Forecasting method: hierarchical reconciliation

Forecasting · ~6 minute read

The problem nobody warns you about

Most contact centres do not run a single queue. They run a hierarchy: total contacts across the operation, broken down by channel (voice, chat, email), each channel broken down by skill (billing, claims, complaints, retention), each skill possibly broken down by region or product. The planner’s job is to forecast each level of this hierarchy. The annoying problem that follows is that the levels almost never add up. Forecast each leaf queue independently and sum the leaves, and the total is different from a forecast made on the total directly. The same is true at every level in between. The discrepancy is not a bug; it is a mathematical consequence of fitting independent models to related data. Hierarchical reconciliation is the family of methods that resolves it.

The three approaches

Three approaches to forecasting a hierarchy have dominated practice for decades.

Top-down. Forecast the top of the hierarchy (the total volume), then disaggregate down to the leaves using historical proportions. Each leaf gets a fixed share of the total. Top-down is easy, the parts add up to the whole by construction, and the top-level forecast is usually well-behaved because it has the most data. The weakness is that the leaf forecasts are constrained to follow historical proportions, so any change in the mix — a channel growing faster than the others, a skill that used to be small becoming large — is invisible to the model.

Bottom-up. Forecast each leaf independently, then sum to get the higher levels. The leaf forecasts can respond to their own dynamics, but the noise in each leaf compounds when you add them up, and the total at the top usually has higher error than a direct top-level forecast would have produced. Bottom-up is also vulnerable to small queues with sparse data; their forecasts can be wild, and the wildness propagates upward.

Middle-out. Forecast at some intermediate level (channel, say), then disaggregate downward to skills and aggregate upward to total. This can capture the best of both approaches if the middle level is chosen well, but the choice is a judgement call.

The modern alternative: reconciliation

Hierarchical reconciliation methods, developed in the academic forecasting community over the last fifteen years, take a different approach. Forecast every node in the hierarchy independently (top, middle, leaves) using whichever method suits each one best. The forecasts will not add up. Then apply a mathematical reconciliation step that adjusts all the forecasts simultaneously so they do add up, while preserving as much of the information in the independent forecasts as possible. The output is a coherent set of forecasts at every level, each one informed by the others.

The standard method in this family is MinT (Minimum Trace), which finds the reconciliation that minimises the total variance of the reconciled forecast errors. There are several variants — MinT(ols), MinT(wls), MinT(shr) — that differ in how they estimate the error covariance structure. For most contact centre operations, MinT(shr) (the shrinkage estimator) is a robust default. The R package fable and the Python package hierarchicalforecast implement these methods cleanly.

Why this matters for contact centres

Hierarchical reconciliation is not just an aesthetic improvement. Three practical benefits make it worth the effort.

Forecasts are coherent. When operations and finance look at the same hierarchy, they see numbers that add up. This sounds trivial but the absence of it is a real source of friction in operations where planning and finance reconcile separately.

Small-queue forecasts improve. A small skill with noisy history gets its forecast partially informed by the larger, better-behaved totals. The reconciliation pulls the wild leaf forecast toward something more sensible. For operations with many small skills, this is genuinely valuable.

Top-level accuracy benefits too. The reconciled top-level forecast uses information from the leaves that a pure top-down forecast cannot see. When one channel is genuinely growing faster than the others, the reconciled total picks this up faster than the top-down approach.

When to bother

Reconciliation is worth the effort when three conditions hold. The hierarchy has multiple levels. A two-level hierarchy (total and a handful of leaves) probably does not justify the modelling investment. Four-level hierarchies (total, channel, skill, queue) usually do. The forecasts are used at multiple levels. If only the leaf forecasts matter operationally, the discrepancy at the top is uninteresting. If finance uses the total, operations uses the channels, and team leaders use the leaves, coherence matters. The operation is mature enough to invest. Reconciliation requires a working pipeline of independent forecasts at every level, plus the tooling to run the reconciliation step. For operations still building basic forecasting capability, that investment is premature.

Practical setup

A workable hierarchical reconciliation setup looks like this. Build independent forecasts at every node using whichever method suits — Holt-Winters, Prophet, or regression with drivers for the larger nodes; simpler methods for very small leaves. Construct the hierarchy matrix that describes which nodes aggregate into which. Apply MinT (or another reconciliation method) once per forecast cycle to produce the coherent set. Publish the reconciled forecasts; archive the raw independent forecasts for diagnostic use. Refit the reconciliation method occasionally (quarterly is fine) but recompute the reconciliation every forecast cycle.

Common mistakes

Three patterns recur. Reconciling forecasts that were not produced independently. If you forecast the total and then disaggregate to leaves (top-down), there is nothing for reconciliation to fix; the forecasts already add up. Reconciliation needs independent inputs to work on. Using top-down or bottom-up by habit. Most contact centres default to one or the other without considering reconciliation. The default is rarely optimal. Ignoring the variance estimation. The reconciliation step relies on an estimate of how errors at each node co-vary. A poor estimate (or the default OLS, which assumes the errors are uncorrelated) can produce reconciliation that hurts more than it helps. Use a shrinkage estimator unless you have a strong reason to choose otherwise.

Conclusion

Hierarchical reconciliation is the right approach for any contact centre with a meaningful hierarchy of queues whose forecasts are used at multiple levels. It produces coherent numbers, improves small-queue forecasts, and tends to lift top-level accuracy as well. The investment is non-trivial — tooling, pipeline, modelling expertise — but for operations that have outgrown a simple top-down or bottom-up approach, the move is one of the cleanest accuracy upgrades available. The planners who adopt it well treat the reconciled forecast as the published number, keep the independent forecasts as diagnostic artefacts, and review the reconciliation method’s assumptions annually. Done well, the result is a planning function whose numbers add up and whose forecasts are quietly better than the operation realises.

Pair this with using AI for contact centre forecasting — hierarchical reconciliation is one of the methods that genuinely benefits from modern tooling — and with multi-skill scheduling for the operational context that creates these hierarchies in the first place.