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 $10.00 a box and the dealer that sells old lettuce is willing to pay $1.50 a box. Past history says that tomorrow’s demand for lettuce averages 250 boxes with a standard deviation of 34 boxes. How many boxes of lettuce should the supermarket purchase tomorrow? For z, use NORMSINV(critical ratio) in Excel

Answer 1

The problem is based on the concept of under stocking and over stocking and can be solved as follows

Given Data :-

Cost per box = $4

Salvage value per box =$ 1.5

Selling Price per box = $ 10

Average Demand of Lettuce = 250 boxes

Standard deviation of the demand (sigma) = 35 boxes

Shortage Cost / box = Cs = Selling Price of one box – Cost of one box = 10 – 4 =$ 6 per box

Excess Cost / Box = Ce = Cost per Box – Salvage value of one box = 4 – 1.5 = $ 2.5

Service Level = Cs/(Cs + Ce) = 6 / 8.5 = 0.705

The z value for a service level of 0.705 was found using excel to be 0.541395085.

Therefore the the optimal stock level = X = Average Demand + Z * sigma = 250 + 0.541 *35 = 269 Boxes