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Operations Analytics: Simulation

SCOT 500M, Spring 2023

Individual Project: Due Next Class on Canvas

A few guidelines for this project:

This assignment is to be done entirely individually.

You may discuss it only with the professor or the TA.

Develop a comprehensive report for the case.

Include printouts or screen shots of any models you develop and simulation analyses. (I do

not need to see all trials, though). These are submitted separately.

To facilitate grading, please adhere to the following:

o Include your Student ID

Monte Carlo Simulation using

Excel / Crystal Ball / @Risk / Python

Case: AirJet Airlines

Background

AirJet operates a nonstop flight from St. Louis to Miami, scheduled to depart on May 23, at 10 am. This particular route does not face any significant competition, and the airplane used for this flight has a net capacity of 180. All seats on the plane are economy-level type, and there are no prior seating assignments (think, e.g., of Southwest Airlines).

As commonly practiced in airline revenue-management systems, AirJet limits itself to a set of prices (“fares”) from which it chooses which one(s) to activate in any given time. For this flight, AirJet considers two fares only: A low-fare of $300, and a high-fare (HF), which is a decision variable. In the base case, the high-fare price is HF = $1,200.

Since variable costs – the marginal costs of flying an additional passenger – are negligible, AirJet is primarily interested in maximizing revenues via smart activation (opening and closing) of the low fares and setting prices.

Important Note: while this example has a few similarities with the SkyJet case we analyzed, the example is very different. Do NOT USE your SkyJet model as a starting point. It will only confuse you. In this simulation, you do not need to consider the timing of selling tickets, or of customer arrivals.

The Demand Model

AirJet has a simple model for predicting demand for flights. Based on historical data, they found that there are generally two types of customers: High Value (HV) customers, and Low-Value customers (LV). There are sufficient LV customers to purchase any tickets available to them.       Demand from High-Value customers depends on the price offered, and is random. Demand follows a Normal Distribution. However, the mean of the Normal Distribution depends on the price offered, using the following equation:

Mean Demand (u) = 110 −

The standard deviation of the distribution is always 20.

For example, in the base case, HF = 1,200, and µ = 70. The distribution of demand by High-Value customers is N(70,202).

When the HF price changes, mean demand changes, too.

Pricing and Tickets Policy

The pricing policy currently used by AirJet is based on the concept of Protection Level. The idea is that there are tickets reserved for High-Value customers. The protection level is the number of tickets reserved to be sold at the High Fare. Assuming that Low Value customers arrive before High Value customers, the airline reserves tickets for the High Value customers.

In practice, this means that all tickets not protected, will be sold to Low Value customers at LF.

In the base case, the protection level is 50 tickets. The traditional thinking is quite risk-averse, and wants to assure that nearly all seats on the flight are sold. Setting a higher protection level may lead to empty seats on a flight.

To clarify, since there are 180 seas on the flight, and 50 are reserved to be sold at HF, 130 tickets on this flight will be sold at the price ofLF (=$300). Once these 130 tickets are sold, only the High Fare is available for customers that show up to purchase tickets.

While 50 tickets are reserved for the high value customers, not all of these are guaranteed to be sold. If demand by HV is less than 50, some seats will remain empty on the flight. Even in the base case, where HF = $1,200, and µ = 70, there is still a chance that demand by HV customers is less than 40. Although in the base case, this probability is low.

Revenue

A primary objective is to maximize revenue. Revenue is based simply on the price of each ticket sold. There are other metrics of interest, such as the number of HF tickets sold.

Assignment

Part I – Base Case (2 points)

Evaluate the current policy employed by AirJet. In the base case, there are 180 seats on the flight. The protection level is 50 seats, with the remainder (130) sold at the Low Fare of $300. When High Fare is set at $1,200. As described earlier, in this case, the distribution of HV customers is N(70,202).

Develop a simulation and run the simulation for at least 1,000 trials.

Throughout your report, include analyses of the following metrics: (1) Revenue, (2) Number of seats sold at HF, (3) and Number of seats sold at LF.

Part II – Adjusting the High Fare price (4 points)

AirJet realizes that its current price of $1,200 for High Fare may not be optimal. Evaluate different prices for High Fare. The LF of $300 is constant throughout this analysis. What price maximizes revenue? Find the optimal HF price to the nearest $100. Use HF prices of $1,000, $1,100, $1,200,

$1,300, $1,400, and so on. Only use prices that are rounded to $100.

Note: remember that mean demand changes with price.

Develop a graph of average Revenue as function of High Fare price

Part III – Adjusting both Protection Level and High Fare price (4 points)

AirJet realizes that its current price of $1,200 for High Fare may not be optimal. Evaluate different prices for High Fare. The LF of $300 is constant throughout this analysis.

In addition, the protection level of 50 is not optimal. With only 180 seats on the flight, the highest reasonable protection level is 110 seats. In this analysis, suggest alternatives for High Fare price (in increments of $100: $1,000, $1,100, $1,200, $1,300, $1,400, and so on.) and protection level (in increments of 10 seats: 20, 30, 40, 50, 60, etc.).

Suggest ONLY 20-40 reasonable combinations for HF price and protection level and evaluate revenue. You will NOT find the optimal combination, and are not expected to do so.

Develop a graph of Revenue as function of seats sold at price HF. From this graph, is it

true that selling more seats at HF almost always maximizes revenue?