Safety stock works only when its assumptions match the replenishment process

Available stock is a physical and quality judgement. Inventory position is a planning judgement. Confusing them can make a reorder rule fire when sufficient supply is already committed, or fail to fire when the recorded supply cannot be used. GFT defines usable on-hand stock as accepted material at the item location, less quantities whose reservation has not already been netted from requirements. Quarantine, rejected lots, unapproved shade lots and stock reserved for another order are not interchangeable with free stock. Material requirements planning likewise depends on consistent item definitions, requirements and supply netting rather than an undifferentiated stock total.[S07]

For this chapter, inventory position is IP = U + F - B - C. U is usable unreserved on-hand quantity. F is firm outstanding supply expected to become usable, expressed in the same item unit. B is backorders, meaning unfilled demand retained as an obligation. C is other relevant commitments that have not already reduced U or the demand forecast. This is a proposed GFT convention built from standard inventory-position logic, not a claim that one formula fits every ledger.[S05][S07] The implementation must document whether allocations sit inside U, inside C or inside netted demand. They must appear once, never twice.

Consider an illustrative fabric record with 800 accepted metres in the store, 150 metres quarantined for shade inspection, 250 metres reserved to a confirmed uniform order, and a firm purchase order for 600 metres. Backorders total 100 metres. No other commitment remains outside the demand calculation. Usable unreserved stock is 800 - 150 - 250 = 400 metres if the 800-metre book balance includes both quarantined and reserved material. Inventory position is then 400 + 600 - 100 = 900 metres. Subtracting the reservation again when netting requirements would understate supply by 250 metres; treating quarantine as usable would overstate it by 150 metres. The example demonstrates reconciliation, not a recommended stock level.

The firm-receipt term needs the same discipline. A supplier confirmation is not proof that the full quantity will arrive on the stated date or pass inspection. Research on uncertain supply identifies censoring in both demand and supply observations, so an accepted or observed quantity can be only a truncated view of what was requested or dispatched.[S22] In the Cameroon sector context, where the inherited annex records about 95 percent of cotton fibre exported raw and about 5 percent processed locally against a national 50 percent local-processing ambition by 2030, a garment factory scaling repeat uniform or basics production cannot equate gross inbound deliveries with usable stock.[R06][R07] Inspection literature stored in the same annex reports manual fabric-defect detection at 60 to 70 percent accuracy, missing 20 to 30 percent of defects, compared with computer-vision inspection above 90 percent across more than 40 defect types at up to 60 metres a minute.[R29] That inspection boundary is an inherited literature benchmark rather than a measured GFT factory result, but its planning implication is direct: GFT would admit a receipt into F only when its quantity, item version, promised usable date and quality-release status meet an approved rule. Disputed quantities, unapproved specifications and unreliable dates should be excluded or represented through explicit receipt scenarios rather than counted at full face value.[S22][R29]

This boundary also clarifies what the reorder point is not. It is not a physical minimum that must always remain on the shelf. Because the trigger uses inventory position, outstanding firm supply can legitimately keep IP above the threshold while physical stock is low. Conversely, physical stock can look ample while unusable lots and outstanding commitments make the effective position inadequate. The planner should be able to inspect every component of the calculation and the event time of every receipt.

A fixed-lead-time model removes an uncertainty that many replenishment processes actually contain. The stochastic-lead-time literature explicitly challenges the constant-lead-time assumption and shows why its distribution matters to inventory behaviour.[S24] However, replacing a fixed L with an average lead time inside σ_d√L is not a sufficient correction. Lead-time variability changes both the number of daily demands accumulated and the variability of that accumulation.

Let D_L denote demand during a random lead time L. Conditional on a particular realised lead time, independent identically distributed daily demand gives E[D_L | L] = μL and Var(D_L | L) = Lσ_d². The law of total variance then gives Var(D_L) = E[Var(D_L | L)] + Var(E[D_L | L]). Under stationarity and independence between daily demand and lead time, this becomes Var(D_L) = E[L]σ_d² + μ²Var(L). The first term is demand variability accumulated over the expected horizon. The second is variability caused by an uncertain number of demand days.[S05][S24]

The units verify the derivation. If μ is pieces per day and σ_d² is pieces squared per day, while L is days, both terms reduce to pieces squared. A formula that adds Var(L) directly to daily demand variance would mix days squared with pieces squared and should be rejected. This check is simple enough to perform manually and catches a consequential class of spreadsheet errors.

For an illustrative comparison, retain mean daily demand of 100 pieces and daily residual standard deviation of 20 pieces. Let random lead time have mean 10 days and standard deviation 3 days, independently of demand. Then E[L]σ_d² = 10 × 400 = 4,000 pieces squared, while μ²Var(L) = 100² × 3² = 90,000 pieces squared. Total lead-time-demand variance is 94,000 pieces squared and its standard deviation is 306.59 pieces. At the same illustrative z = 1.644854, safety stock becomes 504.30 pieces and expected lead-time demand remains 1,000 pieces, giving a reorder point of 1,504.30 pieces before rounding.[S05][S24]

The comparison with the fixed-lead-time case is stark: the illustrative safety stock rises from 104.03 to 504.30 pieces because lead-time standard deviation of 3 days introduces the second variance term. This is not a general ratio that should be transferred to another item. Lower mean demand would reduce the μ²Var(L) contribution, while a lower lead-time variance would reduce it directly. A model that combines a shorter average lead time with a wider tail can therefore require more protection even when the average looks improved.

The independence condition is equally important. Demand and lead time can worsen together when seasonal order peaks consume supplier capacity or when a disruption affects both material availability and customer requests. The stochastic-lead-time manuscript identifies dependence between lead times and demand as an area requiring further work, which cautions against treating independent-model outputs as universal.[S24] Similarly, inventory research on correlated merchandise notes that "it is difficult to control the stock management of correlated marketable merchandise when using an inventory control method that was developed under the assumption that the demands are not correlated."[S0501] When multiple garment sizes, colours or component trims share a fabric base or respond to the same institutional tender, serial and cross-item correlations invalidate simple sum-of-variances rules. If orders also change supplier congestion, lead time is endogenous to the buying rule rather than an external random draw. In those circumstances, GFT would use joint historical blocks, probability-inequality bounds or explicit scenarios linking order size, demand state and usable receipt instead of applying the two-term formula as though independence had been proved.[S24][S0501]

A practical policy record should consequently store more than mean and standard deviation. It should retain the observation window, number of completed and open orders, calendar convention, exclusions and their reasons, the assumed dependence model, and the person or role authorised to approve it. Sparse data may support a broad scenario range but not a confident variance estimate. The output should say so rather than conceal sampling weakness behind additional decimal places.