Question

The local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week the supermarket can buy fresh lettuce for $4.00 a box. The lettuce is sold for $16.00 a box and the dealer that sells old lettuce is willing to pay $2.50 a box. Past history says that tomorrow's demand for lettuce averages 252 boxes with a standard deviation of 34 boxes. How many boxes of lettuce should the supermarket purchase tomorrow?

Answer 1

Cost of underage, Cu = Selling price - Purchase price = 16 - 4 = 12
Cost of overage, Co = Purchase price - Salvage value = 4 - 2.5 = 1.5

So,

The newsvendor critical ratio, CF = Cu / (Co + Cu) = 12 / (1.5+12) = 0.889

For optimal order size, the cumulative probability F(z) equals the CF.

So,

F(z) = 0.889
or, z = 1.22 (from standard normal tables)

So, the optimal order size = mean demand + z * Stdev = 252 + 1.22*34 = 294 boxes