YOLO.com makes cool headphones and is based in the beautiful Greek island of Ikaria. Due to the recent pandemic, YOLO is concerned about how any additional supply chain disruptions might affect the availability of a magnet which is essential for their headphones. It is the start of February and YOLO must commit to a magnet quantity for delivery in July. Each magnet ordered in February will cost YOLO 40/unit. YOLO estimates that demand for magnets in July at a price of 70/unit will be normally distributed with a mean of 250,000 and a standard deviation of 200,000. If YOLOs demand in July exceeds its regular order (the amount ordered in February) then YOLO can obtain additional units on the spot market. The spot market price for these magnets in July is estimated to be 50/unit. Magnets not used in July will certainly be used in August. However, magnets ordered in March for August delivery are expected to cost 36/unit. Furthermore, due to physical storage costs and opportunity costs of capital there is a 1/unit cost to hold each magnet from one month to the next.

(a) Can we apply the newsvendor model here in order to decide on the optimal number of magnets to order in February? If so, why? (10 marks)

(b) Calculate the optimal number of magnets YOLO should order in February. (20 marks)

Answer:

(c) Find the optimal expected number of magnets to be obtained through the spot market