CAN YOU ANSWER AT LEASt THE FIRST FOUR PARTS
Posted: Wed May 04, 2022 1:40 pm
CAN YOU ANSWER AT LEASt THE FIRST FOUR
PARTS
P3. Pinarello Pinarello is preparing the capacity to produce its newest model carbon fiber bicycle frame. It is designed to be lightweight, rigid laterally (to facilitate efficient transfer of power), compliant vertically (to allow for dampening of road vibration), and compatible with the latest component technologies. Because component technologies evolve quite rapidly, the frame will be produced and sold for only one season.
Because it takes 6-8 months to develop the tooling that is required to produce the frame, Pinarello needs to decide how much tooling (e.g., molds for the frames) to purchase long before they begin receiving orders from retailers, so they have a good amount of uncertainty about the volume of demand at the time that they determine the amount of tooling to purchase. Once they receive the tooling, they will have received enough orders from retailers that they will effectively know the full amount of demand for the new frame. However, because the amount of tooling that they purchase will determine their production capacity, they will produce and sell the minimum of demand volume and production capacity given the available tooling. They will never produce a unit that they do not sell, but they may have capacity that goes unused. The timeline for the new frame is shown below. Pinarello observes the demand volume (d) K units of Pinarello chooses its volume (K) of capacity. production capacity are ready to be used. Pinarello produces and sells a quantity S = Min{d,K} Time 6-8 months Capacity is expensive. There is a fixed cost of $8,000,000 for designing the molds. This does not depend upon the number of molds and has to be paid if they purchase even a single unit of capacity (it can be avoided if they choose NOT to build any capacity). In addition, each unit of capacity costs $600. Thus, the total cost of purchasing K units of capacity is $8,000,000+ $600 x K. After the capacity has been developed, it costs an additional $300 for materials and labor to produce a frame, and they sell each frame for $3,000. Production capacity has no value at the end of the selling season. Recall that, because they produce the frames after observing the demand, they produce and sell the minimum of demand and capacity. At the time that Pinarello must choose the amount of capacity to purchase, its probabilistic assessment of the demand is as shown below: Scenario 1 Scenario 2 Scenario 3 Sceanrio 4 Scenario 5 0.15 0.2 0.3 0.2 0.15 Probability Demand 5,000 7,500 10,000 12,500 15,000
a) If Pinarello purchases 10,000 units of capacity, what will be the expected amount that it will produce and sell? What will their expected revenue? How about their expected material and labor costs? How much will they have spent on capacity? What will be their expected profit? b) If the demand turns out to be lower than the amount of capacity that Pinarello chooses to purchase, by how much would each unit of unneeded capacity have reduced its profit? c) If the demand turns out to be higher than the amount of capacity Pinarello chooses to purchase, by how much would each unit of unsatisfied demand have reduced its profits, i.e., for each unit of unsatisfied
demand, how much higher would its profits have been had it purchased the unit of capacity to be able to satisfy that demand? d) What do your answers to b) and c) tell you about whether K = 10,000 is the optimal amount of capacity? How much capacity would you recommend that they purchase, and what would be their expected profit with that amount of capacity? e) Pinarello has been approached by a marketing research firm that uses machine learning to analyze click patterns in social media and predict demand. The marketing research firm claims that if Pinarello employed them, Pinarello would "know" their actual demand realization at the time that they need to choose their capacity. How much should Pinarello be willing to pay for this? f) Suppose that the fixed cost for designing the molds were $12,000,000 instead of only $8,000,000. How would this affect your answer to part d), i.e., when they do not observe the demand until after they have purchased capacity, how much capacity should they purchase, and what would be their expected profit? g) Continuing from part f), how much would Pinarello be willing to pay for this information with the higher fixed costs?
PARTS
- Can You Answer At Least The First Four Parts 1 (22.72 KiB) Viewed 47 times
Because it takes 6-8 months to develop the tooling that is required to produce the frame, Pinarello needs to decide how much tooling (e.g., molds for the frames) to purchase long before they begin receiving orders from retailers, so they have a good amount of uncertainty about the volume of demand at the time that they determine the amount of tooling to purchase. Once they receive the tooling, they will have received enough orders from retailers that they will effectively know the full amount of demand for the new frame. However, because the amount of tooling that they purchase will determine their production capacity, they will produce and sell the minimum of demand volume and production capacity given the available tooling. They will never produce a unit that they do not sell, but they may have capacity that goes unused. The timeline for the new frame is shown below. Pinarello observes the demand volume (d) K units of Pinarello chooses its volume (K) of capacity. production capacity are ready to be used. Pinarello produces and sells a quantity S = Min{d,K} Time 6-8 months Capacity is expensive. There is a fixed cost of $8,000,000 for designing the molds. This does not depend upon the number of molds and has to be paid if they purchase even a single unit of capacity (it can be avoided if they choose NOT to build any capacity). In addition, each unit of capacity costs $600. Thus, the total cost of purchasing K units of capacity is $8,000,000+ $600 x K. After the capacity has been developed, it costs an additional $300 for materials and labor to produce a frame, and they sell each frame for $3,000. Production capacity has no value at the end of the selling season. Recall that, because they produce the frames after observing the demand, they produce and sell the minimum of demand and capacity. At the time that Pinarello must choose the amount of capacity to purchase, its probabilistic assessment of the demand is as shown below: Scenario 1 Scenario 2 Scenario 3 Sceanrio 4 Scenario 5 0.15 0.2 0.3 0.2 0.15 Probability Demand 5,000 7,500 10,000 12,500 15,000
a) If Pinarello purchases 10,000 units of capacity, what will be the expected amount that it will produce and sell? What will their expected revenue? How about their expected material and labor costs? How much will they have spent on capacity? What will be their expected profit? b) If the demand turns out to be lower than the amount of capacity that Pinarello chooses to purchase, by how much would each unit of unneeded capacity have reduced its profit? c) If the demand turns out to be higher than the amount of capacity Pinarello chooses to purchase, by how much would each unit of unsatisfied demand have reduced its profits, i.e., for each unit of unsatisfied
demand, how much higher would its profits have been had it purchased the unit of capacity to be able to satisfy that demand? d) What do your answers to b) and c) tell you about whether K = 10,000 is the optimal amount of capacity? How much capacity would you recommend that they purchase, and what would be their expected profit with that amount of capacity? e) Pinarello has been approached by a marketing research firm that uses machine learning to analyze click patterns in social media and predict demand. The marketing research firm claims that if Pinarello employed them, Pinarello would "know" their actual demand realization at the time that they need to choose their capacity. How much should Pinarello be willing to pay for this? f) Suppose that the fixed cost for designing the molds were $12,000,000 instead of only $8,000,000. How would this affect your answer to part d), i.e., when they do not observe the demand until after they have purchased capacity, how much capacity should they purchase, and what would be their expected profit? g) Continuing from part f), how much would Pinarello be willing to pay for this information with the higher fixed costs?