Tammi’s Truck Stop sells Seat-o-Nails cushions, which are specially designed to keep drivers awake on the road. Her accessories supplier makes deliveries every Tuesday, at which times she can get as many cushions as she wants (the supplier’s truck carries a large number of cushions). The cushions cost $40 wholesale, and Tammi sells them for $65. She also uses a 35 percent interest rate to evaluate the cost of holding inventory. Today it is Tuesday, Tammi has 12 cushions in stock, and the supplier has just arrived. Assuming that the weekly demand is normally distributed with mean 35 and standard deviation 10, answer the questions below. (hint: use newsvendor model)How many cushions should Tammi buy if sales are lost when she runs out of stock during the week?Reconsider part (a) if unmet demand is not lost but it is back ordered, and it costs Tammi $12 to mail the cushion to the customer.

Explanation:

(a) The cost of underage(Cu) will be the opportunity cost for lost sales which will be:

= 65 - 40

= 25

The cost of overage(Co) will be the holding cost which will be:

= 40 x 35%/52

= 40 × 0.35/52

= 40 × 0.0067308

= 0.269

The Critical ratio will be:

= Cu/(Cu + Co)

= 25/(0.269+25)

= 0.9894

For the optimal condition,

F(z) = Critical ratio = 0.9894,

therefore, z = normsinv (0.9894) = 2.30

Therefore, the optimal stock will be calculated as:

= Mean demand + (z × Stdev)

= 35 + (2.30 × 10)

= 35 + 23

= 58 units.

We should note that Tammi already has 12 cushions in stock, therefore the order quantity will be:

= 58 - 12

= 46 units

(b) Cu = 12

Co = 0.269

Critical ratio will be:

= Cu/(Co + Cu)

= 12 / (12 + 0.269)

= 0.9781

Therefore, z = normsinv(0.9781) = 2.0

Then, the optimal stock will be:

= 35 + (2.0 × 10)

= 35+20

= 55 units

We should note that Tammi already has 12 cushions in stock, therefore the order quantity will be:

= 55 - 12

= 43 units

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