BUSF_A01.qxd

Inventories

order size increase, the annual costs of placing orders decrease but holding costs

increase. Total cost drops as inventories level increases until, at point M, it reaches a

minimum and starts to increase. What we want to know is the size of order quantity

Ethat will minimise the total cost: in other words, we need to identify point M.

Since Mis the same as E/2, that is, half of the optimum order quantity, the total cost

and, therefore, the expression plotted as such in Figure 13.5, is:

+

• that is, annual order placing cost plus annual inventories storage cost.
  We can discover where this total will be a minimum (point M) using differential cal-
  culus. It will be a minimum where the differential of the expression (with respect to E)
  is equal to zero, the point of zero slope.
  Differentiating with respect to Egives:

+= 0

so:

E=^2 AC

H

H

2

−AC

E^2

HE

2

AC

E

Economic order quantity

A business uses 1,000 units of a particular inventories item each year. The costs of holding

one unit of it for a year are £3 and the cost of placing each order is £30. What is the most

economical size for each order?

Example 13.2

E=

=

=141.4, say 141 units

Thus each order will be placed for 141 units (or perhaps a round figure like 140 or 150),

necessitating about seven orders being placed each year.

D

F

2 ×1,000 × 30

3

A

C

2 AC

H

Solution

We should note the weaknesses of this model, the most striking of which are as

follows:

l Demand for inventories items may fluctuate on a seasonal basis, so that the

diagonals in Figure 13.4 may not all be parallel, or even straight.