InfiniSynapse
What is economic order quantity?什么是经济订货量？
Economic order quantity (EOQ) is the replenishment lot size that minimizes annual ordering cost plus annual inventory holding cost under a defined set of assumptions. It answers how much to order, not when to order.
经济订货量（EOQ）是在一组明确假设下，使年度订货成本与年度库存持有成本之和最低的补货批量。它回答“订多少”，而不是“何时订”。
Small, frequent orders reduce average cycle stock but create more purchase-order, receiving, inspection, setup, and administrative events. Large, infrequent orders reduce those events but tie up more cash and space while increasing exposure to damage, shrinkage, and obsolescence. EOQ locates the mathematical balance between those opposing cost curves.
小批量、高频订货会降低平均周期库存，却增加采购订单、收货、检验、换线和管理事件；大批量、低频订货会减少这些事件，却占用更多资金和空间，并增加损坏、损耗与过时风险。EOQ 寻找两类相反成本曲线的数学平衡点。
Use the result as a transparent baseline, not an automatic instruction. A feasible policy must still respect minimum order quantities (MOQ), case packs, truck or container economics, storage limits, supplier calendars, shelf life, cash constraints, and service requirements.
应把结果视为透明基线，而不是自动指令。可执行政策仍需满足最小起订量、箱规、整车或集装箱经济性、仓储限制、供应商日历、保质期、现金约束与服务要求。
The EOQ formula and total-cost logicEOQ 公式与总成本逻辑
For an order quantity Q, annual ordering cost is (D ÷ Q) × S because D ÷ Q is the expected number of orders. With inventory falling steadily from Q to zero and replenishment arriving at once, average cycle stock is Q ÷ 2, so annual holding cost is (Q ÷ 2) × H. The relevant annual cost function is therefore:
对于订货量 Q，年度订货成本为 (D ÷ Q) × S，因为 D ÷ Q 是预计年订货次数。在库存从 Q 稳定降至零、补货一次到齐时，平均周期库存为 Q ÷ 2，因此年度持有成本为 (Q ÷ 2) × H。相关年度成本函数为：
Differentiating this function with respect to Q and setting the result to zero gives Q² = 2DS/H. Purchase cost D × unit price is omitted when unit price does not change with order quantity, because that constant cannot move the minimum. When price changes by tier, purchase cost must be restored and feasible candidates must be compared.
对该函数关于 Q 求导并令导数为零，可得 Q² = 2DS/H。当单价不随订货量变化时，采购成本 D × 单价是常数，不会改变最小点，因此省略；如果单价随阶梯变化，则必须把采购成本加回并比较可行候选方案。
Define EOQ inputs without mixing units定义 EOQ 输入并避免单位混用
| Input输入 | Definition定义 | Practical data source实务数据源 |
|---|---|---|
| D | Expected demand in units per year每年的预期需求量 | Clean shipments or unconstrained demand forecast; correct stockout-censored history清洗后的出货或无约束需求预测；修正受缺货压制的历史 |
| S | Incremental cost triggered by one order or setup每次订单或生产准备触发的增量成本 | Buyer time, approval, freight minimums, receiving, inspection, invoice handling, setup loss采购工时、审批、最低运费、收货、检验、发票处理、换线损失 |
| H | Cost to hold one unit for one year持有一件库存一年的成本 | Unit cost × annual carrying rate, with documented capital, storage, insurance, shrink, and obsolescence components单位成本 × 年持有率，并记录资金、仓储、保险、损耗和过时组成 |
The time bases must match. If D is monthly, H must also be a monthly per-unit cost; this page annualizes both. Convert cases, kilograms, meters, or eaches consistently. Do not feed annual demand in cases and holding cost per each. If H is calculated from a carrying rate, use H = unit acquisition cost × annual carrying rate and document which cost components are already included to avoid double counting.
时间口径必须一致。如果 D 按月，则 H 也必须是单位月持有成本；本页统一按年。箱、千克、米或件等数量单位也要一致，不能把按箱的年需求与按件的持有成本混用。若以持有率计算 H，则使用“单位采购成本 × 年持有率”，并记录已包含的成本组成，避免重复计算。
Classical EOQ assumptions and fit test经典 EOQ 假设与适用性检验
Consumption is treated as constant through the planning period.
规划期内消耗被视为恒定。
The whole lot becomes available together; a fixed lead time affects timing, not Q.
整批同时可用；固定提前期影响下单时点，而非 Q。
Lost-sales and backorder costs are outside the standard formula.
丢失销售和延期交货成本不在标准公式内。
S and H do not change by order; quantity discounts are absent.
S 与 H 不随订单变化，也不存在数量折扣。
The model also treats the item independently and assumes sufficient capacity, capital, and supplier availability. These assumptions rarely hold perfectly. EOQ remains useful when deviations are small enough that the cost curve is relatively flat around the result and when teams explicitly test operational alternatives.
模型还把单品独立处理，并假定产能、资金和供应能力充足。现实中这些假设很少完全成立；若偏离较小、最优点附近成本曲线较平缓，并且团队会显式检验运营替代方案，EOQ 仍然有用。
Economic order quantity calculator经济订货量计算器
Enter positive values on the same annual basis. The calculator reports the unconstrained mathematical result before MOQ, pack-size, capacity, price, or shelf-life adjustments.
请输入采用相同年度口径的正数。计算器输出的是在考虑 MOQ、箱规、容量、价格或保质期约束之前的无约束数学结果。
Rounding is a business decision. Compare the nearest feasible lower and higher quantities after applying the pack size, MOQ, pallet configuration, and capacity. Because the cost curve is often shallow near EOQ, a practical rounded quantity may have almost the same relevant cost.
舍入是业务决策。应用箱规、MOQ、托盘配置和容量后，应比较最接近的较低与较高可行数量。由于 EOQ 附近的成本曲线通常较平缓，实用的舍入批量可能具有几乎相同的相关成本。
Worked EOQ example: from inputs to annual costEOQ 完整算例：从输入到年度成本
Suppose a SKU has annual demand D = 10,000 units, ordering cost S = $50 per order, and annual holding cost H = $2 per unit. EOQ = √(2 × 10,000 × 50 ÷ 2) = √500,000 = 707.1 units. A planner might initially test 707 units, then round to an operationally feasible case or pallet quantity.
假设某 SKU 年需求 D = 10,000 件，每次订货成本 S = 50 美元，单位年持有成本 H = 2 美元。EOQ = √(2 × 10,000 × 50 ÷ 2) = √500,000 = 707.1 件。计划员可先测试 707 件，再按可执行的箱数或托盘数舍入。
At Q = 707.1, annual ordering cost is (10,000 ÷ 707.1) × $50 = about $707.11. Annual holding cost is (707.1 ÷ 2) × $2 = about $707.11. Their equality is a useful arithmetic check. The combined relevant cost is about $1,414.21. Average cycle stock is 353.55 units; any safety stock would be added separately.
当 Q = 707.1 时，年度订货成本为 (10,000 ÷ 707.1) × 50 美元 ≈ 707.11 美元；年度持有成本为 (707.1 ÷ 2) × 2 美元 ≈ 707.11 美元。二者相等可作为算术校验。相关总成本约为 1,414.21 美元，平均周期库存为 353.55 件；安全库存需另行加上。
Interpret EOQ with sensitivity, not false precision用敏感性分析解读 EOQ，而非追求虚假精度
EOQ changes with the square root of each input. If annual demand doubles while S and H remain constant, EOQ rises by √2, or about 41%, not 100%. A 25% error in an input therefore produces a much smaller percentage error in Q. This robustness explains why a rounded policy can perform well even when costs are estimated.
EOQ 按各输入的平方根变化。若年需求翻倍而 S、H 不变，EOQ 增加 √2，即约 41%，而不是 100%。因此，输入存在 25% 误差时，Q 的百分比误差会小得多。这种稳健性解释了为何成本为估计值时，舍入后的政策仍可能表现良好。
Do not confuse a precise-looking decimal with a precise decision. Build a candidate table around Q—perhaps 80%, 90%, 100%, 110%, and 120% of EOQ—then calculate ordering, holding, purchase, transport, handling, expiry, and capacity effects. The right operational recommendation is the lowest-cost feasible policy, not necessarily the raw square root.
不要把精确的小数外观误认为精确决策。应围绕 Q 建立候选表，例如 EOQ 的 80%、90%、100%、110% 与 120%，再计算订货、持有、采购、运输、搬运、过期与容量影响。正确建议是成本最低的可行政策，不一定是未经调整的平方根。
EOQ vs reorder point and safety stockEOQ、再订货点与安全库存的区别
EOQ controls lot size. A reorder point controls the inventory position that triggers an order. In a continuous-review policy, reorder point is commonly expected demand during lead time plus safety stock. Safety stock protects against uncertainty; cycle stock Q/2 arises from replenishment lot size.
EOQ 控制批量。再订货点控制触发订单的库存位置。在连续检查政策中，再订货点通常为提前期预期需求加安全库存。安全库存应对不确定性，而周期库存 Q/2 来自补货批量。
The basic EOQ formula does not include lead time because a known, constant lead time changes when the order is placed, not the economically balanced lot size. It also does not include safety stock in Q. However, safety stock increases average inventory and total holding cost. Teams evaluating the complete policy should report average inventory as Q/2 + safety stock and monitor service and cost together.
基础 EOQ 公式不含提前期，因为已知且固定的提前期改变下单时点，而不改变经济平衡批量；公式也不把安全库存计入 Q。但安全库存会增加平均库存与总持有成本。评估完整政策时，应按 Q/2 + 安全库存报告平均库存，并同时监控服务与成本。
Adjust EOQ for discounts, MOQ, packs, and capacity针对折扣、MOQ、箱规与容量调整 EOQ
Quantity discounts: calculate a feasible EOQ for each price tier using the tier's H when holding cost depends on unit price. If the computed EOQ is below a tier threshold, test the threshold quantity. Compare total annual cost including D × price, ordering cost, and holding cost across all feasible candidates. The cheapest unit price is not automatically the lowest total cost.
数量折扣：若持有成本随单价变化，应按每个价格阶梯的 H 计算可行 EOQ。若计算值低于该阶梯门槛，则测试门槛数量。比较所有可行候选的年度采购成本 D × 单价、订货成本与持有成本；最低单价并不自动等于最低总成本。
MOQ and pack size: convert the theoretical result to feasible multiples, then compare candidates immediately above and below. Capacity and cash: test the peak on-hand inventory, storage footprint, receiving labor, payment timing, and working-capital limit. Transport: model full-pallet, full-truck, or container economics separately rather than hiding them inside an arbitrary S.
MOQ 与箱规：把理论结果转换为可行倍数，再比较上下相邻候选。容量与现金：检验峰值现货库存、仓储占地、收货工时、付款时点和营运资金上限。运输：应单独建模整托、整车或集装箱经济性，而不是把它们隐藏在任意设定的 S 中。
A practical EOQ implementation workflow可执行的 EOQ 实施流程
- Define the decision grain.定义决策粒度。 Use SKU-location-supplier when order cost, lead time, price, or constraints differ. Document ownership and review cadence.当订货成本、提前期、价格或约束不同时，使用 SKU-地点-供应商粒度，并记录负责人和审查频率。
- Prepare traceable inputs.准备可追溯输入。 Clean demand, order, receipt, item-cost, and policy data. Separate fixed per-order activity from per-unit costs.清洗需求、订单、收货、物料成本与政策数据，区分每单固定活动与单位变动成本。
- Calculate a baseline and sensitivity range.计算基线与敏感性区间。 Produce EOQ, order frequency, cycle days, average cycle stock, and relevant annual cost; vary D, S, and H.输出 EOQ、订货频率、周期天数、平均周期库存和相关年度成本，并改变 D、S、H 测试。
- Apply constraints and compare candidates.应用约束并比较候选。 Add price tiers, MOQ, packs, shelf life, transport, cash, and capacity. Keep each adjustment visible.加入价格阶梯、MOQ、箱规、保质期、运输、现金和容量，并让每项调整可见。
- Pilot, monitor, and govern exceptions.试点、监控并治理例外。 Test selected segments, review service and cost outcomes, record overrides, and set recalculation triggers.选择分群试点，审查服务与成本结果，记录人工覆盖，并设定重算触发条件。
When the standard EOQ model is not enough标准 EOQ 模型何时不够用
Use an economic production quantity model when inventory is produced and received gradually rather than arriving all at once. Use a shortage or backorder model only when shortages are intentionally allowed and their costs can be estimated. For intermittent demand, uncertain lead time, service targets, substitution, multi-echelon inventory, or shared capacity, simulation or stochastic optimization may represent the decision better.
当库存逐步生产并入库、而非一次到齐时，使用经济生产批量模型；仅在有意允许短缺且短缺成本可估算时，使用短缺或延期交货模型。对于间歇性需求、不确定提前期、服务目标、替代关系、多级库存或共享容量，仿真或随机优化可能更合适。
Perishable, seasonal, fashion, promotional, and end-of-life items require explicit shelf-life and markdown logic. A one-year average can hide peaks and create waste. The inventory forecasting guide explains demand estimation, while the inventory optimization software guide covers broader constrained decision support. Those intents complement rather than replace this formula page.
易腐、季节性、时尚、促销和生命周期末期商品需要显式的保质期与降价逻辑。年度平均值可能掩盖峰值并造成浪费。库存预测指南解释需求估计，库存优化软件指南讨论更广泛的约束决策支持；这些意图与本公式页互补，而非相互替代。
Validate EOQ before and after deployment在部署前后验证 EOQ
Backtest the proposed policy against historical order and receipt events, but avoid pretending historical demand was fully observable during stockouts. Compare current and candidate policies on order count, average and peak inventory, carrying cost, freight, receiving workload, expedites, stockouts, expiry, write-offs, and working capital. Segment results by item economics and demand behavior rather than relying only on a portfolio average.
应使用历史订单与收货事件回测建议政策，但不要假装缺货期间的历史需求完全可观测。比较现行与候选政策的订单数、平均及峰值库存、持有成本、运费、收货工作量、加急、缺货、过期、核销和营运资金；按商品经济性与需求行为分群，而不是只看组合平均值。
Set recalculation triggers for material changes in demand level, unit cost, carrying rate, order process, supplier terms, MOQ, pack size, warehouse capacity, or service policy. Monitor the planned quantity against actual order quantity and record reasons for overrides. A governed EOQ table should show source periods, units, formulas, assumptions, constraint adjustments, owner, approval date, and next review date.
当需求水平、单位成本、持有率、订单流程、供应商条款、MOQ、箱规、仓储容量或服务政策发生重大变化时，应触发重算。监控计划数量与实际订货量，并记录覆盖原因。受治理的 EOQ 表应显示数据期间、单位、公式、假设、约束调整、负责人、批准日期与下次审查日期。
Analyze EOQ inputs and policy outcomes across connected data跨关联数据分析 EOQ 输入与政策结果
Prepare demand history and forecasts, purchase orders, order-line counts, receipts, item costs, carrying-cost assumptions, MOQ and pack rules, current policy quantities, inventory balances, service outcomes, freight, and exception logs. InfiniSynapse can be used as an analysis layer to explore connected data, compare segments, investigate cost assumptions, and review observed outcomes around an existing inventory process.
请准备需求历史与预测、采购订单、订单行数、收货、物料成本、持有成本假设、MOQ 与箱规规则、现行政策数量、库存余额、服务结果、运费和例外日志。InfiniSynapse 可作为分析层，探索关联数据、比较分群、调查成本假设，并审查现有库存流程的实际结果。
Capability boundary: this page does not present InfiniSynapse as an automatic replenishment or execution system. It does not automatically optimize or approve EOQ, create purchase orders, replenish or allocate stock, operate a WMS, schedule production or transport, manage suppliers, or write transactions back to ERP.
能力边界：本页不把 InfiniSynapse 描述为自动补货或执行系统。它不会自动优化或批准 EOQ、创建采购订单、补货或分配库存、操作 WMS、安排生产或运输、管理供应商，亦不会向 ERP 回写交易。
Open the InfiniSynapse analytics workspace打开 InfiniSynapse 在线分析工作区Economic order quantity FAQ经济订货量常见问题
What is economic order quantity?什么是经济订货量？
EOQ is the order size that minimizes annual ordering cost plus annual inventory holding cost under the classical assumptions.
EOQ 是在经典假设下，使年度订货成本与年度库存持有成本之和最低的订货批量。
How do you calculate EOQ?如何计算 EOQ？
Use EOQ = √(2DS/H), where D is annual demand, S is cost per order, and H is annual holding cost per unit. Keep time and quantity units aligned.
使用 EOQ = √(2DS/H)，其中 D 为年度需求量，S 为每次订货成本，H 为单位年持有成本；时间与数量单位必须一致。
Does EOQ include safety stock?EOQ 是否包含安全库存？
No. Basic EOQ determines cycle-stock lot size. Safety stock protects against uncertainty and is added separately when reporting average inventory.
不包含。基础 EOQ 决定周期库存批量；安全库存应对不确定性，在报告平均库存时另行加入。
What is the difference between EOQ and reorder point?EOQ 与再订货点有什么区别？
EOQ answers how much to order. Reorder point answers when to order, commonly using expected lead-time demand plus safety stock.
EOQ 回答订多少；再订货点回答何时订，通常由提前期预期需求加安全库存构成。
When should standard EOQ not be used?何时不应直接使用标准 EOQ？
Use a variant or constrained model when demand or lead time is highly variable, items are perishable, shortages are planned, production is gradual, discounts matter, or shared capacity constrains decisions.
当需求或提前期高度波动、商品易腐、计划允许短缺、生产逐步入库、折扣重要或共享容量构成约束时，应使用变体或约束模型。
Is InfiniSynapse an automatic replenishment system?InfiniSynapse 是自动补货系统吗？
It is positioned here as an analytics layer for connected demand, order, receipt, cost, and inventory data—not as a system that automatically approves EOQ, creates orders, replenishes inventory, or writes ERP transactions.
本页将其定位为关联需求、订单、收货、成本与库存数据的分析层，而不是自动批准 EOQ、创建订单、执行补货或回写 ERP 交易的系统。
EOQ sources, limitations, and editorial noteEOQ 资料来源、限制与编辑说明
North Carolina State University's Supply Chain Resource Cooperative presents the basic EOQ inventory model. The University of Kentucky's inventory management notes show annual ordering cost, annual holding cost, classical assumptions, and their equality at the optimum. Virginia Cooperative Extension and Virginia Tech provide an applied inventory-management example and EOQ derivation.
北卡罗来纳州立大学供应链资源合作中心介绍了基础 EOQ 库存模型。肯塔基大学的库存管理教学资料展示了年度订货成本、年度持有成本、经典假设及最优点两类成本相等的关系。Virginia Cooperative Extension 与 Virginia Tech 提供了应用型库存管理示例和 EOQ 推导。
Formula suitability still depends on data quality, cost definitions, demand behavior, lead time, service policy, constraints, and business judgment. This educational page and calculator do not replace procurement, supply-chain, accounting, financial, statistical, or inventory-control advice. For monitoring design, see InfiniSynapse's live guide to a focused data dashboard.
公式适用性仍取决于数据质量、成本定义、需求行为、提前期、服务政策、约束和业务判断。本教育页面及计算器不替代采购、供应链、会计、财务、统计或库存控制建议。关于监控设计，可参阅 InfiniSynapse 已上线的聚焦型数据仪表板指南。