Exact finite-scenario inventory order
Enumerate every admissible one-period order quantity and minimize exact expected purchase, fixed-order, leftover and unmet-demand costs under caller-supplied demand scenarios. Return all optimal quantities and scenario arithmetic; no demand forecast, service guarantee or order placement.
workflow-assurance · Operation ID: inventory-scenarios-optimize
Choose this operation when
- Supply integer inventory and demand in one unit, positive relative scenario probabilities and nonnegative cost assumptions
- All replenishment arrives before demand and every positive order follows the declared multiple and minimum
Outside this profile
- Forecasting, multi-period inventory, uncertain lead time, backorder carryover, shelf life, multiple products or capacity coupling
- Real procurement, inventory availability checks, service-level promises or profit optimization
- Investment advice, high-impact decisions about people, or validating the truth of caller assumptions
Exact release references
Static JSON contract · Markdown reference · Fixed example response
Complete input schema
{
"$schema": "https://json-schema.org/draft/2020-12/schema",
"type": "object",
"properties": {
"onHand": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
},
"scenarios": {
"minItems": 1,
"maxItems": 32,
"type": "array",
"items": {
"type": "object",
"properties": {
"id": {
"type": "string",
"minLength": 1,
"maxLength": 64
},
"demand": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
},
"probabilityWeight": {
"type": "string",
"pattern": "^[1-9][0-9]{0,8}$"
}
},
"required": [
"id",
"demand",
"probabilityWeight"
],
"additionalProperties": false
}
},
"order": {
"type": "object",
"properties": {
"minimumPositive": {
"type": "integer",
"minimum": 1,
"maximum": 1000000
},
"maximum": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
},
"multiple": {
"type": "integer",
"minimum": 1,
"maximum": 1000000
}
},
"required": [
"minimumPositive",
"maximum",
"multiple"
],
"additionalProperties": false
},
"costs": {
"type": "object",
"properties": {
"purchasePerUnit": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]{0,11})(?:\\.[0-9]{1,6})?$"
},
"holdingPerUnit": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]{0,11})(?:\\.[0-9]{1,6})?$"
},
"shortagePerUnit": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]{0,11})(?:\\.[0-9]{1,6})?$"
},
"fixedPositiveOrder": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]{0,11})(?:\\.[0-9]{1,6})?$"
}
},
"required": [
"purchasePerUnit",
"holdingPerUnit",
"shortagePerUnit",
"fixedPositiveOrder"
],
"additionalProperties": false
},
"quantityUnit": {
"type": "string",
"minLength": 1,
"maxLength": 64
},
"costUnit": {
"type": "string",
"minLength": 1,
"maxLength": 64
}
},
"required": [
"onHand",
"scenarios",
"order",
"costs",
"quantityUnit",
"costUnit"
],
"additionalProperties": false
}
Complete output-envelope schema
{
"type": "object",
"required": [
"operation",
"version",
"result",
"provenance"
],
"properties": {
"operation": {
"const": "inventory-scenarios-optimize",
"type": "string"
},
"version": {
"const": "0.29.0",
"type": "string"
},
"result": {
"$schema": "https://json-schema.org/draft/2020-12/schema",
"type": "object",
"properties": {
"profile": {
"type": "string",
"const": "finite-scenario-single-period-inventory-v1"
},
"externalRequests": {
"type": "number",
"const": 0
},
"execution": {
"type": "boolean",
"const": false
},
"assumptionsVerified": {
"type": "boolean",
"const": false
},
"status": {
"type": "string",
"const": "optimal"
},
"quantityUnit": {
"type": "string",
"minLength": 1,
"maxLength": 64
},
"costUnit": {
"type": "string",
"minLength": 1,
"maxLength": 64
},
"orderQuantity": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
},
"availableQuantity": {
"type": "integer",
"minimum": 0,
"maximum": 2000000
},
"expectedCost": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
},
"worstCost": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
},
"expectedShortage": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
},
"expectedLeftover": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
},
"suppliedScenarioStockoutProbability": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
},
"optimalOrderQuantities": {
"minItems": 1,
"maxItems": 512,
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
}
},
"candidates": {
"minItems": 1,
"maxItems": 512,
"type": "array",
"items": {
"type": "object",
"properties": {
"orderQuantity": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
},
"expectedCost": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
},
"worstCost": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
}
},
"required": [
"orderQuantity",
"expectedCost",
"worstCost"
],
"additionalProperties": false
}
},
"chosenScenarios": {
"minItems": 1,
"maxItems": 32,
"type": "array",
"items": {
"type": "object",
"properties": {
"scenarioId": {
"type": "string",
"minLength": 1,
"maxLength": 64
},
"probability": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
},
"demand": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
},
"shortage": {
"type": "integer",
"minimum": 0,
"maximum": 1000000
},
"leftover": {
"type": "integer",
"minimum": 0,
"maximum": 2000000
},
"cost": {
"type": "object",
"properties": {
"numerator": {
"type": "string",
"pattern": "^(?:0|[1-9][0-9]*)$"
},
"denominator": {
"type": "string",
"pattern": "^[1-9][0-9]*$"
}
},
"required": [
"numerator",
"denominator"
],
"additionalProperties": false
}
},
"required": [
"scenarioId",
"probability",
"demand",
"shortage",
"leftover",
"cost"
],
"additionalProperties": false
}
},
"model": {
"type": "object",
"properties": {
"period": {
"type": "string",
"const": "single-period"
},
"replenishment": {
"type": "string",
"const": "all-ordered-units-before-demand"
},
"unmetDemand": {
"type": "string",
"const": "penalized-without-carryover"
},
"demandSource": {
"type": "string",
"const": "caller-supplied-finite-scenarios"
},
"probabilityModel": {
"type": "string",
"const": "normalized-positive-relative-weights"
}
},
"required": [
"period",
"replenishment",
"unmetDemand",
"demandSource",
"probabilityModel"
],
"additionalProperties": false
},
"tieBreak": {
"type": "string",
"const": "smallest-order-quantity; all-optimal-quantities-also-returned"
}
},
"required": [
"profile",
"externalRequests",
"execution",
"assumptionsVerified",
"status",
"quantityUnit",
"costUnit",
"orderQuantity",
"availableQuantity",
"expectedCost",
"worstCost",
"expectedShortage",
"expectedLeftover",
"suppliedScenarioStockoutProbability",
"optimalOrderQuantities",
"candidates",
"chosenScenarios",
"model",
"tieBreak"
],
"additionalProperties": false
},
"provenance": {
"type": "object",
"required": [
"inputSha256",
"outputSha256",
"deterministic",
"externalRequests"
],
"properties": {
"inputSha256": {
"type": "string",
"pattern": "^[a-f0-9]{64}$"
},
"outputSha256": {
"type": "string",
"pattern": "^[a-f0-9]{64}$"
},
"deterministic": {
"const": true
},
"externalRequests": {
"const": 0
}
}
}
},
"additionalProperties": false
}
Fixed example
One accepted fixed example, not a custom-input trial. No operation runs when this static page is requested.
Example input
{
"onHand": 3,
"scenarios": [
{
"id": "low",
"demand": 4,
"probabilityWeight": "1"
},
{
"id": "normal",
"demand": 8,
"probabilityWeight": "2"
},
{
"id": "high",
"demand": 12,
"probabilityWeight": "1"
}
],
"order": {
"minimumPositive": 4,
"maximum": 12,
"multiple": 2
},
"costs": {
"purchasePerUnit": "2",
"holdingPerUnit": "1",
"shortagePerUnit": "7",
"fixedPositiveOrder": "3"
},
"quantityUnit": "units",
"costUnit": "caller-defined cost units"
}
Example response
{
"operation": "inventory-scenarios-optimize",
"version": "0.29.0",
"result": {
"profile": "finite-scenario-single-period-inventory-v1",
"externalRequests": 0,
"execution": false,
"assumptionsVerified": false,
"status": "optimal",
"quantityUnit": "units",
"costUnit": "caller-defined cost units",
"orderQuantity": 6,
"availableQuantity": 9,
"expectedCost": {
"numerator": "22",
"denominator": "1"
},
"worstCost": {
"numerator": "36",
"denominator": "1"
},
"expectedShortage": {
"numerator": "3",
"denominator": "4"
},
"expectedLeftover": {
"numerator": "7",
"denominator": "4"
},
"suppliedScenarioStockoutProbability": {
"numerator": "1",
"denominator": "4"
},
"optimalOrderQuantities": [
6
],
"candidates": [
{
"orderQuantity": 0,
"expectedCost": {
"numerator": "35",
"denominator": "1"
},
"worstCost": {
"numerator": "63",
"denominator": "1"
}
},
{
"orderQuantity": 4,
"expectedCost": {
"numerator": "24",
"denominator": "1"
},
"worstCost": {
"numerator": "46",
"denominator": "1"
}
},
{
"orderQuantity": 6,
"expectedCost": {
"numerator": "22",
"denominator": "1"
},
"worstCost": {
"numerator": "36",
"denominator": "1"
}
},
{
"orderQuantity": 8,
"expectedCost": {
"numerator": "24",
"denominator": "1"
},
"worstCost": {
"numerator": "26",
"denominator": "1"
}
},
{
"orderQuantity": 10,
"expectedCost": {
"numerator": "28",
"denominator": "1"
},
"worstCost": {
"numerator": "32",
"denominator": "1"
}
},
{
"orderQuantity": 12,
"expectedCost": {
"numerator": "34",
"denominator": "1"
},
"worstCost": {
"numerator": "38",
"denominator": "1"
}
}
],
"chosenScenarios": [
{
"scenarioId": "high",
"probability": {
"numerator": "1",
"denominator": "4"
},
"demand": 12,
"shortage": 3,
"leftover": 0,
"cost": {
"numerator": "36",
"denominator": "1"
}
},
{
"scenarioId": "low",
"probability": {
"numerator": "1",
"denominator": "4"
},
"demand": 4,
"shortage": 0,
"leftover": 5,
"cost": {
"numerator": "20",
"denominator": "1"
}
},
{
"scenarioId": "normal",
"probability": {
"numerator": "1",
"denominator": "2"
},
"demand": 8,
"shortage": 0,
"leftover": 1,
"cost": {
"numerator": "16",
"denominator": "1"
}
}
],
"model": {
"period": "single-period",
"replenishment": "all-ordered-units-before-demand",
"unmetDemand": "penalized-without-carryover",
"demandSource": "caller-supplied-finite-scenarios",
"probabilityModel": "normalized-positive-relative-weights"
},
"tieBreak": "smallest-order-quantity; all-optimal-quantities-also-returned"
},
"provenance": {
"inputSha256": "e9bd47771b7ab5ca743bc425d2ff7a74a1233428d38fead34e0639f779c794c2",
"outputSha256": "11a18148d92b8f02fda0cf2acaf2441beb31688c28e80deaeceba054958ad0a5",
"deterministic": true,
"externalRequests": 0
}
}
Bounds and precision
JavaScript IEEE-754 numbers; use strings for large integer IDs/exact decimals where the schema accepts strings. No lossless numeric parsing.
{
"global": {
"requestBytes": 131072,
"responseBytes": 524288,
"jsonDepth": 32,
"jsonNodes": 20000,
"requestsPerMinute": 60,
"paidAttemptsPerMinute": 20,
"idempotencyHours": 24
},
"operation": {
"inputBytes": 48000,
"outputBytes": 192000,
"jsonNodes": 8000,
"depth": 12,
"scenarios": 32,
"orderCandidates": 512,
"maximumCandidateScenarioEvaluations": 16384,
"maximumChosenScenarioEvaluations": 32,
"quantityMaximum": 1000000,
"decimalIntegerDigits": 12,
"decimalFractionDigits": 6,
"probabilityWeightDigits": 9
}
}
Complete schemas, descriptions and cross-field validation may impose additional limits.
Proposed price and protocol definitions
{
"unit": "one successful operation call",
"proposedNominalUsd": "0.008",
"sixDecimalTokenBaseUnits": "8000",
"subscription": false,
"includesPayerWalletOrNetworkFees": false,
"liveQuoteVerified": false,
"condition": "Actual SDK challenge is authoritative only within the caller's explicit authorization; configured six-decimal token peg is an operator assertion, not a conversion guarantee."
}
Protocol definitions: x402, mpp. MPP uses Tempo charge. Paid MCP execution is unsupported. All runtime readiness is not evaluated in this build.
API path templates, not endpoints on this documentation host
{
"x402": "/v1/x402/inventory-scenarios-optimize",
"mpp": "/v1/mpp/inventory-scenarios-optimize"
}
Required headers
{
"Content-Type": "application/json",
"Idempotency-Key": "random 16–128 character operation identifier"
}
Actual SDK challenge amount, asset, network, recipient and wallet costs must pass independent authorization. Preserve identical key, body, protocol and credential on retries; on PAYMENT_UNCERTAIN stop and reconcile.
Execution profile and provider conditions
{
"deterministic": true,
"externalRequests": 0,
"maxExternalRequests": 0,
"resultSnapshotPersisted": false,
"fixedExampleIsIllustrativeSnapshot": false,
"requiresPayment": true,
"supportsMcpExecution": false
}
Deterministic supplied-input operation with no external requests or stored request/result bodies. Payment infrastructure retains payment metadata and hashes.
Failure handling
- HTTP 400: Malformed JSON, missing/invalid idempotency key, or payment identifier mismatch Correct the request before payment
- HTTP 402: Payment challenge or rejected payment Use official protocol SDK; inspect payment outcome before another payment
- HTTP 409: Idempotency conflict, duplicate proof, or PAYMENT_UNCERTAIN Keep original key, body, and proof; reconcile uncertainty with operator; never blindly repay
- HTTP 413: Input or generated output too large Reduce input; no payment attempted for validation failure
- HTTP 415: Unsupported media type or compression Send uncompressed application/json
- HTTP 422: Schema or service-specific semantic validation failure Correct input using returned error code; no payment attempted
- HTTP 429: Request/payment-attempt rate exceeded Wait for rate limit window; preserve existing payment identity
- HTTP 503: Payment configuration/provider/state unavailable, or live DNS preparation failed before settlement Check readiness; DNS preparation failures may retry the identical key/body/credential only; uncertainty requires reconciliation
Declared requirements
Before any paid call, refresh the live operation contract and POST the complete bounded budgeted plan to the separate API's /preflight. Unknown requirements block selection; compatible preflight is not permission to spend.