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4. Diagram the Problem - Part 2
In this lesson, we will design and build the complete influence diagram for our Zippy Airways case study.
Understanding the Influence Diagram (00:03)
Based on the problem statement, the outcome of our model should be the increased profit Zippy Airways would have had in the last three months with an overbooking model. To diagram this problem, we can consider the additional revenue they would have gained for each flight, and the additional costs they would have incurred for each flight.
Additional Revenue (00:34)
The additional revenue for a flight is the number of additional bookings multiplied by the price per additional booking. The price per booking is a parameter, as the problem statement specifies we should keep pricing constant. The number of additional bookings is an intermediate variable, that depends on the plane’s capacity, which is a parameter, and the number of bookings, which is an intermediate variable. Finally, the number of bookings depends on demand, which is a parameter, and the booking limit we impose, which is a decision variable.
In an influence diagram like this, we model the variables that have relationships, but we don’t specify formulas or other details of those relationships. This keeps the diagram simple at this early stage of the modeling process.
Additional Costs (01:29)
The additional costs of overbooking depend on the number of customers “bumped” or moved to another flight, and the cost of bumping a customer. The bumping cost is a parameter, while the number of bumped customers is an intermediate variable. The number of bumped customers depends on the number of no shows, which is a parameter, and the number of extra bookings, from our revenue model.
Once we have established the additional revenue and costs for a flight, we use these as intermediate variables to determine the output, which is the additional profit for a single flight from implementing an overbooking policy.
An influence diagram like this doesn’t always capture all the complexity of certain variables, like demand. This is acceptable at an early stage, as additional complexity can always be added at a later stage.
The problem statement for Zippy Airways points to additional profit for the previous three months as the outcome from our model. Given that we have the operating data for each flight, the easiest way to build this model could be to calculate the additional profit per flight during that time period and to add these numbers together at the very end. Additional profit will be made up of additional revenues minus additional costs. Let's break the influence diagram into two separate parts to solve for these two values. Additional revenue is the number of additional bookings on a flight multiplied by average price for the additional booking. This price is going to be a parameter because our problem statement tells us to keep pricing the same. Additional bookings will depend on the capacity of the plane and the total number of bookings for the flight. The total number of bookings for the flight is a function of demand and the booking limit that we can impose. This booking limit is part of the over booking policy which we do control. Hence it's a decision variable. Note that the influence diagram doesn't show the formula that calculates total bookings in this case. It just tells you that a relationship exists between bookings and demand and the booking limit. We can add the formula later if we wish to the influence diagram but for now, let's keep the diagram simple and just show the relationships. Now let's take a look at additional costs per flight. This is simply the cost of bumping a customer multiplied by the number of bumped customers. The number of bumped customers is a function of the number of extra bookings we take on in a flight and the number of no-shows. When we now connect our additional revenue and additional costs to the final outcome, additional profit, our influence diagram for a single flight is complete. You might have noticed the two parameters, demand and unit bumping cost have a lot more complexity associated with them than what I'm showing here. Whenever I draw a first influence diagram for a problem, I'll often intentionally leave out pockets of complexity like this to keep the initial version of the model as simple as possible. I can always add these pockets of complexity in later iterations. Now that our influence diagram for Zippy is complete we can go about translating this diagram into a model in Excel.