Gab AI · research example
Inspect the feasible options. Reproduce the optimum.
An executed twelve-combination model. Compare a stated capacity scenario and inspect the code; the result is conditional on inputs.
INTEGER ALLOCATION / TWO OPTIONScoefficients
A resource limit. A choice you can explain.
Best feasible choice1 A + 2 B
Supplied value points13
Eight feasible pairs out of twelve. The staff limit binds; one material unit remains.
| A | B | Staff h | Material | Points | Constraint check |
|---|
Points are supplied priorities, not revenue or measured impact. Extra capacity is an assumption.
Inspect the runnable enumerator
/* ALLOCATION CORE START */
const options = [{"name": "A", "staff": 4, "material": 3, "value": 5, "maximum": 2}, {"name": "B", "staff": 2, "material": 4, "value": 4, "maximum": 3}];
function enumerateAllocation(staffCapacity, materialCapacity) {
if (!Number.isSafeInteger(staffCapacity) || !Number.isSafeInteger(materialCapacity) || staffCapacity < 0 || materialCapacity < 0) throw new TypeError('Resource capacities must be nonnegative safe integers.');
const pairs = [];
for (let a = 0; a <= options[0].maximum; a++) for (let b = 0; b <= options[1].maximum; b++) {
const staff = a * options[0].staff + b * options[1].staff;
const material = a * options[0].material + b * options[1].material;
const value = a * options[0].value + b * options[1].value;
const feasible = staff <= staffCapacity && material <= materialCapacity;
const reason = feasible ? 'Feasible' : staff > staffCapacity && material > materialCapacity ? 'Both limits' : staff > staffCapacity ? 'Staff limit' : 'Material limit';
pairs.push({a, b, staff, material, value, feasible, reason});
}
const feasible = pairs.filter(pair => pair.feasible);
const maximum = Math.max(...feasible.map(pair => pair.value));
return {pairs, feasible, best: feasible.filter(pair => pair.value === maximum), maximum};
}
/* ALLOCATION CORE END */Resource-allocation-model.txt
Baseline resource limits Baseline capacity is eight staff hours and twelve material units. Option counts must be nonnegative integers. At most two units of A and three units of B may be chosen. Choosing zero of an option is permitted. Objective and units Maximize supplied value points, not money or a measured business outcome. Each A contributes five points and each B contributes four points. Staff hours and material units are separate constraints. There is no minimum-demand requirement, randomness, interaction benefit or causal interpretation in this model. Explicit capacity scenario For comparison only, consider ten staff hours while keeping twelve material units and the same option limits. Those two extra hours are an assumption, not confirmed availability. The scenario does not change the option values or material requirements. Scope of the result This is a twelve-combination toy model. Exhaustive enumeration can establish its optimum under these supplied deterministic assumptions. It does not establish a real-world allocation, statistical validity, fairness, future demand or the quality of the value-point assumptions. Review the formulation and resource data before using an optimization result.
Resource-allocation-options.csv
Option A coefficients One unit of A needs four staff hours and three material units and contributes five value points. Its maximum count is two. Option B coefficients One unit of B needs two staff hours and four material units and contributes four value points. Its maximum count is three. Independent verification targets At baseline, A = 1 and B = 2 use eight staff hours and eleven material units for thirteen value points. With the ten-hour scenario, A = 2 and B = 1 use ten staff hours and ten material units for fourteen points. Enumerate every allowed count pair before calling either optimal.