Forecast Reconciliation

A hierarchical approach where a high-level aggregate forecast is generated first and then disaggregated or allocated down to lower-level nodes based on historical proportions.

• Process: Forecast total category demand, then distribute to individual SKUs based on their average sales mix.
• Strength: Produces highly stable aggregate numbers and is simple to compute.
• Weakness: Ignores distinct demand patterns and volatility at the granular item level, potentially masking localized stockout risks.
• Example: A national sales forecast of 10,000 units is split to regional warehouses purely by their 12-month average contribution percentage.

A granular methodology where statistical forecasts are generated independently at the most detailed level and then summed upward to produce higher-level forecasts.

• Process: Forecast each SKU at each location separately, then aggregate to regional and national totals.
• Strength: Captures unique demand signals, seasonality, and volatility at the execution level where inventory decisions are made.
• Weakness: Individual forecast errors compound during summation, often leading to a less accurate aggregate forecast without correction.
• Example: A machine learning model predicts daily sales for every individual store-SKU combination, and the corporate financial plan is the sum of these predictions.

A hybrid strategy that selects an intermediate level of the hierarchy as the anchor point. Forecasts are generated at this middle tier, then summed up to the top and allocated down to the bottom.

• Process: Generate forecasts at the product category or regional level, aggregate for the CEO-level view, and prorate down to the SKU level.
• Strength: Balances the stability of top-down with the detail of bottom-up, often capturing the 'sweet spot' of forecastability.
• Weakness: The accuracy is highly dependent on selecting the correct middle level; a poor choice inherits the flaws of both other methods.
• Example: Forecasting at the 'Product Family per Distribution Center' level, then pushing those numbers up to the national level and down to individual stores.

A statistical regression approach that optimally combines all base forecasts to produce a coherent set that minimizes total forecast variance. The Minimum Trace (MinT) estimator weights forecasts based on the covariance of historical errors.

• Process: Calculate the full hierarchy's base forecasts, then multiply by a mapping matrix that minimizes the sum of forecast error variances.
• Strength: Mathematically proven to produce the most accurate reconciled forecasts by leveraging information from every node.
• Weakness: Requires estimating a large covariance matrix, which can be computationally intensive for massive hierarchies with thousands of nodes.
• Example: Using the hts package in R or scikit-hts in Python to apply the MinT shrinkage estimator to a retail hierarchy with 5,000 SKU-location combinations.

A simple, deterministic reconciliation method that forces alignment by distributing the difference between the top-down and bottom-up forecasts based on a fixed proportion of historical volume.

• Process: Calculate the gap between the aggregate forecast and the sum of the bottom-level forecasts, then allocate this gap to each bottom node based on its historical demand share.
• Strength: Extremely fast, transparent, and easy to explain to non-technical stakeholders.
• Weakness: Assumes a static relationship between nodes, ignoring changes in trends or volatility, which can distort the final forecast if a product's mix is shifting.
• Example: A financial controller adjusts the bottom-up sales pipeline forecast to match the quarterly revenue target by spreading the $2M gap across product lines based on last quarter's revenue split.

An advanced approach that treats each node in the hierarchy as a rational agent with its own local forecast. Reconciliation is achieved through a cooperative game where nodes negotiate to reach a consensus forecast.

• Process: Apply Shapley value attribution to determine the contribution of each node's local forecast to the final coherent forecast.
• Strength: Provides a mathematically fair allocation of the reconciliation adjustment, giving more weight to nodes with historically higher accuracy.
• Weakness: Computationally expensive and complex to implement, typically reserved for high-value, low-volume planning scenarios.
• Example: A pharmaceutical supply chain uses Shapley-based reconciliation to align conflicting demand signals from regional sales directors and the global epidemiology forecasting team.

The two fundamental hierarchical approaches that reconciliation must bridge. Top-down generates a forecast at the aggregate level and disaggregates it to lower levels based on historical proportions. Bottom-up forecasts each item independently and sums them upward. Reconciliation optimally combines both, using the independent bottom-up forecasts as a base and adjusting them to match a more statistically stable top-level constraint.

The Minimum Trace (MinT) estimator is the gold-standard statistical method for forecast reconciliation. It calculates a weighted least-squares adjustment that makes base forecasts coherent across the hierarchy while minimizing the variance of the reconciliation errors. Unlike simple proportion-based methods, MinT uses the covariance matrix of the base forecast errors to determine the optimal weight for each node, producing the most accurate coherent forecasts possible.

A structured data framework where time series are organized into a tree or graph based on logical aggregation constraints. Examples include:

• Geographic hierarchy: Item → Store → Region → Country
• Product hierarchy: SKU → Brand → Category → Division
• Temporal hierarchy: Daily → Weekly → Monthly → Quarterly Each node's value must equal the sum of its children, a constraint that base statistical forecasts invariably violate without reconciliation.

The mathematical property ensuring that forecasts at different levels of a hierarchy satisfy the aggregation constraints defined by the summing matrix. A set of forecasts is coherent if the forecast of a parent node exactly equals the sum of the forecasts of its child nodes. Reconciliation is the process of projecting incoherent base forecasts onto the coherent subspace, minimizing the distance from the original statistical predictions.

The cross-functional business process that consumes reconciled forecasts. S&OP aligns demand, supply, and financial plans on a monthly cycle. Reconciled forecasts are critical because they provide a single, unified demand number that prevents the finance, sales, and supply chain teams from operating with conflicting volume assumptions. Without reconciliation, the S&OP process fractures into debates over whose disconnected forecast is correct.

A critical distinction in the workflow. The base forecast is the raw statistical output generated independently at each hierarchical node using models like ARIMA or ETS. These base forecasts are statistically optimal in isolation but mathematically incoherent. The reconciled forecast is the post-processed output that has been adjusted to satisfy all aggregation constraints, trading a small amount of local accuracy for global consistency.