1. (60 points) Please refer to article (1) about BART, article (2) about express lanes on I- 66, and article (5) about buses in Westchester, NY. a) (15 points) Compare and contrast the approaches to peak load (and congestion) in these three transportation systems. Be as specific as possible. b) (15 points) What appear to be the capacity constraints in each system? c) (15 points) Would you say, given these capacity constraints in each system, that the route structure and frequency of departures (use more generally) have been optimized? d) (15 points) Who could be said to be the decision maker in each system? What would seem to be that decision makers objective function?

2. (60 points) Under construction at UC Davis is a new classroom building, with the largest new classroom designed to hold 500 students. There is no classroom near this size, the current ones being for 300 and 1000 (the ARC). All classrooms above 180 in size are heavily in demand, especially during the hours of 10 am to 2 pm. a. (10 points) Given that no department now can schedule classes for 500 students at a time, how do you suppose departments will react to the possibility? What part, if any, of their entire schedule will they re-arrange? Consider ARE in particular. AREs largest class is ARE 115A, taught every Quarter to 300, using 1 professor and 4 TAs across 8 sections. b. (10 points) In your answer to part a, what are your taking as inflexible in a departments schedule of courses through a year? Be as explicit as possible. c. (10 points) With the opening of the 500-person classroom, do you expect there to be relief for the heavily used classrooms of around 180 in size? Explain your reasoning. d. (15 points) Suppose the 500-person classroom is itself very popular. How should the UCD Registrar, who has the responsibility, allocate the time slots across departments who request that classroom? Explain your reasoning. e. (15 points) Which of the 12 articles considered for this final would you suggest as offering an insight into the problem of scheduling classrooms at UCD? Name the article and explain the insight.

1a. (8 points) Towards the end of article (4) on Deliveroo is mention of the "Frank" algorithm. How do you suppose this algorithm works? What is it trying to minimize (or maximize)? Be as mathematical in your notation as possible. 1b. (8 points) What do you suppose are the capacity constraints in Deliveroo's system, as optimized by the Frank algorithm? When and why might these capacity constraints have shadow prices? 1c. (6 points) The Orion algorithm seems to solve a similar problem. Why did Deliveroo simply not lease Orion from UPS, do you suppose?

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Please answer all questions in a detailed manner.