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

Given:

ROP = 100 chairs without safety stock

Stockout cost = $70 per chair per year

Carrying cost = $30 per chair per year

Orders per year = 10 times

Annual stockout costs = the sum of the (units short x the probability x the stockout cost/unit
x the number of orders per year)

Stock out = Demand – ROL

Thus, for the demand of 0 unit and 100 units there no stock out

Let’s consider the

1. Safety stock = SS = 0 chair. or ROL = 100 + 0 = 100

If Demand is 200 chairs and ROL = 100 chairs, then stock out = 200 – 100 – 0 = 100 units, with a probability = 0.2

If Demand is 300 chairs and ROL = 100 chairs, then stock out = 300 – 100 – 0 = 200 units, with a probability = 0.4

If demand is 400 chairs and ROL = 100 chairs, then stock out = 400 – 100 – 0 = 300 chairs, with a probability = 0.2

Expected Annual stockout cost = [(100 chairs)(0.2) + (200 chairs)(0.4) + (300 chairs)(0.2)] x [($80)(10)] = $112,000

Inventory holding cost = $0

Total Cost = $112,000

2. SS = 100 chairs or ROL = 100 + 100 = 200

If Demand is 200 chairs and ROL = 200 chairs, then stock out = 200 – 200 = 0 units, with a probability = 0.2

If Demand is 300 chairs and ROL = 200 chairs, then stock out = 300 – 200 = 100 units, with a probability = 0.4

If demand is 400 chairs and ROL = 200 chairs, then stock out = 400 – 200 = 200 chairs, with a probability = 0.2

Expected Annual stockout cost = [ (100 chairs)(0.4) + (200 chairs)(0.2)] x [($80)(10)] = $56,000

Inventory holding = SS units x holding cost = 100 chairs x $30 = $3,000

Total cost = $56,000 + $3000 = $59,000

3. SS = 200 chairs or ROL = 100 + 200 = 300

If Demand is 200 chairs and ROL = 300 chairs, then stock out = 0 units, with a probability = 0.2

If Demand is 300 chairs and ROL = 300 chairs, then stock out = 0 units, with a probability = 0.4

If demand is 400 chairs and ROL = 300 chairs, then stock out = 400 – 300 = 100 chairs, with a probability = 0.2

Expected Annual stockout cost = [ (100 chairs)(0.2) ] x [($80)(10)] = $14,000

Inventory holding = SS units x holding cost = 200 chairs x $30 = $6,000

Total cost = $14,000 + $6000 = $20,000

3. SS = 300 chairs or ROL = 100 + 300 = 400

If Demand is 200 chairs and ROL = 400 chairs, then stock out = 0 units, with a probability = 0.2

If Demand is 300 chairs and ROL = 400 chairs, then stock out = 0 units, with a probability = 0.4

If demand is 400 chairs and ROL = 400 chairs, then stock out = 0 units, with a probability = 0.2

Expected Annual stockout cost = [ 0 ] x [($80)(10)] = $0

Inventory holding = SS units x holding cost = 300 chairs x $30 = $9,000

Total cost = $0 + $9000 = $9,000

Minimum total cost if $9,600 for the safety stock of 300 chairs or ROL of 400 chairs.

Thus optimal safety stock level should be 300 chairs or ROL of 400 chairs