Skywest Airlines is a regional carrier providing jet service to smaller airports for American Airlines, United, and Delta. This project will consider one route that Skywest operates for United Airlines: service from Chicago O'Hare (ORD) to Houghton/Hancock, MI (CMX). This route is flown twice each day (during the winter season) using 50-seater Canadair Regional Jets (CRJ-200). The service on this route is considered to be "Essential Air Service" and is therefore subsidized by the Government - details on this subsidy are provided below. While there are many variables that need to be considered in modeling the profit that Skywest would realize in operating this route, for the purposes of this project, we will simplify and eliminate some of the variables. We will also assume that all of the flights will operate as scheduled (i.e., none are canceled) and that all flights during a month will follow the same parameters (i.e., there is no difference in number of tickets/passengers depending on the day of the week or for any special events such as Winter Carnival, Finn Fest, or Michigan Tech's graduation).

Part 1 - Development of the Simulation Model

You will develop a simulation model using uniform distribution between 0 and 1 - i.e., U(0,1) as the basis of your simulation of each variable. Note that each variable described here should be based on a separate U(0,1) so you should have 4 different U(0,1) variables in your model:

1) Number of Seats (Tickets) Sold: this will be assumed to be normally distributed with a mean of 42 and a standard deviation of 8. Airlines routinely "oversell" their flights, so it is acceptable to sell more than 50 seats on a given flight.

2) Ticket Sales Price: the average ticket price (in hundreds of dollars) on the flight can be modeled as exponentially distributed with a parameter (λ) of 0.6. As this may result in very low prices, SkyWest Airlines has decided that the lowest ticket price will be $50 and you need to set that threshold in your model. Note that we are simplifying the modeling here - you really should consider each ticket priced differently, but, for simplicity, we will consider every ticket priced the same at this "average."

3) Number of Passengers on the flight: The percentage of passengers showing up for the flight will range between 91 - 100% of the number of tickets sold and the percentage of passengers actually showing up for the flight can be assumed to be uniformly distributed. Note that this might result in an "oversold" flight - i.e., more passengers arrive than there are seats on the flight. Details on how this situation will be modeled are provided below. Remember that it is impossible for a fraction of a passenger to show up, so you will need to appropriately round the figure you determine. Also, if a passenger fails to show up for his/her flight, the ticket would be worthless and there is no need to offer a refund or accommodate on a future flight.

4) Subsidy under the "Essential Air Service" program is as follows: $40 per seat that is occupied and $60 per unoccupied seat. However, if the ticket sales price exceeds $400, there will be no subsidy.

5) Variable Operational Costs (fuel, baggage handling, food, etc.) can be assumed to be normally distributed with a mean of $60 and a standard deviation of $15 for each seat that is occupied and normally distributed with a mean of $40 and a standard deviation of $10 for each seat that is unoccupied

Fixed Costs

The fixed costs for each flight (airplane lease, staffing costs, landing fees, etc.) are $1000 per flight, regardless of the number of passengers on the flight.

Oversold Flights

If a flight is oversold, each passenger who cannot be accommodated will be paid $500 and will be offered a seat on the next flight. When you develop your model, you must therefore add any passengers who are from an oversold flight onto the next flight. Remember that this could actually oversell that subsequent flight.

Part 2 - Financial Analysis based on the Simulation Model

For this part, in order to simplify the calculations, we shall not consider the "time value of money" - i.e., most companies would discount future earnings versus present ones, but, in order to simplify the calculations, you do not need to consider any internal interest rates, etc. This is appropriate since we are modeling only one month of operations (60 flights).

Calculate the true average profit (loss) on a flight, based on your simulation of 60 flights over the course of a month.

Next, determine the 95% confidence interval for the true average monthly profit (loss) for Skywest Airlines on the ORD-CMX route, assuming that there are 2 flights per day and 30 days in a month. Base this confidence interval on 12 runs of your monthly simulation model.

Calculate the 95% lower confidence bound on the proportion of flights that are profitable, based on your 12 months of flight simulation data.