Y.-S. and K.-J. Wang (2018). A Two-Stage Stochastic Optimization Model for Warehouse Configuration and Inventory Policy of Deteriorating Items. Computers & Industrial Engineering, 120; 83–93
Maddikunta, P. K. R., Q.-V. Pham, D. C. Nguyen, T. HuynhThe, O. Aouedi, G. Yenduri, S. Bhattacharya, and T. R. Gadekallu (2022). Incentive Techniques for the Internet of Things: A Survey. Journal of Network and Computer Applications, 206; 103464
Mohamadi, N., S. T. A. Niaki, M. Taher, and A. Shavandi (2024). An Application of Deep Reinforcement Learning and Vendor-Managed Inventory in Perishable Supply Chain Management. Engineering Applications of Artificial Intelligence, 127; 107403
Pakhira, R., S. Sarkar, and U. Ghosh (2020). Study of Memory Effect in an Inventory Model for Deteriorating Items with Partial Backlogging. Computers & Industrial Engineering, 148; 106705
Parvathi, P. and S. Gajalakshmi (2013). A Fuzzy Inventory Model With Lot Size Dependent Carrying/Holding Cost. IOSR Journal of Mathematics, 7(6); 106–110
Pramanik, P. and M. K. Maiti (2019). An Inventory Model for Deteriorating Items with Inflation Induced Variable Demand under Two Level Partial Trade Credit: A Hybrid ABC-GA Approach. Engineering Applications of Artificial Intelligence, 85; 194–207
Priyan, S. and P. Mala (2020). Optimal Inventory System for Pharmaceutical Products Incorporating Quality Degradation with Expiration Date: A Game Theory Approach. Operations Research for Health Care, 24; 100245
Rizqi, Z. and A. Khairunisa (2020). Integration of Deterministic and Probabilistic Inventory Methods to Optimize the Balance between Overstock and Stockout. In IOP Conference Series: Materials Science and Engineering, volume 722. IOP Publishing, page 012060
Savadkoohi, E., M. Mousazadeh, and S. A. Torabi (2018). A Possibilistic Location-Inventory Model for Multi-Period Perishable Pharmaceutical Supply Chain Network Design. Chemical Engineering Research and Design, 138; 490–505
Shah, N. H., D. G. Patel, D. B. Shah, and N. M. Prajapati (2023). A Sustainable Production Inventory Model with Green Technology Investment for Perishable Products. Decision Analytics Journal, 8; 100309
Silbermayr, L. and M. Waitz (2024). Omni-Channel Inventory Management of Perishable Products under Transshipment and Substitution. International Journal of Production Economics, 267; 109089
Soraya, I. (2016). Model Persediaan Economic Production Quantity (EPQ) Dengan Mempertimbangkan Deteriorasi. Jurnal Matematika UNAND, 3(3); 50–58 (in Indonesia)
Stechlinski, P., J. Jäschke, and P. I. Barton (2019). Generalized Sensitivity Analysis of Nonlinear Programs Using a Sequence of Quadratic Programs. Optimization, 68(2-3); 485–508
Susanti, E., F. M. Puspita, S. S. Supadi, E. Yuliza, and A. F. Ramadhan (2023). Improve Fuzzy Inventory Model of Fractal Interpolation with Vertical Scaling Factor. Science and Technology Indonesia, 8(4); 654–659
Tarigan, D. P., A. Wantoro, and S. Setiawansyah (2020). Sistem Pendukung Keputusan Pemberian Kredit Mobil Dengan Fuzzy Tsukamoto (Studi Kasus: Pt Clipan Finance). TELEFORTECH: Journal of Telematics and Information Technology, 1(1); 32–37 (in Indonesia)
Tiwari, S., L. E. Cárdenas-Barrón, M. Goh, and A. A. Shaikh (2018). Joint Pricing and Inventory Model for Deteriorating Items with Expiration Dates and Partial Backlogging under Two-Level Partial Trade Credits in Supply Chain. International Journal of Production Economics, 200; 16–36
Uthayakumar, R. and S. Karuppasamy (2016). A Pharmaceutical Inventory Model for Healthcare Industries with Quadratic Demand, Linear Holding Cost and Shortages. International Journal of Pure and Applied Mathematics, 106(8); 73–83
Uthayakumar, R. and S. Tharani (2018). An Inventory Model for Deteriorating Pharmaceutical Items with Time Dependent Demand under Complete Backlogging. Communications in Applied Analysis, 22(4); 511–530
Zhou, H., K. Chen, and S. Wang (2023). Two-Period Pricing and Inventory Decisions of Perishable Products with Partial Lost Sales. European Journal of Operational Research, 310(2); 611–626
Authors
Indrawati, Puspita, F. M., Supadi, S. S., Yuliza, E., & Rizki, K. (2024). Inventory Model for Deteriorating Pharmaceutical Items with Linear Demand Rate. Science and Technology Indonesia, 9(1), 148–155. https://doi.org/10.26554/sti.2024.9.1.148-155
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