Question

The probability distribution of monthly sale of a certain item is as follows:

$\begin{array}{ccccccccc}\text{Monthly sales (units)}& 1& 2& 3& 4& 5& 6& 7& 8\\ \text{Probability}& 0.06& 0.08& 0.13& 0.19& 0.26& 0.13& 0.08& 0.07\end{array}$

The carrying cost of inventory is Rs. 50 per unit per month and the shortage cost is Rs. 84 per unit per month. What will be the optimum stock level ?

• A. 4.57 units
• B. 4 units
• C. May be (a) or (c)
• D. 5 units

Answer 1

The correct option is D 5 units

$\begin{array}{ccccccccc}\text{Monthly Sales}& 1& 2& 3& 4& 5& 6& 7& 8\\ \text{Probability}& 0.06& 0.08& 0.13& 0.19& 0.26& 0.13& 0.08& 0.07\\ \text{Cumulative Probability}& 0.06& 0.14& 0.27& 0.46& 0.72& 0.85& 0.93& 1.00\end{array}$

$\text{Critical ratio}=\frac{C_s}{C_h+C_s}=\frac{84}{50+84}=0.6268$
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Critical ratio lies in the range of 0.46 to 0.72. Hence 5 units must be stocked every month.