EOQ、安全库存和再订购点：公式、工作示例和 Odoo 设置

The three numbers that control any replenishment system are: EOQ (economic order quantity — how much to order), safety stock (the buffer against demand and lead-time variability), and the reorder point (the stock level that triggers a new order). The formulas are: EOQ = sqrt(2DS / H), safety stock = z × demand standard deviation × sqrt(lead time), and reorder point = average demand × lead time + safety stock. Get these three right per SKU and you order the right quantity at the right moment; get them wrong and you oscillate between stockouts and dead capital. This guide works each formula with real numbers, gives you the full parameter and data-model table, the service-level z-score trade-off table, and the exact mapping onto Odoo reordering rules.

Key Takeaways

• EOQ = sqrt(2DS / H) balances ordering cost against holding cost — it answers "how much per order", not "when to order"
• The reorder point answers "when": ROP = average daily demand × lead time in days + safety stock
• Safety stock is driven by a z-score you choose: 90% service level uses z = 1.28, 95% uses z = 1.65, 99% uses z = 2.33 — each step up costs disproportionately more stock
• When lead time itself varies, use the combined formula that includes lead-time standard deviation — supplier unreliability often dominates demand noise
• In Odoo, the reordering rule's Min Quantity is your reorder point and Max Quantity should be roughly ROP + EOQ — setting Min = Max is the single most common configuration mistake
• Holding cost H must be annual cost per unit (typically 15–30% of unit cost), and D and H must use the same time basis or EOQ comes out meaningless
• Parameters decay: demand, lead times, and costs drift, so recompute quarterly per A-class SKU at minimum
• Formulas assume reasonably normal, stable demand — for lumpy, seasonal, or new products, use forecast-driven replenishment instead of static rules

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The Three Questions Every Replenishment Policy Answers

A continuous-review replenishment policy (the kind Odoo's reordering rules implement) answers three independent questions:

They are independent levers. EOQ is pure cost optimization and has nothing to do with uncertainty. Safety stock is pure uncertainty management and has nothing to do with ordering cost. The reorder point ties timing together. Practitioners who blur them — for example, inflating order quantities "to be safe" — pay for buffer twice and still stock out, because extra order quantity does not protect the window between hitting the reorder point and the goods arriving.

Parameters and Data Model

Before any formula, you need these inputs per SKU. This table doubles as the data model if you are building a calculation layer or spreadsheet on top of your ERP:

Two data-hygiene rules that wreck more calculations than any formula error:

1. Match time buckets. If your lead time is in days, sigma_d must be the standard deviation of daily demand. Computing sigma from monthly buckets and plugging it into a formula with daily lead time inflates safety stock by roughly sqrt(30), more than five-fold.
2. Use actual lead times, not promised ones. Pull receipt dates minus order dates from your PO history. Suppliers' quoted lead times are marketing; your sigma_LT lives in the gap.

EOQ: The Formula and a Worked Example

EOQ minimizes the total of annual ordering cost (more orders = more fixed cost) and annual holding cost (bigger orders = more average inventory):

EOQ = sqrt(2 × D × S / H)

Total annual cost at EOQ = (D / EOQ) × S  +  (EOQ / 2) × H

Worked example. A distributor sells a power adapter:

• D = 12,000 units/year
• S = 50 USD per order
• Unit cost c = 12 USD; holding rate 20%/year, so H = 0.20 × 12 = 2.40 USD/unit/year

EOQ = sqrt(2 × 12,000 × 50 / 2.40)
    = sqrt(1,200,000 / 2.40)
    = sqrt(500,000)
    ≈ 707 units

Sanity check the economics:

• Orders per year = 12,000 / 707 ≈ 17 orders
• Annual ordering cost = 17 × 50 = 850 USD
• Average cycle stock = 707 / 2 ≈ 354 units; holding cost = 354 × 2.40 ≈ 849 USD

Ordering cost ≈ holding cost — that equality is the signature of a correct EOQ. In practice you would round 707 to a supplier pack size or container quantity (say 700 or 720); the total-cost curve is flat near the optimum, so rounding within ±20% costs almost nothing. That flatness is also why agonizing over precise S and H values is wasted effort — get them roughly right and move on.

Where EOQ misleads: quantity-break pricing (compare total cost at each break point against EOQ), perishables and short-lifecycle goods (cap order quantity at sellable-before-expiry), and supplier minimum order quantities that exceed EOQ (the MOQ wins; your model should flag the excess holding cost it causes).

Safety Stock: The z-Score Decision

Safety stock protects you during the exposure window — the lead time between triggering a reorder and receiving it. The base formula, when demand varies but lead time is stable:

SS = z × sigma_d × sqrt(LT)

Worked example. Same adapter:

• d_avg = 12,000 / 300 selling days = 40 units/day
• sigma_d = 12 units/day (computed from daily sales history)
• LT = 7 days
• Target service level 95%, so z = 1.65

SS = 1.65 × 12 × sqrt(7)
   = 1.65 × 12 × 2.646
   ≈ 52.4  →  round to 53 units

When Lead Time Also Varies

If your supplier's actual lead time swings (and pull the PO history before assuming it does not), use the combined formula:

SS = z × sqrt( LT × sigma_d²  +  d_avg² × sigma_LT² )

Continuing the example with sigma_LT = 2 days:

SS = 1.65 × sqrt( 7 × 144  +  1,600 × 4 )
   = 1.65 × sqrt( 1,008 + 6,400 )
   = 1.65 × sqrt( 7,408 )
   = 1.65 × 86.1
   ≈ 142 units

Read those two results side by side: 53 units against 142 units. The lead-time variability term (6,400) dwarfs the demand variability term (1,008). A supplier who is two days erratic costs you nearly three times the buffer of your own demand noise. This is the quantitative case for supplier reliability programs — shaving sigma_LT from 2 days to 1 day cuts safety stock from 142 to about 97 units, on this one SKU alone.

The Service-Level Trade-Off Table

The z-score is a management decision dressed as a statistic. Each step toward 100% service costs disproportionately more, because z grows faster as you push into the tail:

(SS column uses the simple formula with sigma_d = 12, LT = 7.)

Going from 90% to 99.9% service nearly two-and-a-half times your buffer — on every SKU you apply it to. This is why ABC segmentation matters: target 98–99% on A-class items where a stockout costs real revenue or a production stop, 95% on B-class, and 90% (or less, or none) on C-class long-tail items. We cover the segmentation method in depth in our guide to demand forecasting, ABC analysis, and safety stock.

You can sanity-check your own numbers against ours with the free safety stock calculator.

Reorder Point: Putting Timing Together

ROP = d_avg × LT + SS

Worked example, using the combined-variability safety stock:

ROP = 40 × 7 + 142
    = 280 + 142
    = 422 units

When forecasted available stock touches 422 units, order EOQ ≈ 707 units. Average inventory over time will be roughly SS + EOQ/2 = 142 + 354 ≈ 496 units, worth about 5,950 USD at cost — a number you can now defend line by line in front of a CFO, which is the real point of doing this formally.

One subtlety: the trigger should compare against forecasted available stock (on hand − reservations + incoming receipts), not raw on-hand. If 800 units are already on a confirmed inbound PO, you do not want to reorder at 422 on hand. Odoo's reordering engine handles this correctly out of the box, which brings us to setup. The reorder point calculator implements the same forecast-aware logic if you want to test scenarios first.

Configuring Odoo Reordering Rules with These Values

Odoo's reordering rules (Inventory → Operations → Replenishment, or via the product form) implement a min/max continuous-review policy. The mapping from the formulas:

How the engine behaves: the scheduler computes forecasted quantity (on hand − outgoing reservations + confirmed incoming) at the rule's location. When forecast falls below Min, Odoo generates a draft RFQ (or manufacturing order) for the quantity needed to reach Max, rounded up to the Multiple. Because the trigger uses forecasted stock, inbound POs correctly suppress duplicate orders.

Settings that interact with your math — set them deliberately:

• Vendor lead time lives on the supplier pricelist line of the product. Odoo uses it to schedule the order date backward from the needed date. Keep it equal to the LT you used in the ROP formula, or the timing logic and your buffer math diverge.
• Security Lead Time for Purchase (Inventory settings) moves every order earlier by a fixed number of days. It is a crude, days-based hedge. If you computed safety stock properly with sigma_LT, leave security lead time at zero — using both double-counts lead-time risk across your entire catalog.
• Days to Purchase (how long your own purchasing department takes to convert an RFQ to a confirmed PO) adds to the effective lead time. If RFQs sit two days awaiting approval, either include those 2 days in LT or set this field — once, not both.
• Visibility Days lets the rule consider demand beyond the lead-time horizon (useful when long-dated sale orders should pull replenishment early). Use sparingly; it effectively inflates d_avg × LT.
• Trigger: Auto vs. Manual — Auto lets the scheduler create draft RFQs; Manual only flags suggestions in the Replenishment screen. Start A-class items on Auto, long-tail on Manual until you trust the parameters.
• Scheduler frequency — the stock scheduler runs nightly by default. High-velocity operations can run it more often (it is a scheduled action), but nightly is right for most.

A worked Odoo configuration for our adapter SKU:

Product:           ADAPT-65W
Reordering rule:   Min = 422, Max = 1,129, Multiple = 10
Supplier pricelist: Delivery lead time = 7 days
Route:             Buy
Trigger:           Auto
Result:            When forecasted stock dips below 422, Odoo drafts an
                   RFQ for ~710 units (rounded to multiple of 10),
                   scheduled so goods arrive before stock hits zero
                   in the average case, with 142 units of buffer
                   absorbing the bad cases.

For the broader warehouse-configuration context around these rules — locations, routes, putaway, cycle counting — see our Odoo inventory management best practices guide.

Common Mistakes (Field-Audit Edition)

These are the errors we actually find when auditing live Odoo databases:

1. Min = Max. The rule fires tiny top-up orders constantly — dozens of small POs, no cycle-stock economics at all. Max must exceed Min by approximately one EOQ.
2. Annual demand with monthly sigma. Mixed time bases produce buffers that are wildly wrong in either direction. Recompute sigma at the bucket size matching your lead-time unit.
3. Holding cost as a per-order or flat number. H is annual, per unit. Using unit cost itself as H (a surprisingly common spreadsheet slip) understates EOQ badly because it overstates holding cost by 3–7×.
4. Promised lead times in the pricelist. Supplier says 7, history says 11 with a sigma of 3. Everything downstream of that lie is fiction.
5. Security lead time AND statistical safety stock together. Double-counted buffer across the whole catalog — typically 10–20% excess inventory that nobody can explain.
6. One service level for everything. 99% on the C-class long tail is dead capital; 90% on your hero SKU is lost revenue. Segment first.
7. Set-and-forget parameters. Demand drifts, suppliers change, freight costs move. Recompute A-class quarterly, B-class semi-annually, C-class annually — and always after a supplier change.
8. Static rules on non-stationary demand. Strong seasonality, promotions, or new-product ramps violate the formulas' stable-demand assumption. For those SKUs, use forecast-driven replenishment (or at minimum, seasonal parameter sets) rather than a single year-round Min/Max.

Frequently Asked Questions

What is the difference between reorder point and minimum stock in Odoo?

They are the same number wearing different names. Odoo's reordering rule "Min Quantity" is where you encode your computed reorder point: average demand over lead time plus safety stock. When forecasted available stock falls below Min, Odoo proposes replenishment up to Max. The mistake to avoid is treating Min as "the lowest stock I would like to see" picked by gut feel — derive it from d_avg × LT + SS, or the rule will trigger systematically too early (excess stock) or too late (stockouts).

How do I calculate safety stock when both demand and lead time vary?

Use the combined formula: SS = z × sqrt(LT × sigma_d² + d_avg² × sigma_LT²), where sigma_d is the standard deviation of daily demand and sigma_LT is the standard deviation of lead time in days. The second term — your supplier's unreliability multiplied by your demand rate — frequently dominates the first. In our worked example, adding a 2-day lead-time sigma nearly tripled safety stock from 53 to 142 units, which is why measuring actual receipt history (not supplier promises) is the highest-value data fix in most replenishment projects.

What z-score should I use for a 95% or 99% service level?

Use 1.28 for 90%, 1.65 for 95%, 1.96 for 97.5%, 2.33 for 99%, and 3.09 for 99.9%. These are standard-normal values: a 95% cycle service level means you accept a stockout in roughly 1 in 20 replenishment cycles. Because z grows steeply in the tail, each service-level step costs disproportionately more inventory — moving from 95% to 99% adds about 41% more safety stock. Set service levels per ABC class rather than globally, reserving 98–99% for items where a stockout stops production or loses an irreplaceable sale.

Should Odoo's Max Quantity be the EOQ?

Not the EOQ itself — set Max ≈ Min + EOQ. Odoo replenishes the gap between forecasted stock and Max, so with Min at your reorder point of 422 and Max at 1,129, each triggered order is approximately one EOQ of 707 units (rounded to your pack multiple). If you set Max equal to EOQ alone and EOQ is below your reorder point, the rule produces undersized orders or behaves erratically. And never set Max equal to Min: that degenerates the policy into continuous micro-ordering with none of the EOQ cost savings.

How often should I recalculate EOQ, safety stock, and reorder points?

Quarterly for A-class SKUs, semi-annually for B-class, annually for C-class — and immediately after structural changes: a supplier switch, a freight-cost step change, a demand-pattern shift (new sales channel, lost key customer), or a measured change in lead-time behavior. The inputs decay at different speeds: demand statistics drift fastest, holding-cost rates slowest. Automating the recompute from your ERP's sales and PO-receipt history (then reviewing exceptions instead of editing every rule by hand) is the difference between a policy and a one-off project.

Do these formulas work for seasonal or slow-moving products?

With caveats. The formulas assume demand is reasonably stable and approximately normal. For seasonal items, compute separate parameter sets per season (or drive replenishment from a forecast instead of a static rule). For slow movers with intermittent, lumpy demand — many zero-demand days punctuated by spikes — the normal-distribution assumption breaks down and the z-score buffer becomes unreliable; consider Poisson-based models, a simple Min/Max set from order-cycle logic, or make-to-order. Our demand forecasting and ABC analysis guide covers choosing the right method per demand pattern.