Lagrange Multiplier Optimization for Frozen Whole Chicken Under Storage Limits : Poultry Slaughterhouse Case Study: Optimisasi Multiplier Lagrange untuk Ayam Utuh Beku dalam Batasan Penyimpanan: Studi Kasus Rumah Potong Unggas - Tyara Ariella Farhana; Sumiati Sumiati (Universitas Muhammadiyah Sidoarjo, 2026)
General Background: Poultry slaughterhouses manage inventory of fresh and frozen chicken products to maintain supply continuity and cost efficiency. Specific Background: A poultry slaughterhouse in Sidoarjo experiences overstock in frozen whole chicken products across multiple size categories, exceeding warehouse capacity and increasing inventory costs. Knowledge Gap: Existing company practices do not adequately align production quantities with storage constraints and demand patterns, leading to inefficiencies in multi-item inventory management. Aims: This study aims to determine optimal production quantities of whole frozen chicken using Economic Production Quantity and Lagrange Multiplier methods to minimize total inventory cost under warehouse capacity constraints. Results: The proposed approach reduces total inventory cost from Rp28,644,888,779 to Rp20,019,529,574, achieving cost savings of Rp8,625,359,205 (30.11%) while ensuring required storage volume (120.73 m³) remains within capacity limits (181.8 m³). Forecast-based production planning for 2026 further yields a total cost of Rp16,091,881,801 with feasible storage requirements. Novelty: This study applies a combined EPQ and Lagrange Multiplier approach to a multi-item poultry inventory problem with explicit storage constraints. Implications: The findings provide a practical framework for optimizing production planning and inventory control in poultry processing industries to achieve cost minimization and capacity feasibility. Highlights: Overstock conditions exceed storage limits but are resolved through constrained optimization modeling. Cost reduction reaches 30.11% with adjusted production quantities across three product categories. Forecast-based planning yields feasible storage usage and lower total expenditure for the following year. Keywords: Inventory, Lagrange Multiplier, Optimization, Production