Reassessing EOQ-Based Brown Clay Inventory Control for NPK Fertilizer Production: Model Validation and Scenario Analysis

Abstract

This study reassesses brown clay inventory control for NPK fertilizer production at PT Pupuk Kujang by replacing a purely formula-driven EOQ application with a retrospective quantitative case-study design that integrates descriptive inventory analytics, arithmetic and semantic data auditing, EOQ identity validation, and scenario-based replenishment analysis. The dataset contains twelve monthly observations for 2023 covering procurement volume, replenishment frequency, and reported cost components. Recalculation from monthly entries yields 13,714.42 tons of annual procurement distributed across 594 reported order events. Monthly procurement is highly variable (coefficient of variation = 0.699), while order frequency is similarly dispersed (coefficient of variation = 0.682). January, February, and November alone account for 49.44% of annual procurement. The audit identifies a critical cost-classification problem: the reported "ordering cost" is almost exactly proportional to purchased tonnage at approximately Rp16,000 per ton, indicating a variable procurement expenditure rather than the fixed per-order setup cost required by the classical EOQ model. The reported EOQ of 3,509.87 tons also implies approximately 3.91 replenishments per year, not seven; seven annual orders would imply 1,959.20 tons per order. Consequently, the previously reported 98.4% cost reduction cannot be interpreted as validated EOQ savings because unlike cost bases were compared. Scenario analysis shows that four to twelve annual replenishments would imply average lot sizes of 3,428.61 to 1,142.87 tons, respectively, but economic ranking requires verified ordering cost, holding cost, lead time, storage capacity, and consumption data. The study contributes a reproducible validation framework for industrial EOQ studies and demonstrates that data semantics must be audited before optimization claims are accepted.