BUAD 311

1 BUAD 311 ‐‐‐ Spring 2016 Homework #2 Optimization and Revenue Management (Update: March 21) Due Wednesday, March 30 Students can discuss homework questions with each other or with the TA/instructor, provided that the actual work is done individually. Homework assignments are accepted only via Blackboard, and I expect most students to use Word (You do not need to submit your excel file that includes your LP formulation and solver solution for Q1). Please show your work. You may not receive a full credit if you just provide an answer without showing any work. Q1 (30 points) In this question, your task is to demonstrate that we can use the LP technique to process/capacity analysis. As you can see in the above figure, we are sending oil from the field to the refinery. There are many pumping stations between the oil field and the refinery, but for the purpose of this homework, we consider only two pumping stations. The oil field, pumping stations, and the refinery are connected with pipes. Oil can go only one way. For example, oil can flow from F to A and A to B, but not R to A. Each pipe has a capacity. For instance, the pipe that connects the oil field and the pumping station A has a capacity of 700 barrels/day.   a) (13 points) Formulate an LP to find the capacity of the system.   b) (3 points) Enter your formulation to Excel and use Solver. What is the capacity of the system in barrels‐per‐day? c) (3 points) Using the answer report, calculate the new daily capacity of the system when the capacity of the pipe from the Oil Field to Station B is increased to 700 barrel/day. d) (7 points) Now suppose our goal is to send 700 barrels a day from Oil Field to the Refinery (note that this may be less than the capacity in part b, also ignore part c). The cost of using Station A is $2 per barrel. For Station B is $3 per barrel. Formulate an LP to minimize the cost. e) (2 points) Now enter your formulation from part d) to Excel and use Solver. What is the cost of sending 700 barrels from Oil Field to the Refinery? f) (2 points) Using the sensitivity analysis report, calculate the new daily cost of the system if the cost of using Station B is reduced to $2.5 per‐barrel. Note that it is possible that your formulation may not allow to use sensitivity analysis to answer this question. If that’s the case, go back to part d and revise your formulation. 2 Q2 (24 points) Trojan Resort is an exclusive resort on a private island with 4 ocean front cabins.  There are two types of customers: leisure travelers and jet setters.  Leisure travelers always book their cabins at least two weeks before their intended stays, and pay $500 per night.  Jet setters tend to reserve their cabins late, just a few days before their arrivals, and pay $2,000 per night.  The durations of stay for both leisure travelers and jet setters are the same.    To simplify the calculation, assume that both leisure travelers and jet setters only stay for one night. The distribution of the number of jet setters is given in the following table: Number of Jet Setters 1 2 3 Probability 0.3 0.5 0.2 a) Determine the number of cabins that Trojan Resort should reserve for the jet setters in order to maximize its total expected revenue.   b) Not only the management team wants to know the optimal number of cabins to reserve for jet setters, but they also want to figure out what is the expected revenue if 1, 2, or 3 cabins are reserved. Calculated the expected revenue for the three cases (assuming sufficient leisure traveler demand). c) Suppose the number of leisure travelers is between 1 (inclusive) and 4 (inclusive), with all numbers being equally likely. Furthermore, Trojan Resort decides to reserve 2 cabins for the jet setters. Determine the total expected revenue for Trojan Resort.  (Hint: you may want to draw a decision tree and use your answers from part b) d) Hoping to increase its revenue, Trojan Resort is running an advertising campaign that will attract more leisure travelers to its property.  With the ad campaign, the management estimates that the number of leisure travelers will be uniformly distributed between 4 (inclusive) and 8 (inclusive).   The campaign will not affect the number of jet setters coming to the resort.  Given the anticipated increase in the leisure travelers, how many cabins should Trojan Resort reserve for the jet setters?  How much additional profit is generated through the campaign? Q3 (16 points) Vertigo Air is considering adding a new flight from LAX to Bratislava for the next year. Vertigo Air has the option of either operating this flight in the same time slot as its competing airline Giddy Air, or to choose a different time. Further, it believes the response to the flight will be favorable, neutral, or unfavorable with probabilities 0.3, 0.4, and 0.3 respectively. However, Vertigo Air may invest heavily in advertising and increase the probability of a favorable response to 0.5 while lowering the probabilities of neutral and unfavorable responses to 0.3 and 0.2, respectively. Advertising costs $10 Million. The table below details the revenues generated by operating the flight:    Revenue ($ Million) Decision Favorable Neutral Unfavorable Same Slot as Giddy Air 100 50 10 Different Slot 70 60 30 a) (12 points) Draw the decision tree for Vertigo Air.   b) (4 points) Should Vertigo invest in advertising or not? Should Vertigo choose the same time slot or a different time slot?