Ten hours.
Three jobs. A better allocation.
Job A uses six hours for 30 priority points. Jobs B and C each use five hours for 26. An exact integer optimizer selects B and C: 52 points within the same ten-hour limit.
30
Job A · 6 of 10 hours
52
Jobs B + C · 10 of 10 hours
+22
Priority points in this synthetic example. Not a customer performance claim.
An imported answer can be feasible and suboptimal.
The imported selection of Job A reconciles to 30 points and fits the capacity. It fails the optimality comparison. Those are separate findings.
| Check | Status | Meaning |
|---|---|---|
| declared constraints | passed | Computed allocation uses each item at most once and stays within the supplied capacity. |
| imported constraints | passed | Imported selection respects the declared integer capacity. |
| imported optimality | failed | Comparison with the exact optimum for this bounded 0/1 problem only. |
| numerical reconciliation | passed | Sum of supplied values for the imported selection. |
| source support | not assessed | Input provenance is user supplied; underlying source truth is not checked. |
| formal proof | not assessed | No formal proof checker is invoked. |
| observed performance | not assessed | No real-world outcome is implied by the computed objective. |
The mathematical contract
Maximize Σ valueᵢ × choiceᵢ, subject to Σ costᵢ × choiceᵢ ≤ capacity, with choiceᵢ ∈ {0, 1}.
Uses exact bounded integer dynamic programming, with deterministic tie handling. There is no language-model call. This is a conventional optimization method registered in the LargeQuant runtime.
One capacity constraint. No scheduling, uncertainty or nonlinear dependencies. Units and source data must be appropriate to the intended use.
Inspect inputs
{
"capacity": 10,
"items": [
{
"id": "Job A",
"cost": 6,
"value": 30
},
{
"id": "Job B",
"cost": 5,
"value": 26
},
{
"id": "Job C",
"cost": 5,
"value": 26
}
],
"proposed_ids": [
"Job A"
],
"claimed_objective": 30,
"provenance": {
"source": "Synthetic capacity planning example",
"capacity_unit": "machine-hours",
"objective_unit": "priority points",
"synthetic": true
}
}Inspect computed output
{
"allocation": {
"selected_ids": [
"Job B",
"Job C"
],
"used_capacity": 10,
"objective": 52
},
"baseline": {
"selected_ids": [
"Job A"
],
"used_capacity": 6,
"objective": 30
},
"objective_gain": 22,
"imported_allocation": {
"selected_ids": [
"Job A"
],
"used_capacity": 6,
"objective": 30
},
"checks": [
{
"type": "declared_constraints",
"status": "passed",
"scope": "Computed allocation uses each item at most once and stays within the supplied capacity.",
"evidence": {
"capacity": 10,
"used": 10
},
"checker_version": "LQCAP/1.0"
},
{
"type": "imported_constraints",
"status": "passed",
"scope": "Imported selection respects the declared integer capacity.",
"evidence": {
"capacity": 10,
"used": 6
},
"checker_version": "LQCAP/1.0"
},
{
"type": "imported_optimality",
"status": "failed",
"scope": "Comparison with the exact optimum for this bounded 0/1 problem only.",
"evidence": {
"optimal_objective": 52,
"proposed_objective": 30
},
"checker_version": "LQCAP/1.0"
},
{
"type": "numerical_reconciliation",
"status": "passed",
"scope": "Sum of supplied values for the imported selection.",
"evidence": {
"claimed": 30,
"recomputed": 30
},
"checker_version": "LQCAP/1.0"
},
{
"type": "source_support",
"status": "not_assessed",
"scope": "Input provenance is user supplied; underlying source truth is not checked.",
"evidence": [],
"checker_version": "LQCAP/1.0"
},
{
"type": "formal_proof",
"status": "not_assessed",
"scope": "No formal proof checker is invoked.",
"evidence": [],
"checker_version": "LQCAP/1.0"
},
{
"type": "observed_performance",
"status": "not_assessed",
"scope": "No real-world outcome is implied by the computed objective.",
"evidence": [],
"checker_version": "LQCAP/1.0"
}
],
"method": {
"algorithm": "exact integer 0/1 dynamic programming",
"version": "LQCAP/1.0",
"tie_policy": "retain earlier solution on equal objective",
"precision": "bounded 64-bit integer arithmetic",
"llm_required": false
},
"limitations": [
"One capacity constraint; each item is indivisible and can be chosen once.",
"No scheduling, precedence, uncertainty or nonlinear interactions.",
"Synthetic examples are not domain validation.",
"Source provenance and units are declarations, not independently validated facts."
]
}