Question

1. A product is ordered once each year, and the reorder point without safety stock (dL) is 100 units. Inventory carrying cost is $10 per unit per year, and the cost of a stockout is $50 per year. Given the following demand probabilities during the reorder period, how much safety stock should be carried?

DEMAND DURING REORDER PERIOD	PROBABILITY
0	.1
50	.2
ROP                                                        100	.4
150	.2
200	.1

Answer 1

First let’s create the cumulative probability table.

Demand	Prob	Cumul prob
0	0.1	0.1
50	0.2	0.3
100	0.4	0.7
150	0.2	0.9
200	0.1	1

From the problem we know the cost of overstocking (Co) = 10 and cost of understocking (Cu) = 50

This means the critical ratio = Cu/(Cu+Co) = 50/(50+10) = 0.833

The closes value in the cumulative probability is 0.9. The corresponding demand is 150.

This means we should ideally order 150 units. Out of which the value of dL is 100. This means considering

ROP = dL + safety stock

The value of safety stock = 50

50 units of safety stock should be carried