Question

A stockist wishes to optimize the number of perishable items he needs to stock in any month in his store. The demand distribution for this perishable item is

Demand (in units)	2	3	4	5
Probability	0.10	0.35	0.35	0.20

The stockist pays Rs. 70 for each item and he sells each at Rs. 90. If the stock is left unsold in any month, he can sell the item at Rs. 50 each. There is no penalty for unfulfilled demand. To maximize the expected profit, the optimal stock level is

• A. 3 units
• B. 4 units
• C. 5 units
• D. 2 units

Answer 1

The correct option is B 4 units

$p(d\ge Q)=\text{Probability that the demand for Q units or more}$

$M_P=\text{Marginal profit per unit sold}$

$=90-70=Rs.20$

$M_L=\text{Marginal loss from each unit that is left unsold}$

$=Rs.70-50=Rs.20$

$p(d\ge Q)=\frac{M_P}{M_P+M_L}=\frac{20}{20+20}=0.5$

Demand	Probability that demand at this level	Cumulative Probability
2	0.1	0.1
3	0.35	0.45
4	0.35	0.8
5	0.20	1.00

Hence to maximize profit, the optimal stock level is 4 units.