Determination of Inventory Policy to Address Raw Material Shortages Using Lagrange Multiplier and Capacity Restriction at Coffee Shop X

Elieolsa Wanmilsen C. Putri (Universitas Atma Jaya Yogyakarta, Indonesia)
Fransiska Hernina Puspitasari (Universitas Atma Jaya Yogyakarta, Indonesia)
Ika Murti Kristiyani (Universitas Atma Jaya Yogyakarta, Indonesia)
V. Reza Bayu Kurniawan (Universitas Atma Jaya Yogyakarta, Indonesia)

G-Tech : Jurnal Teknologi Terapan
Vol 10 No 3 (2026): G-Tech, Vol. 10 No. 3 July 2026

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.