Prediction is half the question

"We have a good forecast" and "we know what to do" sound adjacent and are not. A forecast is a statement about the world: demand for Dairy will probably be around here. A plan is a statement about you: the mill will run this many tonnes of each. One of them can be accurate while the other is absent, and that is the normal condition of most operations that have invested in analytics.

The confusion is easy to spot once named. Ask for the plan and you get the forecast back, with a sentence attached about what it implies. The sentence is where the work was supposed to happen, and it was done in somebody's head during the meeting.

• Decision variable. A quantity you get to set. At Ravensworth there are three: tonnes of Standard, tonnes of Dairy, tonnes of Show. Part 1 tonight.
• Objective. The single number being made as big or as small as possible. Here, total margin. Part 1 tonight.
• Constraint. A limit the plan may not cross, written as a rate per tonne and a ceiling. Part 2 tonight.
• Feasible plan. Any set of quantities that breaks none of the constraints. There are a great many of these and almost all of them are poor.
• Optimal plan. The feasible plan with the best objective value. Session 2.
• Binding constraint. One the plan has pushed right up against, with nothing left over. Session 3.
• Shadow price. What one more unit of a limit would be worth, and the range over which that figure survives. Session 3.
• Framing the decision. Choosing which decision to solve at all, and what the options even are, is its own discipline and lives in the decision intelligence course.

Ravensworth would like high margin, full shelves, short lead times and a happy Show customer. Four wishes are not an objective, because the moment two of them pull apart there is no rule for which gives way, and the plan quietly becomes whoever was loudest.

Collapsing four wishes into one number is uncomfortable and it is where the real argument belongs. The discomfort is the point: it forces an exchange rate into the open, in public, before the week starts, rather than leaving it to be improvised in a Thursday call. A plan built on one honest number beats a plan built on four unranked ones.

A constraint is not a preference dressed up. It has two halves and both must be measured: a rate, which says how much of something each tonne consumes, and a ceiling, which says how much of that something exists. Milling takes 1.1 hours for every tonne of Standard, and there are 131 milling hours in the week. Both halves, or it is not a constraint.

The test is whether crossing it is impossible or merely unpopular. Impossible is a constraint. Unpopular belongs in the objective, priced, so that the plan can choose to pay it when the payment is worth making.

One camp holds that most operations cannot honestly write box 3 at all. Ask a plant for its true milling capacity and you get a number from a commissioning document, a different number from the shift supervisor, and a third from whoever pulled the maintenance calendar. Feed made-up ceilings into a solver and you get a confident plan built on fiction, which is worse than an experienced planner's judgement because it is harder to argue with.

The other camp holds that writing the numbers down is precisely how the disagreement surfaces. The three capacity figures were always inconsistent; before anyone wrote them in a row, the inconsistency lived in three heads and never met. On this view a wrong constraint is a finding, not a defect, and the value of the exercise arrives before any plan is computed.

Both are held by people who run real plants, and they lead to different first moves: one starts with a measurement programme, the other starts with a model and lets it fail loudly. Knowing which one the person across the table holds is worth more than winning the argument.

Try a few plans in the box above. Most combinations that fit under all three ceilings are perfectly legal and perfectly mediocre, and there are far too many of them to look through by hand. That is the honest reason this is not a spreadsheet exercise: the number of feasible plans is not large in the sense of being tiresome, it is large in the sense of never finishing.

Notice also which ceiling stops you first as you push each product up. It is not the same ceiling for all three, and it is rarely the one people name when asked what limits the plant.

None of this demotes the forecast. A plan that makes 80 tonnes of something nobody orders is not a good plan, however elegant the arithmetic, and the forecast is the only thing in the building that speaks to that. Demand belongs in the problem, either as a ceiling of its own or in what the plan is judged against afterwards.

The claim is narrower and worth saying exactly: an accurate forecast is necessary and it is not sufficient. It tells you what is coming. The mix, the ceilings and the exchange rate between them decide what you do about it, and a forecast is silent on all three.

Read the four rows again and notice that they are in four different units. Pounds, milling hours, blending hours, tonnes of protein. The top row is the only one denominated in the thing being maximised, which makes it the only row that can be compared across products without a conversion.

This is the seed of the whole week. Any comparison that uses the top row alone is comparing products. Any question about what the mill should run is a question about the three rows underneath, because those are what runs out. Keep the distinction in view when the obvious answer is offered.