Which job should get the scarce machine hour?

When one resource limits the work you can complete, compare the contribution from each job with the amount of that resource it needs. Then respect the demand limit for each job. A high contribution per job can be less useful than a smaller contribution earned in much less time.

This is a scheduling question. The make-or-buy comparison asks which costs disappear when work moves. Here the company is choosing a mix of work inside an unchanged operation.

Two jobs, one machine

Consider a fictional framing studio planning one week. It has forty usable machine-hours after existing commitments and maintenance. A small frame sells for $300 and requires $180 of variable expenses, leaving $120 contribution. A large frame sells for $520 and requires $320, leaving $200.

The small frame takes two machine-hours; the large takes five. These times include setup and checks, with the same required quality maintained. All other resources can support any mix within the forty-hour limit. In particular, at least fourteen finishing hours are available, and each frame needs one.

There is demand for at most ten small frames and eight large ones, all deliverable this week. These are supplied conditions for an invented model, not accepted orders or a market forecast. Only whole frames can be sold; unfinished work brings no revenue in this comparison.

All operating expenses that change with a frame are in its variable amount. The week's other operating expenses, including committed wages, are $1,400 under every choice. Financing, tax and new equipment purchases are outside this operating comparison. There is no overtime or outside supplier available.

Compare the hour, then build the schedule

The small frame contributes $120 over two machine-hours, or $60 per hour. The large frame contributes $200 over five, or $40 per hour. Prioritizing the larger dollar contribution per frame would give the machine to the less productive use of its scarce time.

Start with the ten small frames the model says can be sold. They use twenty hours and contribute $1,200. The remaining twenty hours fit four large frames, contributing another $800. Total contribution is $2,000; subtracting the unchanged $1,400 leaves $600 operating profit from the stated costs.

Check the full figures: ten small and four large frames earn $5,080. Their variable expenses total $3,080. The $2,000 difference reconciles to the contribution calculation.

Using all forty hours for eight large frames instead contributes $1,600, leaving $200 after the same fixed expenses. The machine is equally busy, but the modeled week earns $400 less. Making only the ten small frames also fails to get the most from the available work: it leaves twenty hours unused and a $200 operating loss.

ACCA's limiting-factor explanation distinguishes contribution per unit from contribution per unit of scarce resource. Its separate discussion of throughput accounting uses a different cost definition. The figures here use the stated variable expenses and contribution, not a relabeled throughput measure.

Another limit changes the plan

Now replace the finishing assumption: only nine finishing hours are available this week. The forty machine-hours, demand ceilings, prices, variable costs and $1,400 fixed expenses stay unchanged. Every frame still takes one finishing hour.

The old fourteen-frame plan is impossible. Nor can the studio blindly fill all nine finishing slots with small frames. That would contribute $1,080 and leave twenty-two machine-hours unused.

Under both limits, two small and seven large frames fit: four plus thirty-five machine-hours, and nine finishing hours. Contribution is $240 plus $1,400, or $1,640. After fixed expenses, $240 remains. Eight large frames also fit, but contribute $1,600. Three small and six large frames contribute $1,560.

Checking every whole-frame combination within the supplied demand and both time limits gives two small and seven large as the highest-contribution mix. The one-resource ranking has not become a universal rule for a two-resource problem. Additional deadlines, batches or accepted customer commitments would need to enter the schedule too.

Leave the calculation with the work

Chapter 3 of Infinite Upside follows an attractive booking beyond its payment to the vehicle's positioning and the other bookings it prevents. The studio's machine-hour example applies that question to a different invented operation. What does accepting this work make unavailable?

Identify the actual constraint, the time each complete job consumes and the work customers will genuinely buy. Preserve promises already made before allocating remaining capacity. A contribution calculation can compare feasible choices; it cannot turn a late delivery into an acceptable one.