Logistics & Supply Chain

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

This Logistics & Supply Chain formula category brings together the essential maths behind inventory control, delivery planning, and transport efficiency, from Economic Order Quantity and reorder points to fill rate, truck load factor, and Little’s Law. It’s useful for students, exam revision, and professionals tackling real-world operations, helping them balance stock, speed, and cost with confidence and make smarter supply chain decisions.

Economic Order Quantity

NEWIntermediate

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

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

Reorder Point

ROP = d L

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

Safety Stock

SS = Z \sigma \sqrt{L}

Buffer inventory that absorbs demand variability during lead time.

Inventory Turnover

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

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

Days Inventory Outstanding

DIO = \frac{365}{T}

Average number of days stock sits before being sold.

Little's Law

NEWIntermediate

L = \lambda W

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

Cycle Stock

CS = \frac{Q}{2}

Average working inventory between deliveries, half the order quantity.

Fill Rate

FR = \frac{units\ shipped}{units\ ordered} \times 100

Share of customer demand met immediately from stock.

Capacity Utilisation

U = \frac{output}{capacity} \times 100

How fully productive capacity is being used.

Truck Load Factor

LF = \frac{load\ carried}{capacity} \times 100

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

Cost Per Unit Shipped

C_u = \frac{C_{total}}{n}

Total shipment cost spread across the units delivered.

Fuel Cost Per Kilometre

C_{km} = \frac{P_{fuel}}{E}

Fuel spend for each kilometre from fuel price and economy.

On-Time Delivery Rate

OTD = \frac{n_{on\ time}}{n_{total}} \times 100

Percentage of orders delivered by the promised date.

Perfect Order Rate

NEWIntermediate

POR = R_1 \times R_2 \times R_3 \times R_4

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

Throughput

TH = \frac{units}{time}

Rate at which a facility produces or moves goods.

Dwell Time

D = t_{depart} - t_{arrive}

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

Order Cycle Time

OCT = t_{delivered} - t_{ordered}

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