Page 191 - DMGT206_PRODUCTION_AND_OPERATIONS_MANAGEMENT

Production and Operations Management

Notes Minimum Total Annual Cost: TVC(Q*) = FPQ*
= 900*0.40*40
= ` 14,400.00
The Total Annual Cost under the present system = TVC(Q) = DS/Q + HQ/2

= ` (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: RB = L*D = (6/12)* 1200 = 600 units

The company should place orders for economic lot sizes of 900 units in each order. It should have
a reorder level at 600 units.

Notes EOQ Model with ‘Lead Time’
In the discussion, we considered that lead time is zero. However, if lead time is constant,
the results can be used without any modification.
If lead time is constant and equal to ‘L’ (in weeks), then during lead time, the consumption
is L*D units. This means order will have to be released for quantity QEOQ. 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 = Ro = L*D
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, 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 per cent, 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:
QEOQ =  (2*A*D /r*v) =  (2 *5400*1200)/(0.40*40) = 900 units.
Minimum Total Annual Cost (TC) =  2*A*D*r*v
Contd...

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