{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"reorder-point"},"result":{"entity_type":"calculator","id":"reorder-point","calculator_id":"reorder-point","canonical_url":"https://tttkmbb.com/business/reorder-point","name":"Reorder Point Calculator","title":"Reorder Point Calculator – Lead-Time Demand plus Safety Stock (Service-Level Method)","category":"business","category_name":"Business & Marketing","tool_name":"calculate_reorder_point","featured_mcp_tool":false,"description":"Computes the inventory level at which to place a new order: average daily demand × lead time plus safety stock, where safety stock is either given directly or derived from a service level and the standard deviation of daily demand (z × σ × √lead time).","use_when":"You need the stock level that triggers a purchase order so that demand during the supplier lead time is covered with a chosen service level.","do_not_use_when":"You need the order size rather than the trigger level (use eoq), or lead time itself varies substantially (the formula would need the lead-time variance term).","inputs":[{"name":"daily_demand_units","label":"Average daily demand","type":"number","unit":"units/day","required":true,"min":0,"max":1000000000,"description":"Mean units sold or consumed per day.","example":20},{"name":"lead_time_days","label":"Lead time","type":"number","unit":"days","required":true,"min":0,"max":3650,"description":"Days from placing an order to receiving it.","example":7},{"name":"safety_stock_units","label":"Safety stock","type":"number","unit":"units","required":false,"min":0,"max":1000000000,"description":"Buffer stock to hold. Used when demand_std_dev_daily is not given; 0 if neither is given.","example":50},{"name":"demand_std_dev_daily","label":"Std. deviation of daily demand","type":"number","unit":"units/day","required":false,"min":0,"max":1000000000,"description":"Standard deviation of daily demand; when given, safety stock = z × σ × √lead_time (takes precedence over safety_stock_units).","example":30},{"name":"service_level_percent","label":"Service level","type":"number","unit":"%","required":false,"default":95,"exclusive_min":0,"exclusive_max":100,"description":"Cycle service level (probability of no stockout during lead time) used to derive z; 90 → 1.28, 95 → 1.64, 99 → 2.33.","example":95}],"outputs":[{"name":"lead_time_demand_units","label":"Lead-time demand","type":"number","unit":"units","decimals":2,"description":"daily_demand × lead_time_days."},{"name":"safety_stock_units","label":"Safety stock","type":"number","unit":"units","decimals":2,"description":"Given value or z × σ × √lead_time."},{"name":"z_value","label":"z for service level","type":"number","decimals":4,"description":"Standard normal quantile of the service level (only when computed from demand_std_dev_daily)."},{"name":"reorder_point_units","label":"Reorder point","type":"number","unit":"units","decimals":2,"description":"lead_time_demand + safety_stock."},{"name":"reorder_point_rounded_up","label":"Reorder point (whole units)","type":"integer","unit":"units","decimals":4,"description":"Reorder point rounded up to a whole unit."},{"name":"safety_stock_method","label":"Safety stock method","type":"string","decimals":4,"description":"How safety stock was determined."}],"input_schema":{"type":"object","properties":{"daily_demand_units":{"description":"Mean units sold or consumed per day. Unit: units/day.","type":"number","minimum":0,"maximum":1000000000,"examples":[20],"x-unit":"units/day"},"lead_time_days":{"description":"Days from placing an order to receiving it. Unit: days.","type":"number","minimum":0,"maximum":3650,"examples":[7],"x-unit":"days"},"safety_stock_units":{"description":"Buffer stock to hold. Used when demand_std_dev_daily is not given; 0 if neither is given. Unit: units.","type":"number","minimum":0,"maximum":1000000000,"examples":[50],"x-unit":"units"},"demand_std_dev_daily":{"description":"Standard deviation of daily demand; when given, safety stock = z × σ × √lead_time (takes precedence over safety_stock_units). Unit: units/day.","type":"number","minimum":0,"maximum":1000000000,"examples":[30],"x-unit":"units/day"},"service_level_percent":{"description":"Cycle service level (probability of no stockout during lead time) used to derive z; 90 → 1.28, 95 → 1.64, 99 → 2.33. Unit: %.","type":"number","exclusiveMinimum":0,"exclusiveMaximum":100,"default":95,"examples":[95],"x-unit":"%"}},"additionalProperties":false,"required":["daily_demand_units","lead_time_days"]},"output_schema":{"type":"object","properties":{"lead_time_demand_units":{"description":"daily_demand × lead_time_days. Unit: units.","type":"number","x-unit":"units"},"safety_stock_units":{"description":"Given value or z × σ × √lead_time. Unit: units.","type":"number","x-unit":"units"},"z_value":{"description":"Standard normal quantile of the service level (only when computed from demand_std_dev_daily).","type":"number"},"reorder_point_units":{"description":"lead_time_demand + safety_stock. Unit: units.","type":"number","x-unit":"units"},"reorder_point_rounded_up":{"description":"Reorder point rounded up to a whole unit. Unit: units.","type":"integer","x-unit":"units"},"safety_stock_method":{"description":"How safety stock was determined.","type":"string"}}},"formula":"lead_time_demand = daily_demand_units × lead_time_days; safety_stock = z(service_level) × demand_std_dev_daily × √lead_time_days (or the given value); reorder_point = lead_time_demand + safety_stock","method":"Assumes normally distributed daily demand, independent from day to day, and a fixed lead time; the cycle service level is the probability of not running out before the order arrives, not the fill rate.","sources":[{"name":"Wikipedia – Reorder point","url":"https://en.wikipedia.org/wiki/Reorder_point","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Safety stock","url":"https://en.wikipedia.org/wiki/Safety_stock","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"20/day, 7-day lead time, 50 safety stock","inputs":{"daily_demand_units":20,"lead_time_days":7,"safety_stock_units":50},"expected":{"lead_time_demand_units":140,"safety_stock_units":50,"reorder_point_units":190,"reorder_point_rounded_up":190,"safety_stock_method":"given"},"url":"https://tttkmbb.com/api/v1/calculate/reorder-point?daily_demand_units=20&lead_time_days=7&safety_stock_units=50"},{"name":"100/day, 4-day lead time, σ = 30, 95 % service level","inputs":{"daily_demand_units":100,"lead_time_days":4,"demand_std_dev_daily":30,"service_level_percent":95},"expected":{"lead_time_demand_units":400,"z_value":1.6449,"safety_stock_units":98.69,"reorder_point_units":498.69,"reorder_point_rounded_up":499},"url":"https://tttkmbb.com/api/v1/calculate/reorder-point?daily_demand_units=100&lead_time_days=4&demand_std_dev_daily=30&service_level_percent=95"}],"faq":[{"q":"Why √lead time?","a":"Demand over L independent days has variance L × σ², so its standard deviation is σ × √L; the safety stock covers z of those standard deviations."},{"q":"What if lead time also varies?","a":"Use σ_LT = √(L·σ_d² + d²·σ_L²) as the standard deviation of lead-time demand; this calculator covers only demand variability."}],"tags":["reorder point calculator","safety stock","lead time demand","service level","inventory reorder"],"related":[{"calculator_id":"eoq","reason":"How much to order once the reorder point is reached."},{"calculator_id":"normal-distribution","reason":"Origin of the z value for the service level."}],"links":{"html":"https://tttkmbb.com/business/reorder-point","markdown":"https://tttkmbb.com/business/reorder-point.md","json":"https://tttkmbb.com/business/reorder-point.json","api":"https://tttkmbb.com/api/v1/calculate/reorder-point","schema":"https://tttkmbb.com/api/v1/calculators/reorder-point","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:48:18Z"}