4. Diagram the Problem - Part 2

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In this lesson, we will design and build the complete influence diagram for our Zippy Airways case study.

Lesson Notes

More complex influence diagrams

- More complex influence diagrams are best solved in separate parts
- The first version of the model should focus on agreeing a high-level model structure
- It should be simplified and not contain any complex relationships between variables
- These relationships can be added in later iterations of the model

Case study details: Zippy Airways

Zippy Airways has been operating for 3 months out of Gatwick Airport in London and has 16 flights per day between London and four European cities.

No-overbooking policy... yet

Unlike most other airlines Zippy does not operate an overbooking policy – which allows the airline to sell more tickets than the number of seats (180) available on a flight - thereby increasing revenue. The policy relies on a certain number of customers that book a ticket but do not show up for the flight (no-shows).


If the number of no-shows is greater than the additional tickets sold, no extra cost. If too many passengers show up, however, the airline must pay a ‘bumping cost’ to move passengers to a later flight.

Bumping costs

If a customer gets bumped to another Zippy Airways flight later that day, then Zippy will pay them on average £150 in vouchers for the inconvenience.

If a passenger is bumped from a flight that has no Zippy Airways planes later that day, she will fly home with SloMo Airways, which has an agreement with Zippy to look after all bumped passengers at a cost of £175 per passenger. The passenger still receives the voucher from Zippy.

Additional considerations

Many of Zippy Airways passengers are business customers and would not appreciate being bumped from a flight. It may affect their decision to fly with Zippy in the future


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.