Bias Analysis (MAPE & MASE): Is Our Demand Forecast Systematically Overestimating?

The Scenario

PeakFlow Consumer Goods is a regional FMCG distributor supplying approximately 380 retail outlets across the Mountain West region. Every week, their planning team generates demand forecasts for each SKU in their portfolio — these forecasts directly drive procurement orders, warehouse space allocation, and truck scheduling. One product line in particular, Hydra-Sport isotonic drinks, has been flagged repeatedly by the warehouse operations manager: stockrooms are consistently overstocked at the end of each week, product is sitting longer than target, and the company is paying for storage space and working capital it may not need. The planning team has two full years of weekly data — 104 weeks of forecasted demand alongside the actual units sold — and leadership has asked for a rigorous error analysis before the next quarterly planning review.

The Statistical Challenge

The operations manager suspects the forecasting model is not just inaccurate — it is systematically biased upward, meaning it consistently overestimates demand rather than making random errors that cancel out over time. As the analytics lead, your job is to quantify this suspicion using the right metrics. You'll compute the Mean Absolute Percentage Error (MAPE) to assess overall forecast accuracy, and the Mean Absolute Scaled Error (MASE) to benchmark that accuracy against a naive baseline. Critically, you'll also examine the distribution of forecast errors — whether errors are randomly scattered around zero (unbiased) or consistently shifted in one direction (biased). This distinction is fundamental: a model with a 20% MAPE that's unbiased is fundamentally different from one with a 20% MAPE that always overshoots.

What's at Stake

PeakFlow's CFO has estimated that chronic over-forecasting on Hydra-Sport alone is tying up approximately $240,000 in excess inventory annually and contributing to $38,000 in spoilage and markdowns per year. If your analysis confirms systematic positive bias, the planning team will recalibrate the model using a bias correction factor — a straightforward fix with immediate financial impact. If the errors are found to be random and unbiased, the problem lies elsewhere (perhaps in the supply chain itself), and a different corrective action is needed. Your statistical findings will directly determine which path leadership pursues.