Page 249 - DMGT501_OPERATIONS_MANAGEMENT

Unit 10: Economic Order Quantity

Notes
Example: Understand the EOQ Model and all that has been said earlier in this section on

fixed order quantity policies:
A company, for one of its class ‘A’ items, placed 8 orders each for a lot of 150 numbers, in a year.
Given that the ordering cost is 5,400.00, the inventory holding cost is 40 percent, and the cost
per unit is 40.00. Find out if the company is making a loss in not using the EOQ Model for order
quantity policies.
What are your recommendations for ordering the item in the future? And what should be the
reorder level, if the lead time to deliver the item is 6 months?
‘D’ = Annual demand = 8*150 = 1200 units
‘v’ = Unit purchase cost = 40.00

‘A’ = Ordering Cost = 5400.00
‘r’ = Holding Cost = 40%
Using the Economic Order Equation:
Q EOQ = √ (2*A*D /r*v)
√ (2 *5400*1200)/(0.40*40) = 900 units.
Minimum Total Annual Cost (TC) = √ 2*A*D*r*v

= √ 2*5400*1200*0.40*40
= 14,400.00
The Total Annual Cost under the present system = (1200*5400/150 + 0.40*40*150/2)
= (43,800 + 1200) = 45,000.00

The loss to the company = 45,000 – 14,400 = 30,600.00
Reorder Level (R ) = L*D = (6/12)* 1200 = 600 units
o
The company should place orders for economic lot sizes of 900 units in each order. It should have
a reorder level at 600 units.
Sensitivity Analysis

In the models that we have discussed in this section, we have assumed as if the various parameters
are used such as demand ‘D’, inventory carrying charges factor ‘r’ ordering or set up cost ‘A’, are
known. In real life situations, the value that is used is often an estimate which may be different
from the real value due to a number of causes. Due to practical reasons, it is important to test
the results of the EOQ model and find how sensitive the results are to the changes in various

parameters.
The sensitivity can be explored in various ways. Let us assume that the estimated values of
parameters differ from “true” values by some factor ‘k’. The average inventory will be ‘I’. The
estimated holding cost is ‘m*r’ and the estimated ordering cost is ‘l*A’. The estimated purchasing
cost is ‘n*v’. Then the ratio of the estimated optimal cost and the “true” optimal cost will be given
by the equation:
TC /TC = (1/2)*[(√ m*n/l*k) + √ (l*k/m*n)]
e
To examine the sensitivity of the costs to the errors in estimation of parameters, let us consider a
situation where the estimates of ‘A’, ‘r’ and ‘v’ are correct, i.e., they all correspond to the “true”

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