Economics
Set the result you need. Then find the path that reaches it with the smallest necessary input. The result stays fixed; effort is reduced as far as the rules allow.
Definition
The minimum principle is: achieve a defined result with the least input. The result may be a quantity, delivery volume, minimum quality, service level or legal standard. Input is typically money, time, material, machine hours or staff.
The direction matters: define the target first, then ask how little input still achieves it. Among all paths that reach the target, choose the one with the lowest effort.
Two quantities
Output is what must exist at the end: 1,000 finished parts, 50 answered customer requests per day, a building meeting a standard or a daily ration with defined minimums. Input is what you consume to get there: euros, hours, fuel or steel. That is the quantity to minimise.
Taste, image and comfort are either part of the result, a constraint or not an optimisation target. Once that distinction is clear, the question becomes precise: given the result, what is the smallest sensible input?
Example
A company must deliver 1,000 units. It can choose expensive or cheaper machines, more manual work, other suppliers or different bills of materials. Plan A costs €12,000 and plan B €9,500; both meet quantity and quality, so B wins. Plan C costs €8,000 but delivers only 900 units or fails quality, so it is not a solution.
Why it matters
Money, time, raw materials and capacity are scarce. Where the result is mandatory, spending more without changing the result has no benefit. The same logic appears in production, logistics, purchasing, projects and public services: target fixed, input as small as possible, but never below what the target requires.
Requirements
You need a clear target such as 1,000 units, at least 95% availability or at least 160 g protein per day. You also need a measurable input such as euros, hours, kilograms or kWh. Finally, define which alternatives, capacities, quality levels and legal limits are allowed.
Constraints can be lower bounds, such as minimum performance, or upper bounds, such as maximum risk, capacity, calories or budget. The minimum principle chooses the lowest-input plan inside that permitted space.
Common errors
Admissible vs. optimal
Every plan that meets the target and constraints is admissible. Among those, at least one has the lowest input. That is the plan the minimum principle seeks. “Admissible” means the target is met and constraints hold; “optimal” here means no other admissible plan is cheaper.
Constraints
Without constraints, the minimum would often be trivial and useless: do nothing, spend zero and produce zero. Minimum quantities, maximum capacities, technical dependencies and allowed alternatives force the target and the real boundaries.
The more meaningful the constraints, the clearer the question: which point inside the permitted space has the smallest input?
Formal view
The companion article applies this exact structure to the nutrition calculator: food alternatives, euros as input and nutrient boundaries as the target.
In short
Define the result. Define the rules. Among all paths that achieve both, choose the one with the smallest necessary input. That is the minimum principle: not less result, but less effort for the same result.
See how a cost minimum is built and solved under nutrient constraints.
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