Mining & Mineral Economics

Inventory Models

The Economic Order Quantity, reorder point and total inventory cost that minimise stores and spares spending.

PART 1

Topic Breakdown & Traps

The Engineering Principle

A mine ties up capital in stores and spares. Inventory models find the order policy that minimises total cost, balancing two opposing costs: ordering cost (per purchase order — falls if you order in big batches) against holding (carrying) cost (per unit per year — rises with batch size). The Economic Order Quantity (EOQ) is the batch size that minimises their sum. At EOQ the annual ordering cost equals the annual holding cost. The reorder point is the stock level that triggers a fresh order, set so stock lasts through the lead time (plus safety stock).

The Core Formula Matrix

EOQ:

Q^{*} = \frac{2 D S}{H}

(

D

= annual demand,

S

= cost per order,

H

= holding cost per unit per year)

Minimum total variable cost:

T C^{*} = 2 D S H

(and ordering cost

=

holding cost at

Q^{*}

)

Number of orders/yr:

N = \frac{D}{Q ^{*}}

; cycle time

= \frac{Q ^{*}}{D}

Reorder point:

R O P = d \times L (+ safety stock)

(

d

= demand rate,

L

= lead time)

The ‘IIT Traps’

⚠
**EOQ has the $2 D S$ inside a square root.** Forgetting the root, or the factor 2, is the classic error.
⚠
** $H$ is the holding cost per unit *per year*** — if given as a % of unit price, multiply by price first.
⚠
At EOQ, ordering cost = holding cost — a quick check on your answer.
⚠
Reorder point uses lead-time demand, not annual demand; convert $D$ to the lead-time period.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

At the Economic Order Quantity, the annual ordering cost is:

Q2MEDIUM2 Marks · NAT

Annual demand for a spare is

1200

units, the cost per order is

\

100

, an d t h e h o l d in g cos t i s

6

per unit per year. The Economic Order Quantity is ______ units. (Round to the nearest whole number.)

units

Q3HARD2 Marks · NAT

For the same item (

D = 1200

S=\

100

,

H=\

6

Q^{*} = 200

), the minimum total variable (ordering + holding) cost per year is ______ dollars. (Round to the nearest whole number.)