Question

(8 points) Piyadasa's Fish Market buys fresh tilapia daily for $5.85 per pound and sells it for $7.80 per pound. At the end of each business day, any remaining tilapia is sold to a producer of cat food for $3.50 per pound. Daily demand can be approximated by a normal distribution with a mean of 180 pounds and a standard deviation of 50 pounds. What is the optimal order quantity? 4.

Answer 1

The newsvendor model also called single-period model is nothing but the mathematical model which is used to determine the optimal quantity of perishable product that needs to maintained which is calculated based on fixed price and uncertain demand. Since the product is perishable and demand is uncertain the unsold items are worthless at the end of the day so newsvendor problem is solved to identify the optimal inventory level.

Cost = $ 5.84/pound selling price = $ 7.80/pound salvage value = $ 3.50/pound d = 180 pounds sigma_d = 50 pounds c_s = selling price - cost = 7.80 - 5,85 = $ 1.95 c_0 = cost - savage = 0.453 z value (0.45) = -0.125 or - 0.13 theta = d + z sigma d = 180_(-0.13 times 50) = 180 - 6.5 = 173.5 or 174 pounds value = 5.85 - 3.50 = $ 2.35 service level = c_s/c_s + c_0 = 1.95/1.95 + 2.35 = 1.95/4.3