EOQ with planned backorders calculator API

Compute the optimal order quantity allowing planned shortages: Q* = sqrt(2·D·S/H)·sqrt((H+B)/B), with max inventory and max backorder levels — the backorder-extended Wilson model. Answers 'EOQ when backorders are allowed','optimal order size with shortage cost','how many units can I backorder'.

Price$0.01per request

MethodPOST

Route/v1/calc/logi-eoq-backorder

StatusLive

MIME typeapplication/json

Rate limit120/minute

CacheNo cache

calclogisticsinventoryeoqbackordershortagesupply-chainoptimization

API URLhttps://x402.hexl.dev/v1/calc/logi-eoq-backorder

Integration docs

Example request

{
  "annualDemand": 12000,
  "orderCost": 50,
  "holdingCost": 3,
  "backorderCost": 15
}

Example response

{
  "formula": "Q* = sqrt(2·D·S/H)·sqrt((H+B)/B) ; maxBackorder = Q*·H/(H+B)",
  "optimalOrderQuantity": 692.82,
  "maxInventoryLevel": 577.35,
  "maxBackorderLevel": 115.47,
  "inputs": {
    "annualDemand": 12000,
    "orderCost": 50,
    "holdingCost": 3,
    "backorderCost": 15
  }
}

Input schema

{
  "type": "object",
  "required": [
    "annualDemand",
    "orderCost",
    "holdingCost",
    "backorderCost"
  ],
  "properties": {
    "annualDemand": {
      "type": "number",
      "examples": [
        12000
      ]
    },
    "orderCost": {
      "type": "number",
      "examples": [
        50
      ]
    },
    "holdingCost": {
      "type": "number",
      "description": "annual holding cost per unit H",
      "examples": [
        3
      ]
    },
    "backorderCost": {
      "type": "number",
      "description": "annual backorder cost per unit B",
      "examples": [
        15
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}