Determination of Inventory Policy to Address Raw Material Shortages Using Lagrange Multiplier and Capacity Restriction at Coffee Shop X
DOI:
https://doi.org/10.70609/g-tech.v10i3.10460Keywords:
Budget Constraint, Inventory, Limited Storage, StockoutAbstract
Managing inventory well in a business is extremely important. It is not uncommon that if this is neglected, it will result in lost sales. A coffee shop in Yogyakarta experienced a similar situation. Some coffee menu items have to be unavailable for order due to a shortage of Arabica and Robusta coffee beans. In addition, this café also faces budget constraints for purchasing coffee beans and limited storage space. Therefore, the Lagrange Multiplier method, supplemented with capacity constraints, is used to solve this problem. Based on the calculation results, the optimum order quantity for each type of coffee bean is 3 kg, which does not exceed the maximum storage capacity of 10 kg and is still within the budget of Rp700,000.00. Additionally, reorder point (ROP) and safety stock (SS) calculations were also performed. The SS value was obtained as 0.32 kg (Arabica) and 0.07 kg (Robusta), while the ROP value was obtained as 0.46 kg (Arabica) and 0.13 kg (Robusta). After conducting the inventory simulation, it was found that there were no stockouts of coffee beans, and the inventory costs incurred were Rp3,942,710.55 for Arabica coffee beans and Rp1,097,546.31 for Robusta coffee beans.
References
Alawiyah, A. (2026). Analisis Persediaan dengan Metode Simulasi Monte Carlo dan Model P-Backorder Produk Ascorbic Acid di PT X. Jurnal Logic: Logistics & Supply Chain Center, 4(2), 96-106.
Alnahhal, M., Aylak, B. L., Al Hazza, M., & Sakhrieh, A. (2024). Economic order quantity: A state-of-the-art in the era of uncertain supply chains. Sustainability, 16(14), 5965.
Anderson, E.T., Fitzsimons, G.J., & Simester, D. (2006). Measuring and Mitigating the Cost of Stockouts. Management Science, 52(11), 1751-1763.
Azzi, A., Battini, D., Faccio, M., Persona, A., & Sgarbossa, F. (2014). Inventory Holding Cost Measurement: A Multi-case Study. The International Journal of Logistics Management, 25(1), 109-132.
Castellano, D., & Glock, C.H. (2021). The average-cost formulation of lot sizing models and inventory carrying charges: A technical note. Operation Management Research, 14, 194-201.
Huh, W.T., Janakiraman, G., Muckstadt, J.A., & Rusmevichientong, P. (2009). Asymptotic Optimality of Order-up-to Policies in Lost Sales Inventory Systems. Management Science, 55(3), 404-420.
Indrawati, S., & Madarja, E.R. (2022). Lean Healthcare Improvement Model Using Simulation-based Lean Six-sigma and TRIZ. Mathematical Modelling of Engineering Problems, 9(3), 849-855.
Irawan, E., Ramli, I.R., & Permatasari, I. (2025). Perbandingan Biaya Persediaan Bahan Baku Menggunakan Metode Economic Order Quantity (EOQ, Periodic Order Quantity (POQ) dan Min-Max Inventory Control pada PT. Indonesia Plafon Semesta. Jurnal Rekayasa Industri, 7(2), 156-163.
Isrofi, N., & Utami, N.M.C. (2025). Analisis Optimalisasi Biaya Persediaan Multi-item Single Supplier dengan Kendala Kapasitas Gudang Terbatas. Jurnal Industri, Manajemen dan Rekayasa Sistem Industri, 4(2), 1-13.
Leluc, R., Bertoncello, A., Kadoche, E., & Gourvenec, S. (2023). MARLIM: Multi-Agent Reinforcement Learning for Inventory Management. Paper presented at the 36th Conference on Neural Information Processing Systems.
Liang, A. (2024). Product Return Management at Large Scale: Effective Joint Decision-making Supported by Comprehensive Performance Metrics (Doctoral’s Disertation). University of Michigan.
Lindbӓck, K.A. (1967). The Economic Consequences Of Deviations From Economic Lot Sizes. International Journal of Production Research, 6(2), 97–107. https://doi.org/10.1080/00207546708929771
Manche, A.M. (2024). Multi-echelon Inventory Control Optimization Approach for Industrial Applications (Doctoral’s Desertation). Universite de Lille, France.
Mohamed, A.E. (2024). Inventory Management. In Banyai, T., & Marquez, F.P.G., Operations Management: Recent Advances anf New Perspectives. London, UK: IntechOpen.
Mor, R.S., Kumar, D., Yadav, S., & Jaiswal, S.K. (2021). Achieving cost efficiency through increased inventory leanness: Evidence form manufacturing industry. Production Engineering Archives, 27(1), 42-49.
Munyaka, J.B., & Yadavalli, V.S.S. (2022). Inventory Management Concepts and Implementation: A Systematic Review. South African Journal of Industrial Engineering, 33(2), 15-36.
Nainggolan, O.A.O., & Sunarni, T. (2019). Pengendalian Persediaan The dengan Mempertimbangkan Kendala Biaya Persediaan dan Kapasitas Gudang. Jurnal TEKNO, 16(1), 47-57.
Nirmal, A., Ahmad, & Kristina, J. (2022). Pengendalian Persediaan Bahan Baku Cabai Bubuk untuk Mengeliminasi Stockout dengan Simulasi Monte Carlo. Jurnal Mitra Teknik Industri, 1(3), 329-339.
Oktavia, C., & Djunawan, A. (2024). Potensi Penghematan Biaya Persediaan Logistik Umum Menggunakan Metode EOQ di Rumah Sakit Swasta X. Jurnal Manajemen Kesehatan Yayasan RS. Dr. Soetomo, 10(2), 395-405.
Reid, R.D., & Sanders, N.R. (2013). Operations Management: An Integrated Approach (5th Edition). Wiley.
Sari, R.W., Damayanti, D.D., & Santosa, B. (2016). Perencanaan Persediaan Seluruh Produk Utama, D.M. (2016). Penentuan Lot Size Pemesanan Bahan Baku dengan Batasan Kapasitas Gudang. JITI, 15(1), 64-68.
Sharma, A., Gill, S., & Taneja, A.K. (2024). Inventory Optimization Model with Quadratic Demand Pattern and Non-instantaneous Deterioration Rate with Mixed Cash and Advance Payment Scheme. Indian Journal of Science anf Technology, 17(26), 2763-2777.
Sindu, M.P., & Beena, P. (2024). A Survey on Inventory Model with Lost-Sale. IOSR Journal of Mathematics, 20(6), 14-18.
Soleh, M., Haque, A., & Muda, Y. (2021). Probabilistic Inventory Model Using All Unit Discount Factor and Inflation. Jurnal Fourier, 10(2), 67-73.
Tannady, H., & Pratama, Y.D. (2019). Analisis Perencanaan Persediaan Bahan Baku Menggunakan Metode Economic Order Quantity dengan Pertimabangan Stockout Cost (Studi Kasus PT. Multi Logam Presisi). Spektrum Industri, 17(2), 93-97.
Vania, A., & Yolina, H. (2021). Analysis Inventory Cost Jona Shop with EOQ Model. Jurnal Emacs (Engineering, Mathematics, and Computer Science), 3(1), 21-25.
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Copyright (c) 2026 Elieolsa Wanmilsen C. Putri, Fransiska Hernina Puspitasari, Ika Murti Kristiyani, V. Reza Bayu Kurniawan
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