Two Resource Capacity Bottleneck
Count complete items under two explicitly positive per-item resource requirements, retaining tied limiting resources.
Description
Count complete items under two explicitly positive per-item resource requirements, retaining tied limiting resources.
Two independent per-item resources can impose different whole-item limits. The smaller determines capacity under a fixed-cost model.
When to use this tool
Count complete items under two explicitly positive per-item resource requirements, retaining tied limiting resources.
- Prepare the supplied resourceA, resourceB, perItemA, perItemB fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter resourceA, resourceB, perItemA, perItemB. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.items, result.bottlenecks. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Require nonnegative resource amounts and positive per-item costs. Floor each resource-to-cost ratio, return their minimum and identify A, B or both as bottlenecks when their whole-item limits tie.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| resourceA | resource a. | Finite number |
| resourceB | resource b. | Finite number |
| perItemA | per item a. | Finite number; greater than zero |
| perItemB | per item b. | Finite number; greater than zero |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.items | The items value under the stated formula or text convention. |
| result.bottlenecks | The bottlenecks list in the ordering and representation described above. |
{
"input": {
"resourceA": 10,
"resourceB": 12,
"perItemA": 3,
"perItemB": 4
},
"output": {
"result": {
"items": 3,
"bottlenecks": [
"A",
"B"
]
}
}
}Limitations and assumptions
- Ties concern floored item capacities, not identical remaining resource fractions. No variable item costs or scheduling constraints are modeled.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Check the arithmetic against the actual scheduling or storage policy. Add variable costs, arrivals, concurrent state and overhead in a model that explicitly represents them when they affect the decision.
References
Similar or alternative tools
- Per Item Prefix Capacity Admission
Admit only the longest affordable ordered prefix of explicit per-item costs; after the first failure later cheaper items are not skipped into admission.
- Capacity Reserve Percent Budget
Reserve a ceiling-rounded percentage of integer capacity and expose the usable whole-unit budget; explicit arithmetic, not availability certification.