Decision Models & Analytics Midterm Exam
决策模型与分析期中代考 Steve has a portfolio consisting of three different stocks (Tech, Bio and Airline).The characteristics of Steve’s portfolio are summarized
Instructions: 决策模型与分析期中代考
- You have 1.5 hours to complete this exam. When you are finished, please submit your solutions electronically to NYU Classes.
- You are NOT allowed to use material other than the course materials during the exam. Do not use the Internet and/or talk to anyone during the exam. Please respect the honor code.决策模型与分析期中代考
- The exam is worth 100 points, plus 15 extra credit points. Note that the extra credit points, like other extra credit you earn for the class, will only be applied after the curve.
- Please show all of your work. Do not expect the grader to guess your reasoning. Your grade on the exam will depend on the clarity of your answers, the reasoning you have used, and the correctness of your answers.
Problem 1 (30 points) 决策模型与分析期中代考
Steve has a portfolio consisting of three different stocks (Tech, Bio and Airline). The characteristics of Steve’s portfolio are summarized in the following table. For example, the table shows that he bought 7,000 shares of Tech when it was worth $30. Currently, Tech’s share is priced at $50, and he expects it to have a value of $60 in one year.
Stock | Shares | Cost
(Price at Purchase) |
Current Price | Expected Price Next Year |
Tech | 7,000 | $30 | $50 | $60 |
Bio | 10,000 | $8 决策模型与分析期中代考 | $10 | $15 |
Airline | 2,000 | $45 | $75 | $90 |
Steve needs to immediately raise $150,000 to finance his business venture. To do this, he is planning to sell some of his shares. However, he wants to sell just enough to raise the money he needs because the shares are expected to be worth more in the future.
If he sells shares, then Steve pays transaction costs at the rate of 1% of the amount sold. In addition, he pays taxes at the rate of 30% on capital gains. For example, suppose Steve sells 1,000 Tech shares. He receives 1,000 × $50 = $50,000 for the sale. However, he owes 0.30 × (50,000 – 30,000) = $6,000 of capital gain taxes and 0.01 × 50,000 = $500 of transaction costs. So, by selling 1,000 shares of Tech, Steve nets 50,000 – 6,000 – 500= $43,500.决策模型与分析期中代考
Steve asked you to help him with his problem. Build a linear optimization model to determine how many shares to sell of each stock in order to raise $150,000 (net of capital gains taxes and transaction costs), while maximizing the expected total value of his portfolio next year (for simplicity, ignore future taxes and future transaction costs).
Problem 2 (40 points)
You have been hired by Ola (a ride hailing service like Uber and Lyft that is poised to capture a significant portion of the Indian ride hailing market) because they heard you have done driver-rider matching in your decision models class. Below is a table of riders and drivers on the app at a given time. The table below represents ETAs (expected time to arrive) for different rider-driver pairs. All of the numbers are in minutes.决策模型与分析期中代考
In case this problem looks familiar to you, that’s because we have considered it class, where we formulated the problem of matching drivers to riders to minimize the sum of ETAs, subject to the constraint that each driver can carry only one passenger at a time, and every rider must be offered a ride. But read on.
Rider 1 | Rider 2 | Rider 3 | Rider 4 | Rider 5 | Rider 6 | Rider 7 | Rider 8 | |
Driver 1 | 8 | 4 | 1 | 8 决策模型与分析期中代考 | 2 | 5 | 4 | 10 |
Driver 2 | 2 | 3 | 4 | 7 | 3 | 3 | 5 | 6 |
Driver 3 | 3 | 10 | 4 | 4 | 2 | 1 | 1 | 7 |
Driver 4 | 11 | 7 | 2 | 6 | 4 | 8 | 3 | 5 |
Driver 5 | 5 | 3 | 6 | 4 决策模型与分析期中代考 | 4 | 5 | 5 | 4 |
Driver 6 | 4 | 9 | 12 | 6 | 3 | 4 | 8 | 4 |
Driver 7 | 7 | 6 | 5 | 5 | 2 | 3 | 9 | 1 |
Driver 8 | 4 | 4 | 5 | 7 | 4 | 7 | 2 | 2 |
Driver 9 | 8 | 4 | 2 | 9 | 8 | 6 | 3 | 1 |
(a)(20 points) Ola is now introducing a new shared car option like UberPool. Sharing allows a driver to pick up two passengers instead of one.
When sharing a ride, both ETAs goes up by 30 seconds because of the additional pick-up time. For example, if driver 1 picks up both riders 1 and 2, the ETAs will be 8.5 and 4.5 minutes for riders 1 and 2 respectively. Suppose only riders 1 and 2 have opted in to the shared ride system and are willing to take a share ride (riders 3 through 8 do not want shared rides). Formulate the optimization model to take this new option into account to minimize the sum of ETAs. Please make sure the problem remains linear.决策模型与分析期中代考
(b)(20 points) Implement your model in Excel and find the solution. Report in your writeup both the matching assignment between drivers and riders and the minimum sum of ETAs. Note that the provided Excel template is just a start, you should feel free to add additional variables as you see fit.
Problem 3 (30 points) 决策模型与分析期中代考
You are the general manager of a major consulting firm. You are responsible for accepting or rejecting consulting projects. Right now, you are planning the projects for the upcoming year (it’s January 1st). In order to accept projects, you must have the people available to staff them. There are 2 different types of human resources: partners and consultants. There are also 3 sizes of projects: small, medium, and large. All projects last exactly 1 month. The forecast below shows the number of requested projects starting on the 1st of each month:
Size | Jan | Feb | Mar | April | May | June | July | Aug | Sept | Oct | Nov | Dec |
Small | 1 | 2 | 3 | 4 | 3 | 4 | 2 | 2 | 3 | 3 | 5 | 3 |
Medium | 2 | 2 | 2 | 3 | 2 | 3 | 2 | 3 | 3 | 4 | 3 | 1 |
Large | 3 | 4 | 1 | 2 | 1 | 2 | 1 | 2 | 0 | 4 | 4 | 1 |
The table below shows the number of partners and consultants necessary for projects of different sizes:
Project Size | Partners 决策模型与分析期中代考 | Consultants |
Small | 1 | 2 |
Medium | 2 | 4 |
Large | 2 | 7 |
You have 8 partners and 18 consultants on staff. Every project you accept must be fully staffed, so you will have to decline projects for which you do not have a complete set of workers to assign to them. The revenue per project type is given below:决策模型与分析期中代考
Project | Price ($) |
Small | 200,000 |
Medium 决策模型与分析期中代考 | 700,000 |
Large | 1,500,000 |
What schedule of projects should you accept? That is, how many projects of each size should you accept for each month? Formulate this problem as a linear integer optimization model.
Bonus Problem (15 points)
You are given the following linear optimization problem:
Before you get a chance to solve the problem, an oracle (from the Matrix) shows up and tells you that x1 = 20, x2= 20 is the optimal solution, achieving the maximum value 120.Note that the solution given by the oracle is feasible, as you can check that it satisfies all the constraints. But you are wondering whether 120 is indeed the maximum value as claimed by the oracle. Here comes your task: without solving the above problem, either justify that the oracle is right or show that the oracle is wrong. (Hint: think about how you can use the constraints to do this. Note that any solution that attempts to solve the above problem by hand will not get anycredit.)
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