Question

A local farmer is planning turkey orders for Thanksgiving. Based on previous years’ demand, they expect demand to be normally distributed with mean 100 and standard deviation 25 for 20-lb birds. The farmer plans to charge $40 per turkey and their supplier charges them $25 per bird. Any turkeys they can’t sell by Thanksgiving Day, they will freeze and take to the farmer’s market the following Saturday and sell at a price of $25. At such a bargain, they expect to sell all the leftover turkeys. However, freezing and transportation to the farmers market will cost them $2 per leftover bird. How many turkeys should the co-op order?

Answer 1

Cost of shortage(Cs) = sales price - cost price = 40 - 25 = 15
Cost of overage(Co) = Cost price - salvage value = 25 - 23 = 2

Service level = Cs / (Cs + Co) = 15 / (15 + 2) = 0.88
The Z value that corresponds to a service level of 0.88 is = 1.17

Mean demand = 100
Standard deviation = 25

Optimal stocking level = Mean demand + (Z * Standard deviation)

= 100 + (1.17 * 25) = 129