Model II - EOQ When Shortages Are Allowed
In this case, shortages are permitted which implies that shortage cost
is finite or it is not large. The cost of a shortage is assumed to be
directly proportional to the mean number of units short. Further, all
the assumptions of model I hold good here also. The model is graphed
in the following figure.
where
S = Back order quantity.
M = Maximum inventory level.
t1 = Time during which stock is available.
t2 = Time during which there is a shortage.
t = Time between receipt of orders.
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The cycle time t is the sum of t1 and t2. |
 Example
The Wartsila Diesel Company has to supply diesel engines to a truck
manufacturer at a rate of 10 engines per day. The ordering cost is Rs.
150 per order. The penalty in the contract is Rs. 90 per engine per
day late for missing the scheduled delivery date. The cost of holding
an engine in stock for one month is Rs. 140. His production process
is such that each month (30 days) he starts procuring a batch of engines
through the agencies and all are available for supply after the end
of the month. Determine the maximum inventory level at the beginning
of each month.
Solution.
Given
Demand (D) = 10 engines per day
Shortage cost (Cs) = Rs. 90 per day per engine
Carrying cost (Ch) = 140/30 = 14/3 per engine per day
Ordering cost (Co) = Rs. 150 per order
| M* = |
 |
 |
2 X 10 X 150
-----------
14/3 |
X |
90
-----------
14/3 + 90 |
 |
X |
30 |
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| = 741.65 = 742 engines (approx.) |
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