InfiniSynapse
What is the safety stock formula?什么是安全库存公式？
The general safety stock formula is Safety Stock = Z × σLT, where Z is the service factor and σLT is the standard deviation of demand during replenishment lead time. The calculation of σLT changes with the uncertainty you face: demand variability, lead-time variability, or both.
通用安全库存公式为：安全库存 = Z × σLT，其中 Z 是服务系数，σLT 是补货提前期内需求量的标准差。σLT 的具体算法取决于不确定性来自需求波动、提前期波动，还是二者同时存在。
Safety stock is not average demand, cycle stock, or the reorder point. It is the uncertainty buffer added above expected demand during the replenishment exposure period. Under a continuous-review policy, a common relationship is Reorder Point = Average Lead-Time Demand + Safety Stock. Order quantity is a separate decision.
安全库存不是平均需求、周转库存或再订货点，而是在补货风险暴露期预期需求量之上增加的不确定性缓冲。在连续检查政策下，常见关系是再订货点 = 平均提前期需求量 + 安全库存；订货量则是另一项独立决策。
A formula is useful only when its definition, units, service measure, data window, review cadence, and rounding rule are explicit. The result is a policy input, not a guarantee against every stockout. Promotions, disruptions, censored sales, substitutions, minimum order quantities, shelf life, and multi-echelon dependencies may require a richer model.
只有当定义、单位、服务指标、数据窗口、复核频率和取整规则都明确时，公式才有意义。结果只是库存政策输入，并不能保证杜绝所有缺货。促销、中断、销量受缺货压制、替代、最小起订量、保质期及多级库存依赖可能需要更复杂的模型。
Choose the safety stock formula for your uncertainty根据不确定性选择安全库存公式
Do not select a formula because it is familiar or easy to place in a spreadsheet. Start with how the item is reviewed and replenished, then identify which input varies. All time-based inputs must use the same unit—for example, daily demand with lead time measured in days.
不要因为某个公式熟悉或容易放进表格就直接采用。应先明确物料如何被检查与补货，再识别哪些输入会波动。所有时间相关输入必须使用相同单位，例如日需求必须搭配以天计的提前期。
| Situation情形 | Formula公式 | Use when适用条件 | Key limitation主要限制 |
|---|---|---|---|
| Lead-time demand already measured已直接测量提前期需求 | Z × σLT | Historical forecast errors or demand totals exist for the full exposure period已有完整风险暴露期的历史预测误差或需求总量 | Past exposure periods must represent the future policy历史暴露期必须能代表未来政策 |
| Variable demand, constant lead time需求波动、提前期固定 | Z × σD × √L | Period demand is independent enough and L is stable各期需求近似独立且 L 稳定 | Serial correlation or seasonality can invalidate square-root scaling自相关或季节性可能使平方根缩放失效 |
| Constant demand, variable lead time需求固定、提前期波动 | Z × D̄ × σL | Usage is stable but supplier or transport time varies用量稳定，但供应商或运输时间波动 | Demand variability is ignored忽略了需求波动 |
| Demand and lead time both vary需求与提前期均波动 | Z × √(LσD² + D̄²σL²) | Both sources matter and independence is a reasonable approximation两类波动都重要，且独立性近似合理 | Covariance, review period, and non-normal tails need separate treatment协方差、检查周期和非正态尾部需另行处理 |
About the max-minus-average method: (maximum usage × maximum lead time) − (average usage × average lead time) is a conservative historical heuristic, not a service-level model. A single outlier can dominate it, and it gives no stated stockout probability. Use it only with documented governance and backtesting.
关于“最大值减平均值”法：（最大用量 × 最大提前期）−（平均用量 × 平均提前期）是偏保守的历史启发式方法，不是服务水平模型。单个异常值就可能主导结果，而且它不对应明确的缺货概率，因此只能在有治理和回测的情况下使用。
Define every input before calculating safety stock计算安全库存前定义所有输入
Average demand and its standard deviation per common time unit. Prefer unconstrained demand or corrected history; stockout-censored sales understate demand.
统一时间单位下的平均需求及其标准差。优先使用未受约束需求或修正历史；被缺货压制的销量会低估真实需求。
Average replenishment lead time and its standard deviation in the same time unit. Define start, end, calendar, partial receipts, and exceptional delays.
相同时间单位下的平均补货提前期及其标准差。需定义起止事件、日历、分批收货和异常延迟。
The standard-normal quantile associated with a target cycle service level when normal-model assumptions are acceptable. It is not the service percentage itself.
在正态模型假设适用时，与目标周期服务水平对应的标准正态分位数。它不是直接把服务百分比代入公式。
Continuous review often uses lead time; periodic review may require lead time plus the review interval. Omitting review time can materially understate the buffer.
连续检查通常使用提前期；定期检查可能需要使用提前期加检查间隔。遗漏检查周期会显著低估缓冲。
| Cycle service level周期服务水平 | Z | Interpretation解释 |
|---|---|---|
| 90% | 1.28 | About 90% of replenishment cycles without a stockout under the model模型下约 90% 的补货周期不发生缺货 |
| 95% | 1.65 | A common illustration, not a universal target常见示例值，但不是通用目标 |
| 98% | 2.05 | More buffer and holding exposure需要更多缓冲并增加持有风险 |
| 99% | 2.33 | High protection under the assumed distribution在假设分布下提供较高保护 |
Cycle service level and fill rate are different. Cycle service level is the probability of no stockout during a replenishment cycle; fill rate is the share of demand supplied immediately from stock. The same Z-score does not mechanically produce the same percentage fill rate. Choose the operational objective first, then use a model calibrated to it.
周期服务水平与满足率不同。周期服务水平是一个补货周期内不发生缺货的概率，满足率是从现货即时满足的需求比例。同一个 Z 分数不会机械地产生相同比例的满足率。应先选择运营目标，再使用与之匹配并校准的模型。
Safety stock calculator for variable demand and lead time需求与提前期均波动的安全库存计算器
This calculator applies the independent demand-and-lead-time approximation. Enter demand per period and lead time in that same period. Results are educational estimates; validate the formula against your replenishment policy and historical outcomes before operational use.
本计算器采用需求与提前期相互独立的近似模型。请按同一期间单位输入需求和提前期。结果仅为教学估算，投入运营前必须结合补货政策与历史结果验证。
Worked safety stock calculation example安全库存完整计算示例
Hypothetical example: an item averages 120 units of demand per day, daily demand standard deviation is 30 units, average lead time is 8 days, lead-time standard deviation is 1.5 days, and the selected cycle-service Z-score is 1.65. The units are aligned: demand is daily and lead time is in days.
假设示例：某物料日均需求 120 件，日需求标准差 30 件，平均提前期 8 天，提前期标准差 1.5 天，选定周期服务水平对应的 Z 分数为 1.65。输入单位一致：需求按天统计，提前期也以天计。
- Demand-variability term需求波动项L × σD² = 8 × 30² = 7,200.L × σD² = 8 × 30² = 7,200。
- Lead-time-variability term提前期波动项D̄² × σL² = 120² × 1.5² = 32,400.D̄² × σL² = 120² × 1.5² = 32,400。
- Lead-time demand deviation提前期需求标准差√(7,200 + 32,400) = √39,600 ≈ 199 units.√(7,200 + 32,400) = √39,600 ≈ 199 件。
- Buffer and reorder point缓冲与再订货点Safety stock = 1.65 × 199 ≈ 328.35, rounded up to 329. Expected lead-time demand is 120 × 8 = 960, so ROP ≈ 1,289 units.安全库存 = 1.65 × 199 ≈ 328.35，向上取整为 329 件；提前期预期需求为 120 × 8 = 960，因此再订货点约为 1,289 件。
Lead-time variability contributes most of the variance in this example. That diagnostic matters: improving supplier reliability may reduce the required buffer more effectively than tuning the service factor. If lead time were truly constant, the simpler demand-only result would be 1.65 × 30 × √8 ≈ 140 units—a material difference that shows why formula choice must match observed uncertainty.
在此示例中，提前期波动贡献了大部分方差。这一诊断很重要：提升供应商可靠性可能比调整服务系数更有效地降低所需缓冲。如果提前期确实固定，需求波动公式的结果为 1.65 × 30 × √8 ≈ 140 件；巨大差异说明公式必须匹配实际不确定性。
Prepare demand and lead-time data correctly正确准备需求与提前期数据
Create a documented SKU-location dataset rather than calculating from a single aggregate. Include requested or unconstrained demand, fulfilled quantity, stockout flags, order and receipt timestamps, promised and actual dates, partial receipts, cancellations, returns, substitutions, promotions, product status, supplier, location, and calendar. Preserve forecast snapshots if the buffer is based on forecast error rather than raw demand variation.
应建立有文档说明的 SKU-地点数据集，而不是只用一个汇总数字计算。数据应包括请求需求或未受约束需求、履约数量、缺货标记、下单与收货时间、承诺及实际日期、分批收货、取消、退货、替代、促销、产品状态、供应商、地点和日历。如果缓冲基于预测误差而非原始需求波动，还要保留预测快照。
- Correct censored demand: zero or low sales during a stockout do not prove low demand.修正受压制需求：缺货期间零销量或低销量不代表需求很低。
- Define lead time operationally: purchase-order release to usable receipt differs from supplier ship time.按运营口径定义提前期：采购订单释放到可用入库不同于供应商运输时间。
- Separate regimes: launches, end-of-life items, promotions, strikes, and one-off expedites should not silently shape normal policy.区分不同状态：新品、退市品、促销、罢工和一次性加急不应悄然决定常规政策。
- Use a representative window: too short is noisy; too long mixes obsolete behavior. Record the chosen window and refresh rule.选择代表性窗口：过短会产生噪声，过长会混入过时行为；必须记录窗口与刷新规则。
Implement the formula in a governed spreadsheet or data model在受治理的表格或数据模型中实施公式
- Freeze definitions冻结定义Document SKU-location grain, demand basis, lead-time start and end, review policy, service measure, time unit, exclusions, and rounding.记录 SKU-地点粒度、需求口径、提前期起止、检查政策、服务指标、时间单位、排除规则和取整方式。
- Profile and reconcile数据剖析与核对Check missing dates, duplicates, negative quantities, unit conversions, stockout censorship, receipt matching, and totals against source systems.检查缺失日期、重复、负数数量、单位换算、缺货压制、收货匹配，并与源系统总量核对。
- Segment policy细分政策Group items by value, criticality, demand pattern, shelf life, source flexibility, and consequence of shortage; do not assign one target to every SKU.按价值、关键性、需求形态、保质期、供应灵活性和缺货后果分组，不要为所有 SKU 设置同一目标。
- Calculate transparently透明计算Keep raw inputs, transformed inputs, formula version, result, floor or cap, override reason, approver, and effective date in separate auditable fields.将原始输入、转换后输入、公式版本、结果、上下限、调整原因、批准人和生效日期放在独立可审计字段中。
- Backtest before release发布前回测Replay historical periods without future leakage; compare stockouts, fill rate or cycle service, average inventory, obsolete stock, and expedite behavior.在无未来信息泄漏的情况下重放历史期间，比较缺货、满足率或周期服务、平均库存、过时库存和加急行为。
Protect formula cells, validate ranges, version assumptions, and assign an owner. A spreadsheet can be appropriate for a small controlled scope; the risk comes from silent edits, inconsistent copies, stale source extracts, and undocumented overrides—not from the file format alone.
应保护公式单元格、验证范围、管理假设版本并指定负责人。对于小而受控的范围，表格可以适用；真正的风险来自静默修改、版本不一致、过时数据提取和无记录调整，而不只是文件格式本身。
When a standard safety stock formula is not enough标准安全库存公式何时不够用
Many zero periods and lumpy orders violate smooth normal approximations. Consider empirical lead-time demand, discrete distributions, simulation, or a differentiated stocking policy.
大量零需求期间和块状订单不符合平滑正态近似，可考虑经验提前期需求、离散分布、模拟或差异化备货政策。
Raw historical standard deviation can confuse predictable movement with uncertainty. Use forecast error by horizon and preserve the future seasonal baseline separately.
原始历史标准差可能把可预测变化误当成不确定性，应按预测期使用预测误差，并单独保留未来季节性基线。
Components tied to production plans and suppliers whose delays worsen during demand peaks break independence assumptions. Model covariance, capacity, and common-cause risk.
受生产计划驱动的零件，以及在需求高峰时延迟加剧的供应商，会破坏独立性假设，应建模协方差、产能与共同原因风险。
A mathematically higher buffer may be economically wrong when shelf life, markdown, engineering change, or end-of-life exposure dominates shortage cost.
当保质期、降价、工程变更或退市风险高于缺货成本时，数学上更高的缓冲可能在经济上错误。
Multi-echelon networks add another complication: stocking every node independently can duplicate protection and hide upstream service failures. SAP's multistage documentation, for example, distinguishes demand variability from service variability across a bill of distribution. Treat single-echelon formulas as local approximations, not automatic network optimization.
多级网络还带来另一复杂性：每个节点独立备货可能重复缓冲，并掩盖上游服务失败。例如 SAP 多级库存文档区分分销网络中的需求波动与服务波动。因此，单级公式应被视为局部近似，而不是自动化的网络优化。
Backtest safety stock against service and inventory outcomes结合服务与库存结果回测安全库存
A correct equation can still produce a poor policy when its inputs or assumptions are wrong. Use rolling-origin backtests: at each historical decision date, calculate only from information that was available then, apply the replenishment rule, and measure later outcomes. Compare the candidate with the current policy and a simple baseline on the same SKU-location periods.
即使等式正确，输入或假设错误仍会产生糟糕政策。应采用滚动起点回测：在每个历史决策日，只使用当时可获得的信息计算并应用补货规则，再衡量后续结果；在相同 SKU-地点期间，将候选政策与当前政策及简单基线比较。
After launch, monitor realized service versus target by segment, the frequency and size of overrides, input drift, lead-time shifts, forecast-error changes, and stockout censorship. Establish thresholds that trigger review rather than automatically changing every parameter. Recalculate after structural assortment, supplier, lane, production, or service-policy changes.
上线后，应按分群监控实际服务与目标的差异、调整频率与幅度、输入漂移、提前期变化、预测误差变化和缺货压制。设置触发复核的阈值，而不是自动改变每个参数。商品组合、供应商、线路、生产或服务政策发生结构变化后，应重新计算。
Connect safety stock to reorder point and inventory policy把安全库存连接到再订货点与库存政策
Safety stock does not decide when to order by itself. In a continuous-review system, the reorder point commonly combines expected lead-time demand with safety stock. In periodic review, the protection period often extends through the next review plus replenishment lead time. Order quantity may be driven by economic order quantity, minimum order quantity, pack size, capacity, transport economics, or a target order-up-to level.
安全库存本身并不决定何时订货。在连续检查系统中，再订货点通常由提前期预期需求加安全库存构成；在定期检查系统中，保护期往往覆盖下一次检查间隔加补货提前期。订货量可能由经济订货量、最小起订量、包装规格、产能、运输经济性或目标最高库存决定。
Review related metrics together. The planned InfiniSynapse pages for inventory turnover ratio and days inventory outstanding evaluate inventory velocity and cash exposure; they do not replace service-policy analysis. The planned demand planning software guide addresses system selection and governance rather than this formula's mathematical intent.
相关指标应结合审查。计划上线的 InfiniSynapse库存周转率和库存持有天数页面用于评估库存流动速度和资金占用，并不能替代服务政策分析；计划上线的需求计划软件指南关注系统选型与治理，不同于本页的公式意图。
Decision rule: do not celebrate lower safety stock in isolation. A sound change improves the chosen service-and-cost tradeoff after accounting for stockouts, expedites, waste, and working capital.
决策规则：不要孤立地庆祝安全库存下降。合理变更应在计入缺货、加急、浪费和营运资金后，改善既定的服务与成本权衡。
Analyze safety-stock inputs and outcomes across connected data跨关联数据分析安全库存输入与结果
Prepare SKU-location demand history, stockout flags, forecast snapshots, purchase orders, receipts, lead-time events, inventory balances, service outcomes, and the current policy table. InfiniSynapse can be used as an analysis layer to explore connected data, compare segments, investigate input changes, and review observed outcomes around an existing inventory process.
请准备 SKU-地点需求历史、缺货标记、预测快照、采购订单、收货、提前期事件、库存余额、服务结果和当前政策表。InfiniSynapse 可作为分析层，用于探索关联数据、比较分群、调查输入变化，并审查现有库存流程周边的实际结果。
Capability boundary: this page does not present InfiniSynapse as an inventory execution or replenishment system. It does not automatically set policy, place purchase orders, allocate stock, operate a warehouse, schedule transport, or write transactions back to ERP.
能力边界：本页不把 InfiniSynapse 描述为库存执行或补货系统。它不会自动设定政策、创建采购订单、分配库存、操作仓库、安排运输或向 ERP 回写交易。
Open the InfiniSynapse analytics workspace打开 InfiniSynapse 在线分析工作区Safety stock formula FAQ安全库存公式常见问题
What is the standard safety stock formula?标准安全库存公式是什么？
A common service-level form is SS = Z × σLT. The correct expression for lead-time demand deviation depends on whether demand, lead time, or both vary.
常见服务水平形式为 SS = Z × σLT。提前期需求标准差的具体表达取决于需求、提前期或二者是否波动。
What Z-score should be used?应该使用哪个 Z 分数？
Choose Z from the target cycle service level when model assumptions fit: approximately 1.28 for 90%, 1.65 for 95%, 2.05 for 98%, and 2.33 for 99%. Do not confuse cycle service with fill rate.
当模型假设适用时，根据目标周期服务水平选择 Z：90% 约为 1.28、95% 约为 1.65、98% 约为 2.05、99% 约为 2.33。不要混淆周期服务与满足率。
How do lead-time changes affect safety stock?提前期变化如何影响安全库存？
Longer average lead time increases exposure to demand variation; variable lead time adds uncertainty of its own. Keep units aligned and recalculate after structural supplier or logistics changes.
更长的平均提前期会增加需求波动暴露，提前期自身波动还会增加额外不确定性。保持单位一致，并在供应商或物流发生结构变化后重新计算。
Can safety stock be negative?安全库存可以为负数吗？
A conventional result should not be negative. Negative output usually signals an unsuitable heuristic, bad units, data errors, or policy logic requiring investigation. Apply a documented floor only after finding the cause.
常规结果不应为负。负值通常意味着启发式方法不适用、单位错误、数据问题或政策逻辑需调查；查明原因后才能应用有记录的下限。
Is InfiniSynapse a replenishment system?InfiniSynapse 是补货系统吗？
It is positioned here as an analysis layer for connected demand, lead-time, inventory, and service data—not as a system that places orders, executes replenishment, operates warehouses, or writes ERP transactions.
本页将其定位为分析关联需求、提前期、库存与服务数据的分析层，而不是下单、执行补货、运营仓库或回写 ERP 交易的系统。
Official safety stock references and limitations安全库存官方参考与限制
Oracle NetSuite documents the combined variability equation, the relationship Safety Stock = Lead-Time Demand Standard Deviation × Z-score, and approximate Z values in its Inventory Optimization Calculations. SAP explains that selected service level, replenishment lead time, and forecast accuracy affect safety stock in Calculating the Safety Stock and Reorder Level.
Oracle NetSuite 在库存优化计算文档中说明了组合波动方程、“安全库存 = 提前期需求标准差 × Z 分数”的关系及近似 Z 值。SAP 在安全库存与再订货水平计算文档中解释了服务水平、补货提前期和预测准确率对安全库存的影响。
North Carolina State University's Supply Chain Resource Cooperative distinguishes cycle service level from fill rate in its reorder point tutorial. Formula suitability still depends on demand distribution, review policy, dependence, lost sales or backorders, and business costs. This page is educational and does not replace statistical, financial, accounting, procurement, or inventory-control advice. For monitoring design, see InfiniSynapse's live guide to a focused data dashboard.
北卡罗来纳州立大学供应链资源合作中心在其再订货点教程中区分周期服务水平与满足率。公式适用性仍取决于需求分布、检查政策、相关性、丢失销售或延期交货及业务成本。本页仅供教育参考，不替代统计、财务、会计、采购或库存控制建议。关于监控设计，可参阅 InfiniSynapse 已上线的聚焦型数据仪表板指南。