Integrated Multi-Period Linear Programming for Production Mix and Raw-Material Procurement in an NPK Fertilizer Plant
Abstract
Keywords
Full Text:
PDFReferences
Kementerian Pertanian Republik Indonesia, “Peraturan Menteri Pertanian Nomor 10 Tahun 2022 tentang Tata Cara Penetapan Alokasi dan Harga Eceran Tertinggi Pupuk Bersubsidi Sektor Pertanian,” Kementerian Pertanian. Accessed: Oct. 16, 2026. [Online]. Available: https://peraturan.bpk.go.id/Details/224621/permentan-no-10-tahun-2022
I. M. Fahmid et al., “Study of the impact of increasing the highest retail price of subsidized fertilizer on rice production in Indonesia,” Open Agric., vol. 7, no. 1, pp. 348–359, May 2022, https://doi.org/10.1515/opag-2022-0087.
N. Zečević and S. Jevremović, “A linear mathematical optimization model for variable costs calculation in fertilizer production complex,” International Journal of System Assurance Engineering and Management, vol. 15, no. 6, pp. 2588–2598, Jun. 2024, https://doi.org/10.1007/s13198-024-02278-y.
K. A. Abay, J. Chamberlin, P. Chivenge, and D. J. Spielman, “Fertilizer, soil health, and economic shocks: A synthesis of recent evidence,” Food Policy, vol. 133, p. 102892, May 2025, https://doi.org/10.1016/j.foodpol.2025.102892.
P. Vatsa, D. Miljkovic, and J. Baek, “Linkages between natural gas, fertiliser and cereal prices: A note,” J. Agric. Econ., vol. 74, no. 3, pp. 935–940, Sep. 2023, https://doi.org/10.1111/1477-9552.12532.
P. Alexander, A. Arneth, R. Henry, J. Maire, S. Rabin, and M. D. A. Rounsevell, “High energy and fertilizer prices are more damaging than food export curtailment from Ukraine and Russia for food prices, health and the environment,” Nat. Food, vol. 4, no. 1, pp. 84–95, Dec. 2022, https://doi.org/10.1038/s43016-022-00659-9.
R. K. Jana, I. Ghosh, and P. N. R. Kumar, “An explainable AI-enabled granular ensemble machine learning framework to demystify fertilizer price movements,” Journal of the Operational Research Society, vol. 75, no. 8, pp. 1569–1586, Aug. 2024, https://doi.org/10.1080/01605682.2023.2260908.
J. Kallrath, “Planning and scheduling in the process industry,” OR Spectrum, vol. 24, no. 3, pp. 219–250, Aug. 2002, https://doi.org/10.1007/s00291-002-0101-7.
C.-N. Wang, S.-D. Syu, C.-C. Chou, V. Tinh Nguyen, and D. Van Thuy Cuc, “Two-Stage Production Planning Under Stochastic Demand: Case Study of Fertilizer Manufacturing,” Computers, Materials & Continua, vol. 70, no. 1, pp. 1195–1207, 2022, https://doi.org/10.32604/cmc.2022.019890.
G. Luo, X. Liu, and F. T. S. Chan, “Optimal Ordering Decisions in Portfolio Procurement Considering Spot Price Fluctuation,” Sustainability, vol. 15, no. 14, p. 11169, Jul. 2023, https://doi.org/10.3390/su151411169.
S. K. Devalkar, R. Anupindi, and A. Sinha, “Integrated Optimization of Procurement, Processing, and Trade of Commodities,” Oper. Res., vol. 59, no. 6, pp. 1369–1381, Dec. 2011, https://doi.org/10.1287/opre.1110.0959.
C. Mandl and S. Minner, “Data-Driven Optimization for Commodity Procurement Under Price Uncertainty,” Manufacturing & Service Operations Management, vol. 25, no. 2, pp. 371–390, Mar. 2023, https://doi.org/10.1287/msom.2020.0890.
O. Karabağ and B. Gökgür, “Integrated optimisation of pricing, manufacturing, and procurement decisions of a make-to-stock system operating in a fluctuating environment,” Int. J. Prod. Res., vol. 61, no. 24, pp. 8423–8450, Dec. 2023, https://doi.org/10.1080/00207543.2022.2152127.
X. Zhang, W. Dai, and X. Cai, “Inventory replenishment decisions with uncertain price and demand,” Int. J. Prod. Res., vol. 62, no. 7, pp. 2663–2682, Apr. 2024, https://doi.org/10.1080/00207543.2023.2223701.
R. Güllü and N. Erkip, “Risk pooling under demand and price uncertainty,” Eur. J. Oper. Res., vol. 315, no. 1, pp. 120–129, May 2024, https://doi.org/10.1016/j.ejor.2023.11.028.
D. Zamani Dadaneh, S. Moradi, and B. Alizadeh, “Simultaneous planning of purchase orders, production, and inventory management under demand uncertainty,” Int. J. Prod. Econ., vol. 265, p. 109012, Nov. 2023, https://doi.org/10.1016/j.ijpe.2023.109012.
L. Glomb, F. Liers, and F. Rösel, “A rolling-horizon approach for multi-period optimization,” Eur. J. Oper. Res., vol. 300, no. 1, pp. 189–206, Jul. 2022, https://doi.org/10.1016/j.ejor.2021.07.043.
A. Forel and M. Grunow, “Dynamic stochastic lot sizing with forecast evolution in rolling‐horizon planning,” Prod. Oper. Manag., vol. 32, no. 2, pp. 449–468, Feb. 2023, https://doi.org/10.1111/poms.13881.
D. G. Gioia, E. Fadda, and P. Brandimarte, “Rolling horizon policies for multi-stage stochastic assemble-to-order problems,” Int. J. Prod. Res., vol. 62, no. 14, pp. 5108–5126, Jul. 2024, https://doi.org/10.1080/00207543.2023.2283570.
S. Mohd Baki and J. K. Cheng, “A Linear Programming Model for Product Mix Profit Maximization in A Small Medium Enterprise Company,” International Journal of Industrial Management, vol. 9, pp. 64–73, Jan. 2021, https://doi.org/10.15282/ijim.9.0.2021.5956.
D. H. C. Aziz, N. I. Zulkafli, N. H. Razak, and J. J. Klemeš, “Optimal Fertigation for Automated Fertilizer Blending System by Minimising Fertilizer Cost and Utility Consumption,” Chem. Eng. Trans, vol. 94, pp. 115–120, 2022, https://doi.org/10.3303/CET2294019.
P. Kowalik, “Fertilizer Purchase Optimization as a Problem of Mixed Integer Nonlinear Programming,” EUROPEAN RESEARCH STUDIES JOURNAL, vol. XXIV, no. Special Issue 2, pp. 346–356, Jun. 2021, https://doi.org/10.35808/ersj/2267.
A. Becker et al., “Toward global food security: Transforming OCP through analytics,” INFORMS Journal on Applied Analytics, vol. 52, no. 1, pp. 90–107, Jan. 2022, https://doi.org/10.1287/inte.2021.1111.
B. Azzamouri and V. Hovelaque, “An integrated steering approach to improve a phosphate supply chain efficiency,” Supply Chain Forum: An International Journal, vol. 25, no. 2, pp. 229–245, Apr. 2024, https://doi.org/10.1080/16258312.2023.2282383.
F. Pauli de Bastiani, T. G. Péra, and J. V. Caixeta-Filho, “Fertilizer logistics in Brazil: Application of a mixed-integer programming mathematical model for optimal mixer locations,” Logistics, vol. 8, no. 1, p. 4, Jan. 2024, https://doi.org/10.3390/logistics8010004.
A. Hermawan, Abdurrohim Fatah, and Imas Widowati, “Planning and control of subsidized NPK fertilizer production at PT. Pupuk Kujang Cikampek,” Jurnal Teknologika, vol. 14, no. 2, pp. 548–559, Dec. 2024, https://doi.org/10.51132/teknologika.v14i2.428.
CRU International, “Fertilizer Week: Historical prices monthly series 2013–2025,” CRU Group. Accessed: Oct. 30, 2025. [Online]. Available: https://www.crugroup.com
OECD, “Currency conversions: US dollar exchange rate, average of daily rates, national currency per US dollar, Indonesia (CCUSMA02IDM618N),” FRED, Federal Reserve Bank of St. Louis. Accessed: Oct. 16, 2026. [Online]. Available: https://fred.stlouisfed.org/series/CCUSMA02IDM618N
Q. Huangfu and J. A. J. Hall, “Parallelizing the dual revised simplex method,” Math. Program. Comput., vol. 10, no. 1, pp. 119–142, Mar. 2018, https://doi.org/10.1007/s12532-017-0130-5.
P. Virtanen et al., “SciPy 1.0: fundamental algorithms for scientific computing in Python,” Nat. Methods, vol. 17, no. 3, pp. 261–272, Mar. 2020, https://doi.org/10.1038/s41592-019-0686-2.
Bisnis.com, “Daftar harga pupuk subsidi terbaru usai pemerintah pangkas HET 20%.” Accessed: Oct. 16, 2026. [Online]. Available: https://ekonomi.bisnis.com/read/20251031/99/1925023/daftar-harga-pupuk-subsidi-terbaru-usai-pemerintah-pangkas-het-20
DOI: http://dx.doi.org/10.30829/zero.v10i2.32147
Refbacks
- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Editorial office ![]() Department of Mathematics Faculty of Science and Technology UIN Sumatera Utara Medan Medan, North Sumatra, Indonesia | For authors | Contact |
Open access under CC BY-SA 4.0 · © 2017–2026 Department of Mathematics, UIN Sumatera Utara Medan
.jpg)