Question

Please do not use Excel for any part of this

Green Wave Electronics is selling computer parts for self-assembly to Tulane students. This year, one of its supplier, Angry Tide Co., is planning to release a new hard drive, the SSD2020. Each SSD2020 will cost Green Wave Electronics $340 and will be sold to Tulane students for $500 from September to December of 2020. Given the long lead time and short life cycle of this product, Green Wave Electronics will only get to place a single order for the SSD2020. Using previous sales for similar products, the marketing team forecasts total demand to be 1,000 units. However, historical A/F ratios for those similar items show an overall mean of 1.05 and overall standard deviation of 0.60. It is assumed that, in January 2021, all remaining inventory for the SSD2020 will be sold to Tulane students at a very attractive price of $200.

(a) Using the historical A/F ratios and assuming a Normal distribution for the SSD2020 demand, what do you expect its mean and standard deviation to be?

For all remaining questions, use the demand distribution that you found in a.

(b) What are the underage and overage costs for the SSD2020?

(c) What is the profit-maximizing order quantity for the SSD2020?

(d) What would be the in-stock probability if Green Wave Electronics ordered the profit-maximizing quantity as found in question c?

(e) How many lost sales would be expected if Green Wave Electronics ordered the profit-maximizing quantity as found in question c?

Answer 1

(a)

• Expected demand = Mean A/F ratio x Forecast = 1.05 x 1,000 = 1,050
• StdDev of demand = StdDev of A/F ratio x Forecast = 0.60 x 1,000 = 600

(b)

Cu = cost of underage = Selling price - Purchase cost = 500 - 340 = $160
Co = cost of overage = Purchase cost - Salvage value = 340 - 200 = $140

(c)

Critical ratio, CR = Cu / (Co+Cu) = 160 / (160+140) = 0.533

For optimal order quantity, F(z) = CR = 0.533, So, z = NORM.S.INV(0.533) = 0.084

So, optimal order quantity = Mean demand + 0.084 * SD = 1050 + 0.084*600 = 1,100 units

(d)

The in-stock probability is the critical ratio i.e. 53.33%

(e)

The loss function corresponding to the z value is L(z) = 0.358

So, expected lost sales = 0.358*SD = 0.358*600 = 215 units.