A MATHEMATICAL MODEL WITH INVENTORY- AND SELLING PRICE-DEPENDENT DEMANDS CONSIDERING ALL-UNITS DISCOUNT AND CARBON EMISSION

  • Ni Putu Dittarani Pramesti Center for Mathematics and Society, Department of Mathematics, Faculty of Information Technology and Sciences, Parahyangan Catholic University, Indonesia
  • Taufik Limansyah Center for Mathematics and Society, Department of Mathematics, Faculty of Information Technology and Sciences, Parahyangan Catholic University, Indonesia
  • Dharma Lesmono Center for Mathematics and Society, Department of Mathematics, Faculty of Information Technology and Sciences, Parahyangan Catholic University, Indonesia
DOI: https://doi.org/10.30598/barekengvol18iss1pp0129-0140
Keywords: Inventory, Economic Order Quantity Model, All-units Discount, Carbon Emission

Abstract

Customer satisfaction is a crucial aspect that consistently takes center stage in business operations. In light of this, companies must devise appropriate strategies to fulfill customer demands. Consequently, this study delves into examining various factors that facilitate the supply process, including the application of discounts. Moreover, in line with the advancements in eco-green concepts, businesses have begun considering carbon emission factors concerning storage and distribution, which is further supported by the United Nations Framework Convention on Climate Change (UNFCCC). In this context, the paper presents an enhanced version of the economic order quantity model encompassing all-unit discount and carbon emission factors. The developed model entail inventory management approaches where demand relies on inventory levels, inventory levels coupled with selling prices, time-dependent demand, and exponentially declining demand patterns. The primary objective is to aid companies in optimizing their inventory management by determining the optimal quantity of goods while minimizing overall costs. Sensitivity analysis conducted to observe the influence on the reorder point (T), total inventory cost (TC), and total carbon emission (TE) reveals that lower unit purchase prices, driven by high demand, correspond to larger order quantities. Furthermore, it is worth noting that the higher average carbon emission within warehouses result in increased carbon emissions overall.

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References

B. C. Giri, S. Pala, A. Goswami and K. Chaudhuri, "An inventory model for deteriorating items with stock-dependent demand rate," European Journal of Operational Research, vol. 95, pp. 604-610, 1996.

N. Tashakkor, S. H. Mirmohammadi and M. Iranpoor, "Joint optimization of dynamic pricing and replenishment cycle considering variable non-instantaneous deterioration and stock-dependent demand," Computers & Industrial Engineering, vol. 123, pp. 232-241, 2018.

N. Loedy, D. Lesmono and T. Limansyah, "An Inventory-Dependent Demand Model with Deterioration, All-Units Discount, and Return," IOP Conf Series: Journal of Physics, vol. 1108, p. 012010, 2018.

V. Vora and U. Gothi, "Deterministic Inventory Model for deteriorating Items with Price Dependent Demand Rate and Inflation," International Journal of Scientific Research in Mathematical and Statistical Sciences, vol. 7, no. 6, pp. 20-28, 2020.

J.I. Ichwanto, J.D. Lesmono and T. Limansyah, "An inventory model for estimation of deterioration with time-dependent demand and storage cost," IOP Conf. Series: Journal of Physics, vol. 1940, p.012012, 2021.

W. Adiani, D. Lesmono and T. Limansyah, "Model persediaan dengan permintaan bergantung pada harga jual dan tingkat persediaan dengan faktor deteriorasi," Jurnal Ilmiah Teknik Industri, vol. 18, pp. 183-191, 2019.

N. H. Shah, K. Rabari and E. Patel, "A deteriorating inventory model under overtime production and credit policy for stock- and price sensitive demand function," Operational Research in Engineering Sciences: Theory and Applications, vol. 5, no. 2, pp. 85-98, 2022.

M. Onal, A. Yenipazarli and O. E. Kundakcioglu, "A mathematical model for perishable products with price- and displayed- stock- dependent demand," Computers & Industrial Engineering, vol. 102, pp. 246-258, 2016

T. Limansyah and D. Lesmono, "A mathematical model for inventory and price-dependent demand with discount," IOP Conf. Series: Journal of Physics, vol. 1490, pp. 12-51, 2020.

T. Joviani, D. Lesmono and T. Limansyah, "A Multi-item Inventory Model with Various Demand Functions Considering Deterioration and Partial Backlogging," BAREKENG: Jurnal Ilmu Matematika dan Terapan vol.17, pp. 1069-1080, 2023.

D. Lesmono, T. Limansyah and N. Loedy, "A Joint Return Policy for a Multi-Item Perishable Inventory Model with Deterministic Demands, Return and All-Units Discount," International Journal of Mathematical, Engineering and Management Sciences Vol. 5, No. 3, 416-431, 2020..

R.I.P. Setiawan, J.D. Lesmono and T. Limansyah. "Inventory Control Problems with Exponential and Quadratic Demand considering Weibull Deterioration," IOP Conf. Series: Journal of Physics, vol. 1821 p. 0120571, 2021.

D. Lesmono, T. Limansyah and H. Koswara, "Optimal replenishment policy for multi-item probabilistic inventory model with all-units discount," IOP Conf. Series: Journal of Physics, vol. 1218, p.012036, 2019.

T. Limansyah and D. Lesmono, "Probabilistic Inventory Model with Expiration Date and All-Units Discount," IOP Conf. Series: Materials Science and Engineering, vol. 546, p.052042, 2019.

D. Lesmono and T. Limansyah, "A probabilistic inventory model with deterioration factor and continuous discount function", AIP Conference Proceedings, vol. 2192, p. 060013, 2019.

T. Limansyah, D. Lesmono and I. Sandy, "Economic order quantity model with deterioration factor and all-unit discount," IOP Cond: Series: Journal of Physics, vol. 1490, pp. 12-52, 2020.

A. Duary, S. Das, M. G. Arif and K. M. Abualnaja, "Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraint and partially backlogged shortages," Alexandria Engineering Journal, vol. 61, pp. 1735-1845, 2022.

D. Lesmono, T. Limansyah and S. W. Setiawan, "A Perishable Inventory Model with Return," IOP Conf.Series: Materials Science and Engineering, pp. 1735-1845, 2022.

J. Sicilia, L. A. San Jose and D. Alcade-Lopez-de-Pablo, "Optimal policy for multi-item systems with stochastic demands, backlogged shortages and limited storage capacity," Applied Mathematical Modelling, vol. 108, pp. 236-257, 2022.

R. Y. H. Silitonga, L. R. Kristiana and T. A. Parley, "A Multi-Item Probabilistic Inventory Model that Considers Expiration Factor, All-unit Discount Policy and Warehouse Capacity Constrains," Jurnal Teknik Industri, vol. 23, no. 2, pp. 139-148, 2021.

C.-J. Lu, M. Gu and T.-S. Y. C.-T. Lee, "Impact of carbon emission policy combinations on the optimal production-inventory decisions for deteriorating items," Expert Systems With Applications, vol. 201, pp. 117-234, 2022.

C. Yu, Z. Qu, T. W. Archibald and Z. Luan, "An inventory model of a deteriorating product considering carbon emissions," Computers & Industrial Engineering, vol. 148, pp. 106-694, 2020.

Y.-S. Huang, C.-C. Fang and Y.-A. Lin, "Inventory management in supply chains with consideration of logistics, green investment and different carbon emissions policies," Computer & Industrial Engineering, vol. 139, pp. 106-207, 2020.

S. Benjaafar and M. Daskin, "Carbon footprint and the management of supply chain : Insights from simple models," IEEE transactions on automation science and engineering, vol. 10, pp. 99-116, 2012.

X. Chen, S. Benjaafar and A. Elomri, "The carbon-constrained EOQ," Operation Research Letters, vol. 41, pp. 172-179, 2013.

I. M. Kristiyani and Y. Daryanto, "An inventory model considering all-unit discount and carbon emissions," International Journal of Industrial Engineering and Engineering Management, vol. 1, pp. 43-50, 2019.

Published
2024-03-01
How to Cite
[1]
N. Pramesti, T. Limansyah, and D. Lesmono, “A MATHEMATICAL MODEL WITH INVENTORY- AND SELLING PRICE-DEPENDENT DEMANDS CONSIDERING ALL-UNITS DISCOUNT AND CARBON EMISSION”, BAREKENG: J. Math. & App., vol. 18, no. 1, pp. 0129-0140, Mar. 2024.
Issue
Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Ni Putu Dittarani Pramesti, Taufik Limansyah, Dharma Lesmono

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