Inventory Optimization Models and Simulations

1. 1Split every cost line into three buckets before touching a model: holding, transaction/ordering, and shortage (backorder or lost sale). Then tag each line variable or fixed. The tag matters because only costs that change with Q or with stock level belong in the order-quantity decision.
2. 2Build h, the yearly holding cost of one unit. Include only the variable items: cost of capital on the product, product insurance, obsolescence, damage, loss, theft, spoilage, and inventory counting. Drop the fixed items (employees, warehouse rent or cost of capital, security, lighting and heating, shelving, IT systems) because they do not move with Q. Express h as a percentage of unit cost and multiply by c to get h·c in currency per unit per year.
3. 3Compute yearly holding cost as (h·c)·Q/2. Q/2 is the average cycle stock, which depends on Q alone, not on demand or the number of transactions. Holding cost is therefore proportional to Q.
4. 4Build the transaction cost per order. Fixed part k: supplier admin fee, change-over/set-up time, and client working time on stock analysis, buying and negotiation. Variable part c_T per unit: transport, packaging, reception, inspection, unloading, storing. Check for step-fixed items, such as transport that stays fixed only up to a full truckload.
5. 5Compute yearly transaction cost as k·(D/Q) + c_T·D. The number of orders D/Q is inversely proportional to Q, and the c_T·D term does not change with Q. Plot holding cost rising with Q against fixed transaction cost falling with Q. The order quantity sits where the two pull against each other.
6. 6Price the shortage side separately. Decide whether unmet demand becomes a backorder (order kept, to be filled later) or a lost sale. Where a lost client is a risk, add goodwill g as an extra cost. This shortage cost, set against holding cost, is what drives the service level you target.
7. 7Run a sensitivity check on k and h before committing. Lowering fixed transaction costs lowers the optimal order quantity and so lowers inventory. Test whether cutting change-over time, which is often the largest transaction cost in production, beats optimizing Q around the current k.
8. 8Re-read the assumptions the cost structure rests on: constant demand, a fixed Q, and fixed holding costs excluded. State where they fail so you know when to switch to another model.

Real context from the source: US inventory costs were about $500 billion in 2018 (about 2% of GDP), spread roughly equally across financial costs, storage costs and other costs such as obsolescence, handling and insurance. Holding cost is therefore a multi-part number, not just the cost of capital. Illustrative calculation (the numbers below are invented to show the arithmetic from the source formulas). Take D = 1,200 units/year, c = €10, h = 20% so h·c = €2/unit·year, and k = €50 per order. At Q = 100: holding = 2×100/2 = €100; transactions = 50×(1,200/100) = €600; total €700 (excluding the constant c_T·D). At Q = 400: holding €400, transactions 50×3 = €150, total €550. At Q = 200: €200 + €300 = €500. At Q = 300: €300 + €200 = €500. The cheapest quantities lie between the extremes, because holding cost climbs with Q while transaction cost falls. If change-over improvements halve k to €25, transaction cost at Q = 200 falls to €150, so the same total (€350) is reached with a smaller Q. That is the lean point in the source: lower fixed transaction costs mean a lower optimal order quantity and less inventory.

• If a cost does not change with Q or with stock level (warehouse rent, staff, shelving), then exclude it from h and from the order-quantity decision.
• If fixed transaction cost k is large (long change-over, heavy admin), then expect larger optimal batches; before accepting them, try to cut k, since that lowers the optimal Q and the inventory.
• If a transaction cost is fixed only up to a threshold (e.g., one full truckload), then treat it as fixed only below that threshold and re-check the cost when Q crosses it.
• If unmet demand is lost and not backordered, or a lost client carries lasting cost, then add goodwill g to the shortage cost and aim for higher service rather than a purely holding-driven target.
• If a simple cost model is somewhat less accurate but trusted and used, then prefer it over a more accurate one nobody understands; the source puts the trade at 80% used against 95% ignored.

• Loading fixed warehouse costs into h. The tell: h looks very high and the model recommends tiny orders even though those costs would be paid anyway.
• Treating h as a cost per unit instead of a yearly rate, or forgetting to multiply by c. The tell: units are not €/(unit·year), and holding costs come out orders of magnitude off.
• Ignoring change-over time as a transaction cost in production. The tell: ordering costs look trivial on paper while the plant batches long runs to avoid set-ups.
• Treating shortage cost as zero or only counting the lost margin. The tell: the model recommends thin stock while clients complain, which is the source's trap of low service levels coexisting with dead stock; goodwill g and the backorder-versus-lost-sale distinction are missing.
• Holding the cost structure constant as Q or volume changes. The tell: a cost such as transport behaves as fixed up to a truckload and then jumps, so the 'optimal' Q lands just over a step and the real bill is higher.

• ▸Item and unit cost c: product and currency per unit.
• ▸Yearly demand D: units per year.
• ▸Variable holding items: list capital, insurance, obsolescence, damage, loss, theft, spoilage and counting costs with each yearly % of c.
• ▸Fixed holding items excluded: list warehouse and staff costs you are deliberately leaving out of h.
• ▸h (% of cost) and h·c: sum the variable items, then multiply by c to get currency per unit per year.
• ▸Fixed transaction cost k per order: supplier admin fee, change-over time cost, client working time.
• ▸Variable transaction cost c_T per unit: transport, packaging, reception, inspection, unloading, storing; note any truckload step threshold.
• ▸Shortage treatment: backorder or lost sale, plus goodwill g if a lost client carries extra cost.
• ▸Cost curves at candidate Q values: holding (h·c)·Q/2, transactions k·D/Q, and the sum, for each Q you test.
• ▸Sensitivity note: the Q that results if k is reduced (e.g., by cutting change-over time), and the action it implies.

1. 1Name the metric before you set a number. The source defines four: cycle service level α (the probability of no stockout during a replenishment cycle), period service level α_p (the probability of no stockout in a period), client service level (the probability a client gets the full order from stock, often called OTIF), and fill rate β (the fraction of long-term demand supplied directly from on-hand inventory, also called Type 2). Write the chosen metric next to every target.
2. 2Check which metric your data actually records. The source notes that most safety stock models use cycle service level while most companies record fill rate. Mark each product family as 'model uses X / ERP records Y' so you do not compare unlike quantities.
3. 3Read the targets against the long-term ordering fill rate β > client service level > period service level α_p > cycle service level α. This holds if a period is shorter than a cycle. A cycle service level target and a recorded fill rate are not the same number, so do not treat a gap between them as a miss.
4. 4Use cycle service level for the first safety stock calculation, as the source does for now, and defer fitting to a fill rate target to the fill rate model (Chapter 7). Record that the cycle service level is a stand-in.
5. 5Set safety stock from each product's own demand variability and supply reliability. Reject blanket rules like 'x weeks of average demand'. Safety stock must protect against demand variation during the average lead time, and against the lead-time effects the source lists.
6. 6Compute demand variation at the same time aggregation as the lead time and review period (weekly replenishment means weekly forecast and weekly accuracy). If you cannot forecast at that level, measure accuracy per week from a flat split of the monthly forecast. Do not scale a monthly deviation to daily by dividing by 22, or the reverse.
7. 7Include the review period in the safety stock computation, not only the lead time. The source flags omitting it as a common practitioner error.
8. 8Treat the target itself as a decision, not an input. The source warns targets are often arbitrary numbers, and Chapter 8 sets the optimal level by minimizing cost. Until then, label the target 'provisional' and track a second KPI such as average backlog per period divided by average period demand, which approximates fill rate more conservatively, or the average time an order stays in backlog.

The source's own situation: management hands the planner a service level target, and the planner translates it into 'we take x weeks of average demand as safety stock.' Run it properly. Step 1: ask which metric the target is. If it is a cycle service level, it is the probability of no stockout in a replenishment cycle. Step 2: note that the ERP records fill rate, which is the fraction of demand served from stock. Because β > client service level > α_p > α over the long term, a recorded fill rate above the cycle target does not mean the policy is over-protected. The two measure different things. Step 3: replace 'x weeks' with a calculation from the product's demand variation over lead time plus review period. Compute that variation in the same buckets as replenishment: if the chain reviews weekly, use weekly forecast error, not a monthly deviation divided by 22. Step 4: because positive auto-correlation (a sunny Saturday followed by a sunny Sunday) makes the model undershoot required safety stock, watch realized service for undershoot. Step 5: track average backlog per period divided by average period demand as a conservative fill-rate proxy. The result is one stated metric, one target, and one cross-check, instead of a single unexplained percentage.

• If management gives a bare percentage, then ask which of cycle service level, period service level, client service level (OTIF) or fill rate it is before any calculation.
• If the reported KPI is fill rate and the model uses cycle service level, then do not compare them directly. Expect fill rate β to sit above cycle service level α, and move to the fill rate model (Chapter 7) to fit a fill rate target.
• If a safety stock rule is expressed in weeks of average demand, then replace it with a variability-based calculation per product, since demand volatility and supply reliability differ.
• If demand deviation exists only at monthly level but the supply chain replenishes weekly or daily, then re-measure forecast accuracy at the replenishment bucket, or use a flat split of the monthly forecast per week, rather than scaling by 22.
• If the target was set without a cost rationale, then treat it as provisional and set the optimal level by minimizing cost (Chapter 8).

• Mixing metrics: a cycle service level target is judged against a recorded fill rate. Tell: the two numbers never reconcile and nobody can say which is 'right'.
• Rule-of-thumb safety stock ('x weeks of demand') applied across all products. Tell: volatile products stock out while stable ones carry excess, and the supply chain shows both low service levels and dead stock.
• Omitting the review period from the safety stock calculation and looking only at lead time. Tell: stockouts cluster in policies with long review periods despite 'adequate' safety stock.
• Scaling demand deviation between time buckets (monthly to daily by dividing by 22, or daily to monthly by multiplying). Tell: realized service falls short of target, especially when high-demand periods cluster (positive auto-correlation).
• Chasing a high target without cost logic, or hiding process fluctuation with too much inventory. Tell: the target is a round arbitrary number and inventory is high enough that process owners no longer see variability or feel pressure to improve.

• ▸Product / family: the item or group this target covers.
• ▸Metric named: cycle service level, period service level, client service level (OTIF), or fill rate.
• ▸Target value and who set it: the number, the owner, and whether it is provisional or cost-optimized.
• ▸Metric the ERP actually records: so you can spot a model-versus-recorded mismatch.
• ▸Replenishment bucket: lead time and review period, in the same time units.
• ▸Demand variation measured at that bucket: yes/no, and the method (native forecast or flat split of monthly).
• ▸Safety stock basis: variability-based calculation including review period, or a rule of thumb to be replaced.
• ▸Cross-check KPI: average backlog per period divided by average period demand, or average backlog duration.
• ▸Next action: move to the fill rate model (Chapter 7) or the cost-optimal level (Chapter 8), and by when.

1. 1Separate the two outcomes before measuring anything. A stockout ends in a backorder (the client waits and is frustrated) or a lost sale (the client goes to the competition). The source states you often cannot tell which happened in the short term, so record every unmet unit as 'short' first and classify it later.
2. 2Fix the policy you are measuring, because units short are a property of the policy and its parameters. Write it in the book's notation: (s, Q) continuous review, (R, S) periodic order-up-to, or (R, s, Q) periodic with a reorder point. Note the review period R, reorder point s, order quantity Q or up-to level S, and the replenishment lead time.
3. 3Locate the exposure window. The risk sits between the moment stock hits the reorder threshold and the moment the order arrives. In a periodic policy the review period adds blind time, because you may be 'blocked from making an order when you need it'. The (R, s, Q) policy is riskier still, since it only orders if stock reaches the threshold. List these windows per item.
4. 4Log demand that arrives when on-hand is zero or insufficient as units short, per order cycle. Take the average across cycles as your expected units short. Keep demand, on-hand and orders in the same time buckets so cycles compare cleanly.
5. 5Where the policy is too complex to solve analytically, such as (R, s, Q), (R, s, S) or multi-sourcing with an emergency lane, estimate expected units short by simulation (the source's Chapter 13 approach). Do not force a tractable formula onto a policy it does not fit.
6. 6Price the shortage with explicit, bounded assumptions. The source says backorder and lost-sale costs are hard or impossible to evaluate. Short term, you do not know if the client leaves, and the client may buy a substitute, possibly a more expensive one. Long term, brand damage and word of mouth matter. Pick a penalty range, not a point value, and test how the optimal policy moves across that range.
7. 7Compare policies on expected units short against inventory held. A policy with a review period or an extra order condition needs more safety stock to hold the same shortage level. Quantify that extra stock as the price of the convenience.
8. 8Re-check after each change to lead time, review period or demand variability. These are the drivers of shortage, and the source notes that variability is rising and lead times are lengthening.

Take the source's fixed reorder point policy: 'Order 10 when less than 3 left' (s = 3, Q = 10). A client-visible cycle runs like this. Stock drops to 2, so you order 10 (you still order only 10, not more, because the quantity is fixed). While the order is in transit, suppose 5 more units are demanded. This is an illustrative number, not from the source. Only 2 can be served, so 3 units are short. If the clients wait, those 3 are backorders. If they leave, they are lost sales. The source stresses you cannot know which in the short term, so log '3 short' for this cycle. Repeat this across many cycles and average the result to get expected units short for (s = 3, Q = 10). If you moved to the periodic (R, s, Q) variant, 'every 4 days, order 10 only if stock reaches 5', the exposure window lengthens by the review gap, and the source says extra safety stock must compensate for it.

• If you cannot tell whether unmet demand was waited out or lost, then log it as 'units short' and classify later rather than assuming backorder.
• If the policy has a review period or a conditional order (R, s, Q), then expect higher units short at equal stock, and either add safety stock or accept the shortage.
• If the policy is too complex for a tractable model ((R, s, Q), (R, s, S), multi-sourcing), then estimate units short by simulation.
• If the shortage cost is uncertain, then test the policy across a range of penalty values and choose the setting that holds up across the range.
• If lead time or demand variability changes, then recompute expected units short before trusting the old reorder point.

• Treating every shortage as a backorder. The tell: the sales-recovery rate is assumed, never measured, and sales slip with no visible cause.
• Using a single precise shortage cost. The source says costs are hard to evaluate, and some firms do not even know profit per product. The tell: a point-value penalty with no source or range.
• Ignoring review-period blind time. The tell: shortages cluster just before scheduled review or order days.
• Ignoring substitution. A client may buy a similar item, even a more expensive one. The tell: a stockout is costed as a full loss with no check on what else sold.
• Applying a policy's convenience without its safety-stock cost. The tell: a periodic or conditional order rule is adopted at the same stock level as the continuous review it replaced, and shortages rise.

• ▸Item / SKU: identify the product being tracked.
• ▸Policy and parameters: record the type (s,Q), (R,S) or (R,s,Q) with its values of R, s, Q or S.
• ▸Lead time (and review period R): note the exposure window length in days.
• ▸Cycle start and end dates: bound each order cycle so cycles are comparable.
• ▸Demand during cycle vs. on-hand available: record both so shortage is visible.
• ▸Units short this cycle: unmet units, logged before any classification.
• ▸Outcome classification: backordered, lost or substituted. Mark 'unknown' when you cannot tell.
• ▸Average units short across cycles: the running estimate of expected units short.
• ▸Assumed penalty range (low / high) and its rationale: the explicit, testable cost assumption.

1. 1Split inventory into the three components the source uses before you measure anything. On-hand is physical stock clients can buy, and it divides into safety stock and cycle stock. In-transit is stock en route from a supplier to the warehouse. Keep on-hand and in-transit in separate columns, because only on-hand drives warehouse holding costs.
2. 2Compute the theoretical expected levels per policy. For (s, Q), cycle stock = ½·Q and in-transit = d·L. For (R, S), cycle stock = ½·d·R and in-transit = d·L. With safety stock, expected on-hand = cycle + safety. Do not use the order-up-to level as the expected inventory.
3. 3Set the reorder point and up-to level from lead-time demand. Use s = d·L and S = d·L + d·R, plus safety stock in the stochastic case. If you have a forecast or a visible trend, substitute it for history: s = F_L and S = F_L + F_R. Here F_L is the forecast over the lead time and F_R the forecast over the review period.
4. 4Bound the physical level. On-hand fluctuates between the safety stock floor and safety plus cycle stock. If your measured average sits outside that band, the policy parameters or the measurement are wrong.
5. 5If you simulate, track two variables. hand[t] is the end-of-period level and goes negative with backorders. p[t] is the physical inventory and stays ≥ 0. Use p[t], not hand[t], to price holding costs.
6. 6Do not average the physical level with max(hand[t],0) alone. hand[t] is the period's lowest point, taken after demand is consumed and before the replenishment arrives, so this method undershoots. Improve on it by averaging each period's highest level (reached at the beginning of the period) and its lowest level.
7. 7Run the inventory analysis questions on the result. Do we hold the right amount? What is the expected level? How does it split between safety, cycle and in-transit stock? How much of the total does safety stock account for?
8. 8Check what else sits in the warehouse. On-hold stock (booked by clients but not yet shipped), anticipation stock (built ahead of a busy season) and merchandising stock (shelf-filling goods) are real inventory outside the model. Report them separately so they do not distort the comparison.

The numbers below are assumed for illustration; only the formulas come from the source. Take d = 10 units/day and L = 5 days. Under (s, Q) with Q = 100, s = d·L = 50, cycle stock = ½·Q = 50 and in-transit = d·L = 50. Under (R, S) with R = 10 days, S = d·L + d·R = 50 + 100 = 150, cycle stock = ½·d·R = 50 and in-transit = 50. A planner who reads 'target stock 150' as the expected inventory expects 150 units on-hand. The model says expected on-hand is only about 50, plus safety stock. This is the source's 'confusion curse': the gap between the up-to level and the expected physical inventory widens as lead time grows, and it worsens when orders are placed while others are still waiting to be received. Reading the target as the expected level overstates stock and cash tied up. The source's real-world anchor is the U.S. Census Bureau figure of roughly 1.4 months of sales held by manufacturers, wholesalers and retailers. Use that as a sanity check on your own inventory-to-sales ratio.

• If the policy uses an order-up-to level, then never quote S as the average inventory. Quote ½·d·R + safety stock for on-hand, and d·L separately for in-transit.
• If lead time is long or orders overlap in transit, then expect a larger gap between the up-to level and physical stock, and report in-transit stock explicitly.
• If the inventory is being costed in a simulation, then measure the average physical level p[t] ≥ 0 per period. Avoid max(hand[t],0) alone, because it undershoots.
• If a trend or external insight is known, then set s and S from forecasts F_L and F_R, not from historical averages.
• If service is poor and dead stock exists at the same time, then treat it as a policy and parameter problem, not a quantity problem. Add or cut stock only after checking the safety/cycle/in-transit split.

• Treating the up-to level ('target stock') as expected on-hand. The tell: modeled holding costs far above what the warehouse actually carries, with the discrepancy growing as lead time lengthens.
• Using hand[t] as physical inventory. The tell: negative values during backorders, or a holding-cost estimate that is too low because hand[t] is the period's lowest point.
• Ignoring in-transit stock. The tell: the cash tied up in supply chain inventory exceeds what the warehouse count shows, by roughly d·L.
• Leaving on-hold, anticipation and merchandising stock out of the analysis. The tell: physical counts exceed the model's safety + cycle estimate with no explanation.
• Holding excess safety stock as protection against every fluctuation. The tell: no visible process variation, so process owners have no incentive to improve, yet dead stock keeps accumulating.

• ▸Policy type: write (s, Q) or (R, S).
• ▸Demand per period (d) and lead time (L): enter forecast values F_L and F_R if a trend is known.
• ▸Order quantity Q or review period R: enter whichever your policy uses.
• ▸Reorder point s or up-to level S: s = d·L, S = d·L + d·R, before safety stock.
• ▸Expected cycle stock: ½·Q for (s, Q), or ½·d·R for (R, S).
• ▸Safety stock: the stock held to guarantee the service level against demand or lead time fluctuation.
• ▸Expected on-hand: cycle stock + safety stock. Do not substitute S.
• ▸Expected in-transit: d·L, kept separate from on-hand.
• ▸Other stock outside the model: on-hold, anticipation and merchandising units, each listed separately.
• ▸Measured average physical level (p[t] ≥ 0) versus the expected on-hand above, with the gap noted.

1. 1Define the cost boundary first. Total supply chain cost here is holding + transaction + backorder/lost-sale cost. The closed-form model in the source (C(Q) = hQ/2 + kD/Q + cT·D) covers only holding and transaction. Backorders are treated separately, in Section 2.5.2 for deterministic models and in Chapters 8 and 11 for stochastic ones.
2. 2Split holding costs into variable and fixed. Variable: cost of capital on product, product insurance, obsolescence, damage, loss, theft, spoilage, inventory counting. Fixed: employees, warehouse insurance, rent or capital, security, lighting and heating, shelving and IT. Keep only the variable part in h, because fixed holding costs are incurred whatever Q is.
3. 3Express h as a cost per unit per year. If you have it as a percentage, multiply by unit cost c, so holding cost = (h·c)·Q/2. Q/2 is the average cycle stock.
4. 4Split transaction costs into variable (cT per unit: transport, packaging, reception, inspection, unloading, storing) and fixed (k per order: supplier admin fee, set-up or change-over time, your analysis, buying and negotiation time). Put the per-order costs in k.
5. 5Compute yearly transaction cost as k·(D/Q) + cT·D. Then drop cT·D from the optimization, because it depends only on total demand D, not on Q. The decision function is C(Q) = hQ/2 + kD/Q.
6. 6Find Q* where holding cost equals transaction cost (hQ/2 = kD/Q). Holding cost rises with Q and fixed transaction cost falls with Q, so the minimum sits where the two curves cross.
7. 7Report the full total by adding cT·D back to C(Q*) so the figure reconciles to the ledger. Then price the service side: record backorders and lost sales as a separate line and do not fold them into h or k, since they are hard to value.
8. 8Test the levers. Reducing fixed transaction costs (k) lowers the optimal order quantity and therefore inventory. Re-run C(Q) after each change in k, h or D.

The source gives no numeric case, so these inputs are illustrative assumptions. Take D = 1,000 units/year, k = 50 per order, h = 2 per unit-year, cT = 1 per unit. Setting hQ/2 = kD/Q gives Q* = √(2kD/h) = √50,000 ≈ 223.6 units. Holding cost = 2 × 223.6/2 ≈ 223.6 and transaction cost = 50 × 1,000/223.6 ≈ 223.6, so C(Q*) ≈ 447.2, and the two equal each other as the source predicts. Add cT·D = 1,000 and the reported total is ≈ 1,447.2. Ordering 500 at a time costs 500 + 100 = 600 against 447.2, and ordering 100 at a time costs 100 + 500 = 600. Cutting k from 50 to 25 gives Q* ≈ 158.1 and C ≈ 316.2: smaller batches and less stock, as the source says about lean practice. None of these figures includes backorder cost, which sits outside this model.

• If a cost does not change with Q (fixed holding costs, cT·D), then exclude it from the choice of Q* and add it back only when reporting the total.
• If the holding and transaction cost curves at your chosen Q are far apart, then you are off the optimum: the larger one tells you which direction to move Q.
• If you can cut the fixed cost per order (set-up, admin, buying time), then expect a smaller Q* and less inventory, and re-optimize rather than keeping the old batch size.
• If stock-outs are possible, then do not claim minimum total cost from holding plus transaction alone: add a backorder or lost-sale cost, or enforce a service target instead.
• If you cannot estimate the profit per unit or the lost-sale cost, then do not invent a precise figure: set a service-level target and optimize cost subject to it.

• Including fixed warehouse costs (rent, staff, heating) in h. The tell: h looks far too high and Q* collapses toward tiny orders.
• Putting per-unit transport in k, or per-order fees in cT. The tell: Q* does not respond to a change in order frequency, or responds to the wrong driver.
• Reporting hQ/2 + kD/Q as 'total supply chain cost' without cT·D and without any backorder cost. The tell: the figure does not reconcile to actual spend and ignores out-of-stocks.
• Valuing backorders at an exact figure that ignores substitution, customers who return later, or long-term reputation damage. The tell: a single precise backorder cost nobody can defend, or the unit profit is unknown or possibly negative.
• Treating a minimum-cost Q as fixed. The tell: Q is not revisited after k, h or D changes, or it is imposed by a periodic MRP/DRP schedule rather than the cost model.

• ▸Yearly demand D (units/year): enter forecast or historical annual demand.
• ▸Unit cost c: enter product or production cost per unit.
• ▸Holding rate h (per unit-year, or % of c): include variable items only (capital, insurance, obsolescence, damage, theft, spoilage, counting).
• ▸Fixed cost per order k: sum admin fee, set-up time, buying and negotiation time, stock analysis.
• ▸Variable transaction cost per unit cT: transport, packaging, reception, inspection, unloading, storing.
• ▸Optimal Q* (where hQ/2 = kD/Q): calculate it, then enter holding cost and transaction cost at Q* to confirm they match.
• ▸Current Q: enter the order quantity in use today, then calculate C(Q) = hQ/2 + kD/Q.
• ▸Total modeled cost: C(Q*) + cT·D; compare it with the cost at current Q.
• ▸Backorder / lost-sale notes: record observed stock-outs and the assumptions behind any cost you assign, kept separate from the totals above.

1. 1Write profit as one line before modeling anything: sales revenue minus purchasing, holding, transaction and backorder costs. Every later choice (policy, safety stock, service level) is judged against this line, not against service level or inventory days alone.
2. 2Price the holding side. Split inventory carrying cost into the three roughly equal blocks the passages cite: financial cost, storage cost, and other costs (obsolescence, handling, insurance). Put a number on each block, because 'sleeping cash that is depreciating' is not usable until it is a rate.
3. 3Price the overage side per unit. If leftovers cannot be sold in a later period, overage cost c_o = purchase cost c − salvage value s_v. If they can be sold later, c_o = holding cost h. If you must pay to dispose of them (hazardous goods), add the salvage cost on top of the purchase cost.
4. 4Price the underage side per unit. A lost sale forfeits the profit p − c. Treat it as an opportunity cost, not a cash expense, but include it as an underage cost so the cost-minimizing model also maximizes profit.
5. 5Measure true demand before you price shortages. Sales understate demand whenever you are out of stock, so record inventory over time to flag stock-outs. In those periods substitute the forecast for sales (unconstraining the demand) to break the lost-sales spiral-down.
6. 6Choose the policy with its blind spots in mind. In a periodic review (R, S) policy you cannot order between reviews. An Monday-evening stock-out with a Friday order cycle means four days of possible lost sales, and each lost sale forfeits p − c. Price that exposure before choosing a review period.
7. 7Optimize on total cost with opportunity costs included, then check against the profit line. Do this with the newsvendor model (Chapter 11) or by simulation optimization (Chapter 13) when no closed form exists.
8. 8Choose the model you will actually use. An 80% accurate model that is trusted and always used beats a 95% accurate one nobody understands. Start simple and refine as you learn.

The source's muffin case shows how the cost components combine. A muffin sells for 2€, and any leftover sells for 1€. Because the leftover brings in salvage revenue, the overage cost is reduced to 1€, per the passage. This follows c_o = c − s_v, because leftovers cannot be sold in a later period. Now the other side: if you run out, you lose the sale and forfeit the profit p − c, which is 2€ minus the purchase cost (the purchase cost is not given in the excerpt). That forfeited profit is the underage cost, an opportunity cost rather than cash out of pocket. Change one assumption to see the sensitivity. If the leftovers had to be disposed of at a fee, as with hazardous goods, that fee would be added to the purchase cost and the overage cost would rise. Ordering one extra unit gets more expensive on the overage side and the right order quantity falls. The decision is never 'avoid stock-outs' or 'avoid leftovers' in the abstract. It is a comparison of the two per-unit costs, with profit hidden inside the underage cost.

• If leftovers can be sold in a later period, then use holding cost h as the overage cost. If they cannot, then use c − s_v, and add disposal fees on top of purchase cost when you must pay to dispose.
• If a lost sale cannot be observed (grocery-style B2C where shoppers just buy another snack), then do not use sales as demand. Substitute the forecast for out-of-stock periods and log inventory to flag them.
• If you run a periodic review policy and a stock-out can strand you until the next review, then count the lost sales (p − c each) as a real cost of the review period, not only the lead time.
• If a more complex model would cut costs but users will not trust or understand it, then ship the simpler model. A used 80% model beats an unused 95% one.
• If holding costs look high, then split them into financial, storage and other (obsolescence, handling, insurance) before cutting stock. Cutting inventory without raising service level risks both low service and dead stock.

• Treating lost profit as 'not a real cost' and leaving it out of underage cost. The tell: the model recommends ordering far less than the business wants, and stock-outs are never reflected in the financial analysis.
• Using sales as a proxy for demand. The tell: forecasts and stocking levels drift down over time while out-of-stocks persist, the spiral-down effect.
• Minimizing inventory to cut holding cost. The tell: both low service levels and dead stock appear together, because holding costs fall on paper while lost sales and obsolescence rise.
• Ignoring salvage or disposal in overage cost. The tell: leftover costs in the model do not match the accounting (e.g., salvage revenue of 1€ per muffin not netted out, or disposal fees missing).
• Over-building the model. The tell: an accurate model that planners override or ignore, so no savings reach profit.

• ▸Selling price p: the unit price you charge.
• ▸Purchase cost c: the unit cost you pay your supplier.
• ▸Unit profit (p − c): this is the opportunity cost inside underage cost c_u.
• ▸Can leftovers be sold in a later period? (Yes/No): decides whether c_o = h or c_o = c − s_v.
• ▸Holding cost h: split into financial, storage and other (obsolescence, handling, insurance).
• ▸Salvage value s_v or disposal cost: enter salvage revenue as positive, disposal fees as a cost added to c.
• ▸Overage cost c_o: computed from the two fields above.
• ▸Underage cost c_u: includes unit profit, plus any other shortage costs you can name.
• ▸Out-of-stock flag method: how you record inventory over time and which forecast replaces sales in stock-out periods.

1. 1Draw the network as nodes and edges. Each node is a possible stocking point. Each edge is a customer-supplier relationship between two nodes. Do not start from the org chart or the warehouse list. Start from who supplies whom.
2. 2Classify every node as internal or external. Internal means you have visibility and control, even without full ownership. Stock under vendor managed inventory (VMI) counts as internal if you can see and steer it. External nodes are the ones you cannot steer, so treat them as given inputs.
3. 3Label the echelons (tiers or stages). The echelon touching the external supplier is the supply echelon. The echelon facing customer demand is the demand echelon. One echelon means a single-echelon problem. More than one means a multi-echelon problem.
4. 4Count upstream and downstream links per node and name the topology. Multiple suppliers feeding one node is an assembly structure. One upstream node with several downstream nodes is a distribution structure, for example one central warehouse serving several shops. A node with multiple upstream and downstream links is a general network. If it has return flows or cycles it is cyclic; otherwise it is acyclic. A plain chain with no branching is the serial case that the chapter treats first with the guaranteed-service model (GSM).
5. 5Record who sets policy at each node today. For every node, note whether it picks its own safety stock, order quantity and review period, and whether it can change them without telling the others. If so, you are in a locally optimized network.
6. 6Test for local-optimization damage. Check whether small changes in external demand cause outsized swings upstream (the bullwhip risk). Check whether any node hoards or grabs profitable stock at the expense of the whole chain. Either symptom argues for a global (multi-echelon, MEIO) optimization.
7. 7Before centralizing stock, quantify the pooling effect. Combine two nodes' demand with σ(X+Y) = √(σX² + σY² + 2ρσXσY). Then size safety stock with S_s = z_α · σ_d · √τ. Pooling only reduces demand variability.
8. 8Net the pooling gain against what the passages warn about. Adding a central warehouse raises handling costs and may lengthen total lead times. It does nothing for supply variability, which Chapter 6 treats separately. Then choose the structure, and apply serial or distribution GSM where the topology fits.

The chapter's locally optimized network (Figure 10.4) has three nodes: a production facility, a regional hub and a distribution center. Each node picks its own safety stock, order quantity and review period, and can change them without telling the others. The passages warn that this siloed set-up lets the slightest change in external demand drastically hit the chain, and that nodes may chase profitable stock to the detriment of the whole. Classify it first. It is a three-echelon chain with no branching, so it fits the serial case, with the production facility as the supply echelon and the distribution center as the demand echelon. The fix is a global optimization (MEIO) with aligned policies, not three independent ones. Now take a distributor with one central warehouse and several shops, which is a distribution topology. Pooling two shops of equal demand deviation σ gives σ√(2+2ρ). At ρ = 0 that is about 1.41σ, not 2σ, so safety stock grows far less than the sum of the two. At ρ = 1 it is exactly 2σ and pooling gains nothing. In both cases, supply-side variability stays untouched. Handling costs rise and total lead time may lengthen.

• If each node chooses its own policy without alignment, then treat the network as locally optimized and expect bullwhip-type amplification. Move toward global multi-echelon optimization.
• If a node has several suppliers and one output, then classify it as assembly. If a node has one upstream node and several downstream nodes, then classify it as distribution. If a node has several of both, then it is a general network, and you check for cycles (return flows).
• If you have visibility and control over a stocking point, as under VMI, then model it as internal even if you do not own it.
• If you are considering pooling or centralizing stock, then estimate the combined deviation with the correlation formula. If ρ is near 1, expect little gain.
• If the problem you want to solve is supply variability or long lead times, then do not rely on centralization. It addresses demand variability only and may lengthen total lead time.

• Defining internal nodes strictly by ownership. The tell is that VMI stock sits outside your model even though you can see and steer it.
• Misclassifying the topology, for example calling a network distribution when a node actually has several suppliers. The tell is that the chosen model cannot represent a node with multiple upstream links.
• Letting each echelon run its own rule-of-thumb policy and calling it optimized. The tell is upstream orders swinging more than end demand, or nodes quietly securing stock for themselves.
• Assuming centralization always cuts total stock. The tell is a pooling claim made without the correlation term, or a business case that ignores added handling cost and longer lead time.
• Expecting a central warehouse to absorb supplier unreliability. The tell is that safety stock was cut on a demand-variability argument while lead-time variability stays high.

• ▸Nodes list: name each possible stocking point and mark it internal or external (include VMI points you can see and control).
• ▸Edges list: record each customer-supplier link as upstream node → downstream node.
• ▸Echelon map: assign each node to an echelon and mark the supply echelon and the demand echelon.
• ▸Links per node: record the number of upstream and downstream links for every node.
• ▸Topology class: serial, assembly, distribution, or general (if general, cyclic or acyclic).
• ▸Policy ownership: for each node, who sets safety stock, order quantity and review period, and can they change it without notice (yes/no)?
• ▸Local vs. global verdict: locally optimized or globally aligned, with the bullwhip or rogue-stocking symptoms observed.
• ▸Pooling check: σ of each node pooled, correlation ρ between them, and resulting σ(X+Y) from the formula.
• ▸Centralization trade-off: expected change in handling cost and total lead time, and confirmation that supply variability is out of scope.

1. 1Fix the policy before you size Q. Only (s, Q) (continuous review) and (R, s, Q) (periodic review with a reorder point) hold the order quantity constant. In (R, S) the quantity is whatever brings net inventory up to S, so there is no fixed Q to optimize.
2. 2Check whether orders can be placed at any time. The (s, Q) policy assumes this. If the supplier accepts orders or ships only once a month, it follows its own calendar, so use a periodic policy and treat Q as a by-product of the review schedule.
3. 3List the hard constraints on Q: a full pallet, a truckload, packaging you do not want to break open. Passage 1 states that a fixed Q lets you capture a rebate on every order, and that you can optimize Q against such constraints or costs.
4. 4Name the two forces Q balances: transaction cost per order against holding cost and cycle stock. A larger Q means fewer orders and more stock on hand. A smaller Q means more orders and less stock. Write both costs down for the item. The book develops this trade-off in Chapter 2 (supply chain costs, model optimization, EOQ, sensitivity analysis, extensions).
5. 5Set Q together with the reorder point s as the pair (s, Q). Q is always the same, but the time between orders varies with demand. Do not shrink Q when stock falls below s. With 2 pieces left and s = 3, you still order exactly Q.
6. 6Run a sensitivity check on Q. The book places sensitivity analysis directly after optimization, so test whether nearby values (a round pallet count, a supplier multiple) change the result much. Choose the practical value when the change is small.
7. 7Test the chosen (s, Q) in a simulation before committing. The book recommends simulation to assess the accuracy of a model, and notes that models are abstractions that cannot capture all possible actions to balance supply and demand.
8. 8Revisit Q whenever the constraints change: a new rebate threshold, a different supplier calendar, or an MRP/DRP system that forces a periodic schedule.

The book's own policy is "Order 10 when less than 3 left": s = 3, Q = 10. The stock falls to 2 pieces, below the reorder point of 3. You still order exactly 10, not 11 or 8, because with a reorder point the quantity is always fixed. The time between orders varies as demand varies. The same logic applies at home: with 2 bottles of milk left, you buy 6. Now compare the periodic alternative, "Order up to 13 every 5 days" (R = 5, S = 13). Illustratively, with 2 units on hand at review you order 13 − 2 = 11 units, and with 5 on hand you order 8. The schedule is fixed and the quantity moves every time. A third option, "Order 10 pieces every 4 days only if inventory level reaches 5 pieces," keeps both a fixed schedule and a fixed Q of 10. It suits a supplier who ships on a calendar and a product that is palletized or rebated by the full unit load.

• If the supplier offers a rebate for a full pallet or truckload, then use a fixed-Q policy and set Q at the rebate quantity (or a multiple of it), because every order then earns the reduction.
• If the supplier only takes orders or ships on a set calendar, then do not use a pure (s, Q) policy. Use periodic review with a reorder point and fixed Q, or (R, S), and size Q within that schedule.
• If the product is palletized and breaking packaging is costly, then prefer a fixed Q over an order-up-to quantity that can ask for a single unit.
• If the item is expensive or important and needs close monitoring, then use continuous review with fixed Q, since the risk of stock-out is lower than with periodic review.
• If many items come from one supplier and you want one consolidated order, then accept a periodic policy and a variable quantity instead of forcing a fixed Q per item.

• Treating Q as variable inside (s, Q), for example topping up to a target when stock is at 2. The tell: order sizes differ from order to order, which means you are running (R, S) under another name.
• Assuming continuous review when the supplier works on a monthly calendar. The tell: the reorder point triggers an order the supplier cannot act on until its next window.
• Picking Q from a rebate alone and ignoring holding cost and cycle stock. The tell: stock keeps building between orders and the rebate savings disappear into inventory cost.
• Trusting the model's Q without simulation. The tell: real service or cost results diverge from what the model predicted, because the model assumes customers buy one unit at a time, so the reorder point is hit exactly.
• Letting MRP/DRP settings silently impose a periodic schedule on an item meant to be (s, Q). The tell: orders appear on a daily or weekly cadence regardless of stock reaching s.

• ▸Item and supplier: name the item and the single supplier it comes from.
• ▸Policy in use: (s, Q), (R, S) or (R, s, Q), and whether the supplier accepts orders at any time.
• ▸Supplier calendar: order or shipment windows that force a review period R.
• ▸Unit-load constraints: pallet size, truckload size, minimum multiples, packaging you cannot break.
• ▸Rebate threshold: quantity at which a price reduction applies, if any.
• ▸Transaction cost per order: the cost you pay each time you place or launch an order.
• ▸Holding cost per unit per period: the cost of carrying stock, which drives cycle stock.
• ▸Candidate Q values: the 2–3 realistic quantities (for example the rebate quantity and its neighbors).
• ▸Simulation result per Q: cost and stock-out outcome for each candidate; choose the Q with the best result.

1. 1Write the policy in its (R, S) form before anything else: a fixed interval between orders and an order up-to level S. The review period is the interval. Figure 1.2 states it as 'Order up to 13 every 5 days', so the review period is 5 days and S is 13.
2. 2Find the review period your supply chain already has instead of choosing one. Check three sources: the supplier's order calendar (for example, orders accepted only once a month), the MRP/DRP schedule (often daily or weekly, which makes a periodic policy implicit), and any grouping rule such as one order per supplier or a full-pallet or truckload rebate.
3. 3Record the order day against the delivery day. The source's example is an order on Friday evening, preparation on Monday morning and delivery on Tuesday. That timing gives you the lead time that sits alongside the review period.
4. 4Map the blind spot. Between two reviews you cannot order. In the Friday example, a stock-out on Monday evening means four more days before the next order can be placed. Write down, for each product, the longest stretch during which you cannot react.
5. 5Size safety stock to cover both the review period and the lead time. The source flags the common error as including only the lead time, and Chapter 5 shows how to include the review period. Use the book's method there and do not reuse a lead-time-only safety stock.
6. 6Set the order quantity at each review as S minus the net inventory at that moment. The quantity changes every time while the schedule stays fixed. If you see a constant order quantity, you are running (s, Q), not (R, S).
7. 7Check how the review period interacts with long lead times. The source warns that as lead times lengthen, the gap between the order up-to level and the expected average inventory widens. Re-examine S whenever the review period or the lead time changes.
8. 8Test the chosen review period in a simulation (Chapter 5.3) and against your fill-rate target (Chapter 7.4 covers the impact of order cycle length) before you commit to it.

Take the source's Figure 1.2 policy: 'Order up to 13 every 5 days' with immediate replenishment. The review period is 5 days and S = 13. At one review you count 4 units of net inventory, so you order 9. At the next you count 2, so you order 11. The schedule never moves while the quantity always does. Now use the source's supplier calendar: you order every Friday evening, the supplier prepares the order Monday morning and delivers Tuesday. Suppose you run out of stock on Monday evening. You cannot place an order until the next Friday, four days later, and only after that does the delivery cycle begin. Safety stock must cover that exposure window, so a safety stock computed from lead time alone leaves you short. The review period belongs in the calculation, which is the omission the source says practitioners most often make.

• If the supplier only accepts orders or ships on its own calendar (for example once a month), then treat that calendar as your review period and do not model a continuous reorder point.
• If an MRP/DRP drives ordering on a daily or weekly cycle, then treat the policy as periodic with that cycle as the review period, and compute safety stock on that basis.
• If you need to group many items into one order with a supplier, or you want a pallet or truckload rebate every time, then use a fixed review period with an order up-to level.
• If your safety stock formula uses only lead time, then add the review period before trusting the target.
• If lead times are long, then expect S to sit well above expected average inventory, and re-check S whenever the review period changes.

• Safety stock sized on lead time alone. The tell: stock-outs cluster in the days right after a review, when no order could be placed.
• Mixing up (R, S) and (s, Q). The tell: someone expects a fixed order quantity from a fixed schedule, but quantities vary because they depend on stock at review time.
• Assuming you can order at any time when the supplier works to a calendar. The tell: planned reorder points that fall on days the supplier does not accept orders.
• Ignoring the review cycle forced by MRP/DRP. The tell: the system runs daily or weekly while the safety stock model assumes continuous review.
• Ignoring the effect of long lead times on the up-to level. The tell: a large gap between S and average inventory that no one can explain.

• ▸Product/supplier: name the item and the supplier it is ordered from.
• ▸Review period (days): the fixed interval between orders, taken from the supplier calendar or the MRP/DRP schedule.
• ▸Order day and delivery day: the weekday you order and the weekday goods arrive, for example Friday evening to Tuesday.
• ▸Lead time (days): elapsed time from order to delivery.
• ▸Blind-spot length (days): the longest stretch in which you cannot order after a stock-out, for example Monday evening to the next Friday order.
• ▸Order up-to level S: the target net inventory after each order, for example 13.
• ▸Safety stock basis: confirm it covers review period plus lead time (Y/N); if N, recompute using Chapter 5.
• ▸Order quantity rule: S minus net inventory at review, and a sample calculation.
• ▸Service target and simulation result: the fill rate or cycle service level target, and what the simulation shows.

1. 1Name the risks you are buffering before you size anything. The source separates demand-side risk (actual demand differs from forecast) from supply-side risk (suppliers late versus the announced lead time). Write down which of the two you are covering. The simple demand-only model ignores lead time variability, which is handled separately.
2. 2Define the risk period as lead time plus review period. The source says practitioners often forget the review period and look only at lead time. For (s, Q) the exposure is the lead time. For (R, S) the exposure is lead time plus review period, which matches the up-to level S = dL + dR.
3. 3Measure demand variability per period as forecast error versus actual, not as raw demand swings. Then scale it to the risk period. Per the construct definition, safety stock grows with the square root of the risk period, so a risk period 4 times longer needs 2 times the buffer, not 4 times.
4. 4Choose the service level metric explicitly, either cycle service level (probability of no stockout in a cycle) or fill rate (share of units served). Most safety stock models use cycle service level, but most companies record fill rate. Do not mix them.
5. 5Convert the target into a service level factor (the normal z-score) and multiply it by the demand variation over the risk period. Both inputs scale the buffer. State the assumption that demand is roughly normal. The book gives non-normal demand its own chapter.
6. 6Check the result against the order cycle. In long cycles the cycle stock protects most of the cycle, and safety stock only has to cover the final high-risk stretch before the order arrives. Larger Q in (s, Q), or longer review periods in (R, S), mean a similar fill rate needs less safety stock.
7. 7Treat the service level target as a cost decision. The source warns that targets are often arbitrary and points to cost-based optimization of the service level in Chapter 8. Compare the holding cost of the buffer with the cost of shortage before you freeze the target.
8. 8Verify by simulation or inventory analysis. Compare the achieved service level with the target, and compare expected average on-hand with the order up-to level. Long lead times widen the gap between the two.

The source's Figure 7.7 uses demand d ~ N(100, 25²) per period with a fixed 50 pieces of safety stock, and varies the review period. As the order cycle gets longer, the fill rate stays virtually unchanged at around 95%, while the cycle service level falls to around 60–70%. The reason is that cycle stock guarantees fill rate in long cycles, but the cycle service level depends only on whether the 50 pieces survive the high-risk stretch at the end of the cycle. The risk-period scaling shows the mechanism (my arithmetic, assuming normal demand; the source does not give the exact cycle lengths). With a 1-period risk window, σ = 25 and 50 pieces is z = 2, a cycle service level of about 97.7%. With a 4-period window, σ = 25 × √4 = 50, so the same 50 pieces is z = 1, or about 84%. The buffer stays the same while its protection drops. Judged only by the cycle service level, the policy looks like it is failing, yet customers still receive about 95% of units.

• If the policy is periodic review, then size safety stock on lead time plus review period, not lead time alone.
• If your company reports fill rate but your formula targets cycle service level, then convert the target to a fill rate model (Chapter 7) before comparing against actuals.
• If order cycles or production batches get longer, then expect the same fill rate with less safety stock, and do not read a falling cycle service level as a service failure.
• If the service level target is a round number nobody can justify, then replace it with a cost-optimized target (Chapter 8) before adding more buffer.
• If service is poor while dead stock also exists, then do not simply raise safety stock; the source notes both problems can coexist, so fix the inputs (forecast error, lead time reliability) first.

• Sizing the buffer on lead time only for a periodic review policy. The tell is repeated stockouts in the weeks before replenishment arrives, despite the formula being applied correctly.
• Mixing up terms such as safety stock, reorder point, stock target and expected inventory. The tell is that two teams quote different numbers for the same SKU and neither is wrong under its own definition.
• Using cycle service level as the success metric for long cycles. The tell is a reported 60–70% against a 95% target while customers actually receive about 95% of units.
• Setting service levels arbitrarily, with one uniform number for every SKU. The tell is that nobody can explain the number in terms of cost.
• Over-buffering so that process problems stay hidden. The source warns that too much protection removes the incentive for process owners to improve. The tell is that fluctuations never show up and lead time or forecast quality never improves.

• ▸SKU / location: identify the item and stocking site being sized.
• ▸Policy type: (s, Q) continuous review or (R, S) periodic review.
• ▸Lead time L (periods): the supplier's announced or negotiated lead time.
• ▸Review period R (periods): enter 0 for continuous review; otherwise include it in the risk period.
• ▸Risk period (periods): L for (s, Q), L + R for (R, S).
• ▸Demand variation per period (σ): the standard deviation of forecast error per period.
• ▸Service level metric and target: state cycle service level or fill rate, and the target %.
• ▸Service level factor (z): the normal factor matching the target; the buffer scales with z × σ × √(risk period).
• ▸Check: achieved service level after simulation: record the result and compare it with the target and the cost-optimal level.

1. 1Fix the period first. Pick the bucket (day, week, month) that matches how you order, and keep every demand figure in that bucket. The safety stock formula only works if σd and τ use the same time unit.
2. 2Collect n historical demand observations d_t for the SKU. Compute the mean μd, then the sample standard deviation σd = sqrt(Σ(d_t − μd)² / (n − 1)). Use n − 1 in the denominator, as the source does.
3. 3Compute the coefficient of variation, CV = σd / μd. This is the scale-free measure of variability. Use it to compare SKUs with different volumes and to rank which ones need protection.
4. 4Test the independence assumption before you scale σd over time. The source states Ss = zα·σd·√τ assumes demand in each period is independent of the others. If some periods are positively correlated and others negatively correlated, the √τ scaling is unreliable, so flag the SKU rather than apply the formula blindly.
5. 5Set the cycle service level α with management. Convert it to the service level factor zα = Φ⁻¹(α). Under the cycle-service-level metric, α is the probability of no stock-out within an order cycle.
6. 6Compute the safety stock over the exposure window of τ periods: Ss = zα · σd · √τ. Do this per SKU. Never set it as 'x weeks of average demand' for the whole catalog.
7. 7Keep demand variability and supply variability separate. The formula above covers demand only. Lead-time variability needs its own treatment (Chapter 6). Record both for each SKU.
8. 8If you pool locations or markets (warehouse centralization), recompute σd for the combined demand rather than adding the individual σd values. Pooling reduces demand variability but not supply variability, and it can add handling cost and lengthen total lead time.

The passages give the formulas but no demand data, so these numbers are illustrative. Take two SKUs with the same mean weekly demand μd = 100, a 4-week exposure window (τ = 4) and a 95% cycle service level (zα = Φ⁻¹(0.95) ≈ 1.645). SKU A has σd = 40 per week, so CV = 0.40. SKU B has σd = 10 per week, so CV = 0.10. Safety stock for A is 1.645 × 40 × √4 ≈ 132 units. For B it is 1.645 × 10 × √4 ≈ 33 units. A flat rule of 'one week of average demand' gives both SKUs 100 units. That overprotects B threefold and underprotects A. The source warns that such rules ignore each product's own demand variability. The only input that differs between the two is σd, which is why σd and CV have to be measured per SKU.

• If two SKUs have similar average demand but different CV, then give them different safety stocks. Never apply a uniform 'x weeks of demand' rule.
• If the exposure window τ doubles, then safety stock grows by √2, not 2, provided period demands are independent.
• If you cannot defend independence between periods (some periods positively and others negatively correlated), then do not trust the √τ scaling. Treat the result as an approximation and review it.
• If the problem is volatile demand, then consider pooling demand through warehouse centralization. If the problem is unreliable suppliers, then pooling does not help and you must model lead-time variability.
• If the target service level is raised, then raise zα and expect safety stock to rise in proportion to σd. The highest-CV SKUs absorb most of the extra stock.

• Using weeks-of-cover rules for safety stock. The tell: SKUs with very different volatility carry identical cover.
• Mixing time units, for example a weekly σd with a lead time in days. The tell: safety stock is off by a large, unexplained factor.
• Scaling σd by √τ without checking for correlation between periods. The tell: stock-outs cluster in streaks of consecutive periods instead of arriving independently.
• Computing σd with n instead of n − 1, or from too few observations. The tell: σd is unstable when one more data point is added.
• Attributing every stock-out to demand variability. The tell: demand variation is stable but orders still arrive late, which points to lead-time variability, not demand.

• ▸SKU / location: identify the item and the node being analyzed.
• ▸Period unit and n: state the bucket (day/week/month) and the number of historical observations.
• ▸Mean demand μd: average demand per period over the history.
• ▸Demand std dev σd: sqrt(Σ(d_t − μd)² / (n − 1)), same period unit as μd.
• ▸Coefficient of variation: σd / μd; use it to rank SKUs.
• ▸Independence check: note whether periods look correlated (yes/no/unsure); if not independent, flag the SKU.
• ▸Exposure window τ: number of periods the safety stock must cover, in the same unit as σd.
• ▸Target cycle service level α and zα: set α, then zα = Φ⁻¹(α).
• ▸Safety stock Ss: zα × σd × √τ; also record the supply-variability status separately (Chapter 6).

1. 1Decompose total lead time into its legs before measuring variability. The source lists transportation time, extra handling for multimodal shipments, extra transport from a port or external warehouse when the supplier's quote stops there, customs time, and external events (strikes, thefts, storms, earthquakes, the coronavirus). Record each leg per order, because a supplier's quoted time often covers only part of the total.
2. 2Measure total lead time as order placed to goods usable in your main warehouse, one value per order, including all waiting time. Never use the supplier's announced time as the observation. The source says you can never know exactly when a specific order will be delivered, so you need the history.
3. 3Compute the mean (μ_L) and standard deviation (σ_L) of those observed total lead times. State the model explicitly as Lead time ~ N(μ_L, σ_L²). A supplier can then be late or early versus the announced arrival.
4. 4Tag the causes behind the largest deviations: process variability, production constraints, lack of raw materials, mistakes, defects, planning constraints, external events. This tells you whether σ_L can be reduced at the source or only buffered.
5. 5Size safety stock to cover both layers named in the source: demand variation during the average lead time, and the variation of average demand over the lead-time spread. Do not use a flat rule such as 'x weeks of average demand'. The source calls these rules overly simplistic because they ignore supply reliability.
6. 6Set the target cycle service level α and take z_α = Φ⁻¹(α). Hold safety stock that reflects both σ_L and demand variation, and recompute whenever σ_L changes. Safety stock for demand alone follows S_s = z_α·σ_d over τ periods (eq. 4.3). That is only the demand layer.
7. 7Check the normal assumption against the data. A late tail longer than the early tail breaks the symmetry of N(μ_L, σ_L²). The source treats this under 'Beyond Normality' (skewness, gamma distribution).
8. 8Replay the policy in simulation with sampled lead times. Compare the resulting service level to the target, and judge early deliveries by their extra holding cost and late deliveries by their stock-out risk.

The source's illustration is a supplier whose lead time follows a normal distribution with mean 20 and standard deviation 5 (Figure 6.2). Assume a product sold at a constant amount each day, here a hypothetical d = 100 units/day (the number is mine, not the source's). Average lead-time demand is 20 × 100 = 2,000 units. A delivery at the mean arrives on time only about half the time, so half the orders land late and the on-hand stock is at risk of depletion. For a 95% cycle service level, z = 1.645, so cover 20 + 1.645 × 5 ≈ 28.2 days of demand. With fixed demand the safety stock is z·σ_L·d ≈ 1.645 × 5 × 100 ≈ 822 units, and the reorder trigger covers about 2,822 units. If the supplier's σ_L fell to 2.5, the buffer would halve to about 411 units. The cost of the reliability gap is therefore visible in units. The upside runs the other way: when the supplier is early, you hold surplus inventory and pay useless holding costs.

• If a supplier's quote stops at a port or external warehouse, then add the onward transport, handling and customs time before computing μ_L and σ_L.
• If products share an x-weeks-of-demand rule but suppliers differ in reliability, then replace the rule with a per-product buffer driven by σ_L and σ_d.
• If you consider centralizing warehouses to cut variability, then expect it to reduce demand variability only, not supply variability. Weigh the higher handling costs and possibly longer total lead times.
• If the review period lengthens while safety stock stays fixed, then expect a lower cycle service level, because you face more volatility and need more protection.
• If lead-time history looks skewed rather than symmetric, then test non-normal distributions (e.g. gamma) before trusting normal-based safety stock.

• Using the supplier's announced lead time as the mean. The tell: orders routinely arrive after the 'expected' date and stock-outs cluster just before receipts.
• Measuring only the transport leg and ignoring multimodal handling, customs and external-warehouse transfer. The tell: your measured σ_L is much smaller than what planners experience.
• Treating variability as a demand problem and buffering only with σ_d. The tell: stable-demand products with unreliable suppliers still stock out.
• Assuming warehouse centralization fixes supply uncertainty. The tell: demand variability falls after centralizing but late deliveries and stock-outs persist, while handling costs and total lead time rise.
• Applying a normal model blindly to asymmetric delays. The tell: simulated service level falls short of the target α even though the formula says it should be met.

• ▸SKU / supplier: identify the product-supplier pair being analysed.
• ▸Announced lead time: supplier's quoted time and what it covers (to port, to your door).
• ▸Leg breakdown: transport, multimodal handling, port-to-warehouse transfer, customs times per order.
• ▸Observed total lead times: order-placed to usable-in-warehouse for each past order, including waiting.
• ▸μ_L and σ_L: mean and standard deviation of the observed totals.
• ▸Main variability causes: process, production constraints, raw materials, mistakes, defects, planning, external events.
• ▸Target cycle service level α and z_α = Φ⁻¹(α): the target and its service level factor.
• ▸Demand mean and σ_d per period: needed for the demand layer of the safety stock.
• ▸Safety stock result and normality check: the computed buffer, plus whether the lead-time distribution looks symmetric or skewed.