Page 190 - DMGT206_PRODUCTION_AND_OPERATIONS_MANAGEMENT

Unit 9: Inventory Model and Safety Stocks

Q=Q* 2DS/H = 2DS/FP =EOQ ...(2) Notes
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This equation is known as the EOQ formula. From this formula, the optimal time between
orders can be derived.
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T Q*  D Q D/ 2DS H/    DH 2S/ 
/
The Minimum Total Annual Cost (TC) of holding inventory is given by the formula:
TVC(Q) = DS/Q + HQ/2

If Q = Q*, then:
TVC(Q*) = DS/Q* + HQ*/2
= DSQ*/Q*Q* + HQ*/2

= DSQ */(2DS/H) + HQ*/2)
= HQ*/2 + HQ*/2
TVC(Q*) = HQ* ...(3)
In the above discussion, we considered that lead time is zero. However, if lead time is constant,
the above results can also be used without any modification.
If lead time is say constant (‘ab’ = ‘cd’ = ‘ef’) and equal to ‘L’, then during lead time, the consumption
is L*D units. This means the order will have to be released for quantity Q*, the new order will
arrive exactly after time period ‘L’ at which time inventory level will be zero and the system
will repeat itself.
The inventory level at which the order is released is known as reorder level. It can be
mathematically expressed by the equation:
Reorder Level = RB = LD ...(4)
Where, ‘L’ is given in years and ‘D’ is the annual demand.

Let us work out an example to understand the EOQ Model and all that has been said earlier in
this section on fixed order quantity policies:

Example: A company, ABC Ltd., 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
‘P’ = Unit purchase cost = ` 40.00
‘S’ = Ordering Cost = ` 5400.00
‘F’ = Holding Cost = 40%

Using the Economic Order Equation:
/
Q*  2DS H/   2DS FP  EOQ
= 2 5400 1200* *  0 40 40/ . * 

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