Notesale: Turn your study into money

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Quantitative models for planning
and control of stocks (under
conditions of certainty)
Source: Management and Cost Accounting, Colin Drury

Why do firms hold stocks?
Reasons for holding stocks:

• Transactions motive – holding stocks to meet production and sales
requirements
...

• Speculative motive – when future input prices are expected to
change, a company maintains higher or lower stock levels to speculate
on the expected increase/decrease in future prices
...


Relevant costs for quantitative models
under conditions of certainty
1
...
Ordering costs
• Incremental clerical costs of preparing a purchase
order, receiving deliveries and paying invoices
...
a
...

• When fewer orders are placed, larger average stocks must
be maintained → increase in holding costs
...

• EOQ can be determined using 3 methods:
– tabulation method,
– graphical method, or
– by using a formula
...

• Total annual requirement is 40,000 units
£
£
Required annual return on investment in stocks (10% x £9) 0
...
10
Holding costs per unit
1
...


2
...
)
Order quantity
Average stock in units
No of purchase orders
Annual holding costs
Annual ordering cost
Total relevant cost

100
50
400
£50
£800
£850

200
100
200
£100
£400
£500

300
150
133
£150
£267
£417

400
200
100
£200
£200
£400

500
250
80
£250
£160
£410

600
300
67
£300
£133
£433

800 10,000
400 5,000
50
4
£400 £5,000
£100
£8
£500 £5,008

• The EOQ is 400 units – the point at which the
total annual relevant costs are at a minimum
...
)

Formula method – Example (cont
...
)
Economic order quantity: Q =
where

D = total demand for period
O = ordering cost per order
H = holding cost per unit

Applying the formula to the example:
Q=
= 400 units

Assumptions of the EOQ Formula
• Holding cost per unit will be constant
...


Applying EOQ model to determine
optimum lot size for a production run
• Objective is to find optimum no
...
a
...
)
• Annual demand = 9000 units; optimum prod’n run = 900
units; thus 10 prod’n runs are required p
...

• Assuming 250 working days p
...
, prod’n runs are
undertaken at 25-day intervals
...
a
...

• If 5 days are required for a prod’n run, 180 units (5 days x
36 units/day) will be demanded before any prod’n run is
available → a prod’n run should start when stock level
reaches 180 units
...

• EOQ formula - used as a starting point to determine
optimum quantity to order
...


• Cost savings must be balanced against increased holding
cost
...
) – Example
1
...


2
...

– Re-order point = 2 wks x 120 units = 240 units
...


Determining when to place an order –
demand known with certainty

Controlling stocks using ABC
classification method
1
...

2
...
It is normal for between 10% and 15% of items in stock to
account for between 70% and 80% of the total value of
purchases
...


Other factors influencing the choice of
order quantity
Other factors not incorporated in the models
•Shortage of future supplies
• Future price increases
•Obsolescence

Just-in-time systems
1
...
Batch sizes of one
– The aim is to reduce set-up times, batch sizes and
throughput times, thus minimizing stocks
3
...
1 – p 638 Drury
• A company plans to purchase 90,800 units
...
Price is €200 per box
...

• Cost of holding an item in stock p
...
is 15% of purchase
area
...

• Ordering costs change in proportion to no of orders
placed
...

• Required: Calculate the order qty that would minimise
the cost of the above item, and determine the required
frequency of placing orders, assuming that usage of the
item will be even over the year
...
4 – p 638 Drury
• A company is reviewing the purchasing policy
for one of its raw materials
...
a
...
4kg of material
(20% of material is lost in production process)
...


Example IM24
...
000
1,500
€ 0
...
965
2,500
€ 0
...
940
• Cost of placing each order are €90, of which €40 is an apportionment of
costs not affected by no of orders placed;
• Holding cost of stock p
...
is €0
...
40 is affected in
the short term by amount of stock held;
• Lead time for materials is 1 month; safety stock of 250kg is required
...


Example IM24
...
is considering the possibility of purchasing from a supplier
a component it makes
...

• Co
...

• Av
...

• Annual holding cost is €0
...

• Direct labour costs for the component are €6 per unit, fixed
manuf
...

• Co
...

• Required: Should the company make the component?



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