Warehouses constitute a key component of supply chain networks. An improvement to the operational efficiency and the productivity of warehouses is crucial for supply chain practitioners and industrial managers. Overall warehouse efficiency largely depends on synergic performance. The managers preemptively estimate the overall warehouse performance (OWP), which requires an accurate prediction of a warehouse’s key performance indicators (KPIs). This research aims to predict the KPIs of a ready-made garment (RMG) warehouse in Bangladesh with a low forecasting error in order to precisely measure OWP. Incorporating advice from experts, conducting a literature review, and accepting the limitations of data availability, this study identifies 13 KPIs. The traditional grey method (GM)—the GM (1, 1) model—is established to estimate the grey data with limited historical information but not absolute. To reduce the limitations of GM (1, 1), this paper introduces a novel particle swarm optimization (PSO)-based grey model—PSOGM (1, 1)—to predict the warehouse’s KPIs with less forecasting error. This study also uses the genetic algorithm (GA)-based grey model—GAGM (1, 1)—the discrete grey model—DGM (1, 1)—to assess the performance of the proposed model in terms of the mean absolute percentage error and other assessment metrics. The proposed model outperforms the existing grey models in projecting OWP through the forecasting of KPIs over a 5-month period. To find out the optimal parameters of the PSO and GA algorithms before combining them with the grey model, this study adopts the Taguchi design method. Finally, this study aims to help warehouse professionals make quick OWP estimations in advance to take control measures regarding warehouse productivity and efficiency.