Reading someone else's optimum

A recommendation with arithmetic behind it has a particular kind of authority. It is specific, it is internally consistent, and any objection raised from experience sounds like an objection to the arithmetic, which is the one part that is certainly correct. That is an uncomfortable position to be in for someone who has to sign it and who suspects something is off.

The way out is not to argue with the arithmetic, which will lose. It is to ask what problem the arithmetic solved. Every one of tonight's five questions is about the problem statement rather than about the computation, and all five can be asked by someone who could not derive a single line of the method.

• The objective. The single number being maximised, and whether it is the one the business wants. Session 1 put it in a box; session 5 showed what happens when it is wrong.
• Binding and non-binding. Which ceilings the plan ran out of. Session 3: at Ravensworth, milling and premium protein bind, blending does not.
• Measured against assumed. A ceiling that came off the plant floor and a ceiling that came off a commissioning document are not the same object, and the plan cannot tell them apart.
• Shadow price. What one more unit of a binding limit is worth. Milling 33.7931, blending 0, premium protein 8.2759.
• Validity range. How far that rate survives. Milling to about +0.46 hours, premium protein to about +0.77 tonnes.
• The demand assumption. What the plan was optimised against, and what happens when the week is not that. Session 4: a shortfall of 325 to 338 and a 5th percentile around 3,540 to 3,591.
• Stability. How far the plan moves when the objective shifts slightly. Cheap to test, rarely tested.
• Degeneracy. Several plans tied for best, which would matter here if it were true. It is not: exactly one integer plan reaches 4,656.00.

The objective comes first because everything downstream is conditional on it. There is no point discussing whether a milling hour is worth 33.7931 if the plan was maximising tonnage, because in that plan the figure means something else entirely. Similarly there is little point pressing on the demand assumption before knowing which ceilings are real, since a plan resting on an invented ceiling has a bigger problem than its percentiles.

Question five sits last for a different reason. It is the only one that is a test rather than a request for information, and it works best when you already know what answer you expected. If the objective is sound and the constraints are measured, a plan that moves a long way under a small change of objective is telling you something worth hearing.

This is the one most often skipped, and it is the cheapest to ask. A solver treats every ceiling identically. It does not know that milling hours were timed on the line last month and that the protein figure came from a spreadsheet nobody has opened since the store was reorganised. Both arrive as numbers, both get respected exactly, and the plan pushes right up against whichever of them binds.

What makes it worth asking is the interaction with the binding set. An assumed number that is not binding costs nothing, because the plan never reaches it. An assumed number that binds is carrying the plan. Two questions in sequence, and the pair of answers tells you where the real risk in the model sits without anyone opening the code.

"How confident are you in this?" invites a number that means nothing, because the plan has no interval and the honest answer is that the arithmetic is certain and the problem statement is not. "What is the accuracy of the model?" imports a word from prediction that does not apply to a plan. "Has this been validated?" gets a yes, because the solver was checked, which was not what you meant to ask.

All three fail the same way: they ask about the computation, which is the part least likely to be wrong, and they let the conversation end with reassurance. The five questions are deliberately about inputs and assumptions instead, because those are the parts that carry the risk and the parts a non-specialist can evaluate.

Select the last option in the box. It nudges Dairy's margin up and down by small amounts and re-solves each time, which is exactly the check nobody runs and which costs one solver call per row. Read down the plan column and see how far the mix travels for a change in a single margin figure that most businesses would consider noise.

Whatever the result, the reason to run it is the same. Either the plan is stable, in which case the objective was not carrying much weight and you can stop worrying about it, or the plan is not stable, in which case the objective is the decision and it should be argued about by people rather than assumed by whoever filled the box in.

Notice what Ravensworth's answers are not. They are not reassurances, they are not confidence scores, and they are not a defence of the method. They are five short factual statements, four of which are genuinely satisfying and one of which is an honest gap. That mix is what a well-built piece of work looks like when it is read properly, and a plan that answers all five without a single gap is worth a second look for a different reason.

If the person who built it can answer all five in a couple of minutes, you are in good hands regardless of what the answers are. If the answers take a week to assemble, the problem statement was never written down anywhere, which is itself the finding.

Grant the five questions and there is still a live argument about who should be answering them, and it turns on what you think a handover is for.

One camp says the builder should ship the problem statement as part of the deliverable, every time, without being asked. Objective in a sentence, the binding set, every shadow price with its range, and the plan run against a spread. On this view a plan without its problem statement is an incomplete artefact, in the same way that a figure without units is, and the fact that the recipient can ask for it is no excuse for not providing it. Most recipients do not know to ask, and the ones who do are usually the ones who least need to.

The other camp says that shipping all of it every time is how the important parts get ignored. A deliverable carrying five appendices trains people to skim, and the caveat that matters this week drowns in four that do not. On this view the builder's job is to surface the one or two things that would actually change the decision, in the covering sentence, and the discipline is editorial rather than procedural. Publishing everything is not transparency, it is transferring the work of judgement onto somebody with less context.

Both camps have watched the other one fail. The first produces documents nobody reads; the second produces handovers where the omitted caveat turns out to be the one that mattered, and the builder's judgement about what to surface was the error. Notice that this is a disagreement about how organisations read, not about optimisation, and that the five questions work either way: they are the recipient's half of a contract that the builder may or may not have honoured.