Bottleneck Product Mix Calculator

Why is the most profitable product not the one to make first?

Because "most profitable" usually means per unit, and when a bottleneck gates your output the scarce thing isn't units — it's minutes on the constraint.

The calculator's defaults make the reversal plain. Product 3 has the highest margin of anything on the list at $80 a unit. Product 4 has the lowest at $23. But Product 3 consumes 28 bottleneck minutes and Product 4 consumes 6, so per constrained minute Product 4 returns $5.83 and Product 3 returns $4.11.

Ranked by throughput per bottleneck minute the order is 4, 2, 3, 1, 5. Ranked by margin per unit it's 3, 5, 1, 2, 4 — almost exactly reversed.

The published two-product illustration shows the same thing in miniature: a product at $120 selling price and $40 material returns $4.00 a bottleneck minute, while one at $80 and $25 returns $5.50, because the second takes half the machine time. The cheaper-looking product wins.

The rule is to compute throughput per bottleneck minute for each product, rank descending, and fill demand from the top until the constraint is exhausted. Everything below the cut line waits.

What does ranking on unit margin actually cost?

At the calculator's defaults it turns a profitable month into a loss.

The optimal mix generates $116,190 of throughput against $98,000 of operating expense — a $18,190 profit. Rank the same five products by contribution margin per unit and the mix produces $92,220, which is a $5,780 loss.

A $23,970 swing on identical capacity, demand and prices. Nothing changed except which column you sorted on.

Here's the part that's more useful than the headline. Run the allocation a third way, ranking by contribution per bottleneck minute — the conventional limiting-factor method that deducts labour and overhead as well as material — and you get $116,046. That's $144 below optimal, a rounding error.

So the denominator matters enormously and the numerator barely matters at all. Whether you call it throughput or contribution changes the answer by 0.1%; failing to divide by constraint usage at all changes it by 21%. If you take one thing from this, it isn't "adopt throughput accounting" — it's "divide by the bottleneck."

That reframing also lowers the barrier. You don't need to restructure your management accounts to get most of the benefit. You need one extra column.

What is throughput and why isn't it contribution margin?

Throughput is selling price less direct material cost — and only direct material. Labour and overhead stay out.

That's the deliberate difference from contribution margin, which deducts all variable costs. Throughput accounting treats labour and factory overhead as operating expense because in the short run they don't vary with the mix decision: the operators are there and paid whether you run Product 1 or Product 4 through the cell.

The defaults put Product 1 at $120 price less $40 material, giving $80 of throughput but only $58 of contribution margin after $22 of labour and variable overhead.

Two companion measures come out of the same frame. Cost per bottleneck minute is total operating expense divided by available constraint minutes — $4.08 here. And the throughput accounting ratio is a product's throughput per minute divided by that figure. Above 1.00 the product more than covers the plant's cost of running that minute; below 1.00 it doesn't.

At the defaults, two of five products have a TPAR below 1 — Product 1 at 0.98 and Product 5 at 0.74. Product 1 is still worth making, because it's the marginal filler and something beats nothing on a minute you've already paid for. Product 5 never makes the cut at all.

A plant where most products sit below 1.00 has a capacity problem or a pricing problem, and the ratio tells you which conversation to have.

What is an extra hour of bottleneck capacity worth?

Exactly the throughput per minute of the marginal product — the last one that received capacity — multiplied by sixty. Not the best product, and not the average.

At the defaults the constraint is fully consumed and the marginal product is Product 1, running at $4.00 a minute. So an extra hour is worth $240.

That number is the one to hold against any proposal touching the constraint. An overtime shift, a second-shift operator, a faster fixture, a changeover reduction, an outsourced operation — all of them should be compared to $240 an hour, not to the machine's cost rate and not to the best product's $5.83.

It also moves as you relieve the constraint. Add enough capacity and Product 1's demand gets fully satisfied, at which point the marginal product becomes Product 5 at $3.03 a minute and the next hour is worth only $182. The value of capacity declines in steps as each product's demand ceiling is reached.

The calculator also reports unmet demand at throughput value — $30,080 here, being 67 units of Product 1 and all 240 units of Product 5 that the constraint cannot serve. That's the ceiling on what relieving the bottleneck could be worth this period, and it's usually a more honest target than an uncapped projection.

If idle minutes are greater than zero, the shadow price is zero: you aren't constrained and the ranking exercise is moot.

When does this approach stop working?

Three boundaries, and the first is the one that catches people.

• One binding constraint only. The ranking method is provably optimal when a single resource limits output. With two or more simultaneous binding constraints the greedy ranking can give the wrong answer and you need linear programming. If your plant has a machine and a skilled-operator constraint that both bind, this calculator will mislead you.
• Short run only. Throughput accounting holds labour and overhead fixed because they are fixed over the horizon of a mix decision. Over a longer horizon you can hire, retrain or buy capacity, at which point those costs become variable and the conventional analysis is more appropriate. The ranking is a scheduling tool, not a product rationalisation tool — dropping Product 5 permanently is a different decision from not running it this month.
• The constraint moves. Fix the bottleneck and a new one appears elsewhere, and the ranking can change completely because a different machine's minutes are now scarce. Re-identify the constraint before re-running the mix, every time.

One assumption worth stating too: the model treats demand as a hard ceiling and the mix as freely choosable. In practice customers order baskets, contracts commit you to minimums, and refusing a low-ranked product can cost you a high-ranked one. Treat the output as the economic ranking, then overlay the commercial constraints you actually have.