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 $11.00 a box. The lettuce is sold for $25.00 a box and the dealer that sells old lettuce is willing to pay $3.00 a box. Past history says that tomorrow's demand for lettuce averages 265 boxes with a standard deviation of 42 boxes.

How many boxes of lettuce should the supermarket purchase tomorrow? (Use Excel's NORM.S.INV() function to find the z value. Round your answer to the nearest whole number.)

Number of boxes:

Answer 1

Cost of shortage(Cs) = sales price - cost price = 25 - 11 = 14
Cost of overage(Co) = Cost price - salvage value = 11 - 3 = 8

Service level = Cs / (Cs + Co) = 14 / (14 + 8) = 0.636
The Z value that corresponds to a service level of 0.636 is = 0.348

Mean demand = 265
Standard deviation = SQRT(Sum of variance) = 42

The optimal stocking level can now be calculated using the formula:

Optimal stocking level = Mean demand + Z * Standard deviation

= 265 + (0.348 * 42) = 280