Question

Bombair Retail Store orders accent chairs 10 times per year from Axium Manufacturing. The reorder point without safety stock is 100 chairs. The following demand probabilities during the lead time is shown in the table:

Demand During Lead Time	Probability
0	0.1
100	0.1
200	0.2
300	0.4
400	0.2

The carrying cost is $30 per unit per year and the cost of a stockout is $70 per chair per year. How much safety stock should be carried?    [9 points]

	A.	The company should not carry safety stock
	B.	The company should carry safety stock of 100 units i.e. ROP of 200 unit
	C.	The company should carry safety stock of 200 units i.e. ROP of 300 unit
	D.	The company should carry safety stock of 300 units i.e. ROP of 400 unit

Answer 1

We find the Annual Holding cost for each combination of Safety Stock available and Demand expected as shown below:

The Holding costs are highlighted in green, stock-out costs highlighted in Blue.

The total costs = Holding costs * corresponding probability + Stock out cost * corresponding probability

The above table in the form of formulas is shown below for better understanding and reference:

Here, the calculations are carried out as shown in example below:

Suppose for ROP of 200 and Demand of 100. The additional remaining quantity to be stored will be 200 - 100 = 100

Hence, holding cost for this will be 100 * 30 = $3000

Similarly, if in this case Demand = 300, The stockout cost = 300 - 200 = 100 * 70 = 7000. We multiply these numbers by their corresponding probability and add to get total costs.

The lowest total cost is for ROP of 300. hence, the safety stock should be 200 i.e. ROP of 300 units

Answer: Option C.

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