Cut the Question Into Parts

A tree cuts a question into parts you can work on separately. Two properties make a cut usable, and each fails in its own way.

No overlap. When branches overlap, the same dollars get investigated twice and, much worse, counted twice when the branches are sized, so the opportunity reported is larger than the problem. The test is whether a single fact could appear under both.

No gap. When something relevant falls outside the set, the analysis is systematically biased toward whatever happens to be inside the frame. The test is to assume every branch false and ask whether the problem could still exist.

The tree is the other half of working backward. Skip it and you work only under the lamp you prefer; skip the candidate ranking and you draw an elegant tree of a question nobody is deciding.

The tree, and what sits at its root

At the root is the question that decides the ranking, not the topic. Below it go the components that would all have to hold for the answer to be yes. Below each of those go their own components, until you reach something you could go and check this week. The claim list should fall out of the tree rather than precede it.

A tree for a class-based stocking decision has four branches at the first level.

There must be a real economic difference between items, or classification is sorting for its own sake. The current rule must not already be capturing that difference, or you are proposing to replace the incumbent with itself. You must be able to assign items to classes reliably enough to survive new parts and shifting demand. And the organization must be able to run the result, which decomposes further into whether planners will follow it and whether dealers can go around it.

The last branch is not a technical one, and an intuitive list leaves it off because no query can settle it. It is on the tree because it can change the ranking, which is the only membership test a branch has to pass.

A cut that fails, and the repair

Ask a competent analyst why Meridian Motors’ parts working capital is too high and you will get five genuine causes: poor forecast accuracy, long supplier lead times, too many part numbers, slow-moving and obsolete stock, dealers over-ordering. Every one is real, and the list fails both tests.

It overlaps. Safety stock depends on demand variability and lead time together, so the same dollars sit under forecast accuracy and lead time, and sizing each and summing reports an opportunity larger than the inventory.

It also has a gap. Assume all five false and the working capital is still too high, because the replenishment rule holds every item to the same service target, and a uniform target across items with wildly different economics overstocks the cheap ones however good the inputs are. The missing branch is that the company holds the inventory on purpose, under an incumbent rule nobody has revisited. That branch is the decision, and the first cut left it out.

The repair is a cut where exclusivity is guaranteed rather than hoped for, and partitioning the quantity itself is the reliable way. Inventory on the books is a sum: each item’s on-hand units times unit cost, added across items. Assign each item’s units in layers from the bottom, by a convention stated once. Units up to the safety stock the rule currently targets are protection. Units above that, up to one further order quantity, are cycle stock. Anything above that, and every unit of an item with no demand in twelve months, is surplus. Value each layer at unit cost and add across items. The three totals add to the inventory on the books, because the convention put every unit in exactly one layer.

A partition is not a decomposition into drivers

Forecast error, lead time, and the service target are still in the picture, but as drivers rather than branches: together they set the size of the protection layer, roughly as the target’s safety factor times the spread of demand over the lead time. Drivers that multiply interact. Halve the lead time and the payoff from a better forecast shrinks with it, so there is no fixed share of protection dollars that belongs to forecasting and another that belongs to lead time. Ask how much each driver “contributes,” add the answers, and you count the same dollars twice. The layers can be added because they partition dollars. The drivers cannot, because they share them.

The repaired cut puts the missing branch on the path to the decision: the service target is visibly the parameter that sets how much protection the rule buys. At Meridian, most of the excess cash is protection stock on inexpensive slow movers, the other two layers are small, and the week has one job rather than five.

Choosing the cut

When the quantity can be partitioned, reach for that cut first. It cannot overlap once the convention is written down, and it often shows that most of the quantity lives in one branch. Use a partition whenever you are about to add across branches, and do not mistake a product for one. If you cannot write the partition, you are not ready to add.

The logical cut is the one you need when the question is whether a commitment is right rather than where a quantity sits. Most real work uses both: the partition sizes the problem and says where to look, and the logical cut ranks the alternatives there.

Cut on the dimension the decision turns on. Parts could be divided by distribution center, supplier, vehicle platform, or the economics of a miss, and each yields a defensible tree. Only the last separates the alternatives, because only it distinguishes items the incumbent treats identically and a class-based rule would not.

The fakes have a recognizable smell. “People, process, and technology” looks complete because the words are famous, but a planner padding a minimum because the screen cannot show class because the rule is uniform is one fact counted three times. If you cannot name the single question the branches answer, you are listing themes, and themes overlap by construction. A bucket labeled “other” admits the cut was not exhaustive, and whatever would have killed the ranking will be filed there.

Prune, then go

A tree worked through exhaustively is the default week with better documentation. The value of the tree is that it lets you prune with confidence.

Before investigating anything, mark every branch that cannot change the ranking: because the answer is already known, because the branch is too small to matter, or because nothing learnable in the time available would move the pick. Write the sentence explaining why you are leaving each alone: “we did not get to it” is a different answer from “it is too small a share of the gap to change which rule wins.”

Then do the branch that holds the mass, and come back to the others only if a result on the heavy branch says the mass was elsewhere.

Exhibit 1A branch that cannot change the ranking gets marked and left alone

Strict exhaustiveness is rarely achievable, and the tree stays out of the write-up

Causes in real systems are entangled, and a tree with no overlap anywhere is often unattainable. If you are going to add numbers across branches, non-overlap is essential, because overlap becomes arithmetic error in your favor, the kind that gets found in public. If you are only deciding where to spend three days, some redundancy at the edges costs little. The reader wants the recommendation and the reasons, not the tree; it is scaffolding for a decision about where to spend the week.

A test you can run in five minutes

Take the last breakdown you presented. If its branches were sized and summed, check that every dollar could land in exactly one branch; if two branches are drivers that multiply, the sum is wrong. Then assume every branch false and ask whether the problem still exists. If it does, the missing branch is usually the rule itself, or something a query cannot reach.