Dynamic Pricing and Revenue Management Final Exam. Fall Name: ID: Score:

Transcription

1 Dynamic Pricing and Revenue Management Final Exam Fall 2016 Name: ID: Score: 1

2 1 (12 points) An auto manufacturer can manufacture compact cars for an incremental cost of $5,000 apiece. She faces a logit price-response function for sales in the next month, with parameters C = 40, 000, b = , and ˆp = $12, 000. (i) What price will maximize the total contribution? How many cars will she sell during the month? 2

3 2 (18 points) A company wants to purchase copies of a financial analysis software for its employees to use. There is wide variation in the value the company will gain from having different employees have access to the software. It determines that there are 500 employees who would use the package and that the value to the company from their access is uniformly distributed between 0 and $250 per year. (i) If so, what kind of demand curve the software vendor is facing? That is, d(p) =? (ii) If the vendor sets a single annual license fee of $125, how many copies will it sell to the company, and for how much revenue it earn? (iii) If the vendor adopts a two-tier pricing scheme, licensing the first 250 copies for $125 each but dropping the price to $75 for each additional sale, how many copies will it be able to sell and how much revenue will it earn? 3

4 3 (12 points) The total potential market for a product is D = 20, 000, and willingness to pay is distributed uniformly between $0 and $10. (i) What is the corresponding price-response curve then? (ii) Suppose the current price is $5 for the product. A 1% price increase will incur what percentage a demand decrease? 4

5 4 (16 points) The Rutgers Scarlet Knight Stadium has 50,000 seats. Customers can be segmented into students and the general public. The price-response curves for each of these segments is: General public: d g (p) = (150, 000 4, 000p) +, Students: d s (p) = (30, 000 1, 500p) +. (i) If Rutgers can only charge a single price for a game, what will be the price that maximizes its contribution? With this price, how many seats will Rutgers sell, and how much will it earn? 5

6 5 (18 points) An airline serves a route with a single-flight-daily 100-seat aircraft. The one-way fare for discount tickets is $100, and the one-way fare for full-fare tickets is $150. Discount tickets can be booked up until one week in advance, and all discount passengers book before all full-fare passengers. The airline estimates that full-fare demand is uniformly distributed between 25 and 75, while discount-fare demand is uniformly distributed between 40 and 120. (i) A consultant tells the airline they can maximize expected revenue by optimizing the booking limit. What is the optimal booking limit? (ii) The airline has been setting a booking limit of 44 on discount demand, to preserve 56 seats for full-fare demand. What is their expected revenue per flight under this policy? (iii) What is the expected gain form the optimal booking limit over the original booking limit? 6

7 6 (12 points) An airline is operating the two-flight airline network of San Francisco Denver St. Louis and offering a full fare and a discount fare for each of the three itineraries. There are six ODFs using two resources. The airline has assigned a 100-seat aircraft on flight 1 from San Francisco to Denver and a 120-seat aircraft on flight 2 from Denver to St. Louis; demands and fares are as shown in Table 1. Table 1: Fare and Demand Information # ODF Fare Demand 1 SFO to DIA full fare $ SFO to DIA discount $ DIA to STL full fare $ DIA to STL discount $ SFO to STL full fare $ SFO to STL discount $ The unconstrained demand is 160 on the San Francisco-to-Denver flight and 170 on the Denver-to-St. Louis flight. (i) Formulate a linear program that will maximize the airline s earning. 7

8 7 (12 points) Dell is bidding against Lenovo for an order of 150 laptops. Dell s unit cost is $1,000 per laptop and based on previous experience, Dell s belief is that Lenovo s bid will be uniformly distributed between $1,200 and $1,500 per unit. (i) Assuming that Dell and Lenovo are at parity, what is Dell s optimal price per unit to bid? What is Dell s corresponding probability of winning the bid and expected contribution? 8