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Logistics & Supply Chain

Inventory and delivery maths: EOQ, reorder points, safety stock, turnover and Little's Law

Economic Order Quantity

NEWIntermediate
Q=2DSHQ = \sqrt{\frac{2DS}{H}}

Order size that minimises the combined cost of ordering and holding stock.

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Reorder Point

NEWBasic
ROP=dLROP = d L

Stock level that triggers a new order, covering demand during the lead time.

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Safety Stock

NEWAdvanced
SS=ZσLSS = Z \sigma \sqrt{L}

Buffer inventory that absorbs demand variability during lead time.

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Inventory Turnover

NEWBasic
T=COGSIˉT = \frac{COGS}{\bar{I}}

How many times inventory is sold and replaced in a period.

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Days Inventory Outstanding

NEWBasic
DIO=365TDIO = \frac{365}{T}

Average number of days stock sits before being sold.

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Little's Law

NEWIntermediate
L=λWL = \lambda W

Average items in a system equals arrival rate times average time in the system.

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Cycle Stock

NEWBasic
CS=Q2CS = \frac{Q}{2}

Average working inventory between deliveries, half the order quantity.

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Fill Rate

NEWBasic
FR=units shippedunits ordered×100FR = \frac{units\ shipped}{units\ ordered} \times 100

Share of customer demand met immediately from stock.

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Capacity Utilisation

NEWBasic
U=outputcapacity×100U = \frac{output}{capacity} \times 100

How fully productive capacity is being used.

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Truck Load Factor

NEWBasic
LF=load carriedcapacity×100LF = \frac{load\ carried}{capacity} \times 100

How full a vehicle runs — empty space is wasted fuel and money.

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Cost Per Unit Shipped

NEWBasic
Cu=CtotalnC_u = \frac{C_{total}}{n}

Total shipment cost spread across the units delivered.

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Fuel Cost Per Kilometre

NEWBasic
Ckm=PfuelEC_{km} = \frac{P_{fuel}}{E}

Fuel spend for each kilometre from fuel price and economy.

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On-Time Delivery Rate

NEWBasic
OTD=non timentotal×100OTD = \frac{n_{on\ time}}{n_{total}} \times 100

Percentage of orders delivered by the promised date.

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Perfect Order Rate

NEWIntermediate
POR=R1×R2×R3×R4POR = R_1 \times R_2 \times R_3 \times R_4

Product of on-time, complete, damage-free and correctly documented rates.

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Throughput

NEWBasic
TH=unitstimeTH = \frac{units}{time}

Rate at which a facility produces or moves goods.

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Dwell Time

NEWBasic
D=tdeparttarriveD = t_{depart} - t_{arrive}

How long a shipment or container sits idle at a facility.

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Order Cycle Time

NEWBasic
OCT=tdeliveredtorderedOCT = t_{delivered} - t_{ordered}

Elapsed time from a customer placing an order to receiving it.

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