Demand for organic super fresh lettuce in a local supermarket is 5 with probability 0.2; 6 with probability 0.3; 7 with probability 0.4 or 8 with probability 0.1. Unsold lettuce is given to a food bank with a salvage value of $1.00 per head of lettuce. Cost of the lettuce is $3.00 per unit. Selling price is $6.00 per unit. Using the single-period model, what is the optimal order quantity in number of units of lettuce the supermarket should use?

Question

Quizplus · Accepted Answer

The optimal order quantity is determined by the single-period model (also known as the newsvendor model), which balances the cost of underordering with the cost of overordering. The critical ratio (CR) is calculated as (Selling Price - Cost) / (Selling Price - Salvage Value) = (6 - 3) / (6 - 1) = 3 / 5 = 0.6. We then find the smallest cumulative probability that is greater than or equal to 0.6. The cumulative probabilities are 0.2 (for 5 units), 0.5 (for 6 units), and 0.9 (for 7 units). The first cumulative probability greater than 0.6 is 0.9, corresponding to an order quantity of 7 units.

Demand for Organic Super Fresh Lettuce in a Local Supermarket