Allocating capacity under uncertainty
Whatever the business, many decisions have to be taken under some uncertainty.
A pool will be more crowded on a sunny day, cinemas will be full on a Friday night as will restaurants and pubs. There is always an element of uncertainty in the realisation of the demand for a good or a service. Every business owner knows this and has to adapt to these variations.
In businesses or services with a fixed capacity and a perishable good, such as a room in a hotel or a seat in a theatre or plane, this uncertainty may lead to inefficiencies and a loss of revenue. Revenue management techniques have proved to work well by separating the clients according to their willingness to pay and their constraints. So that fixed capacity is split according to that segmentation, and the revenue manager faces several populations – several demands – each with its own uncertainty pattern.
To illustrate this point, let us take a boat with 100 similar seats departing for a cruise. The company has managed to separate customers into two groups, according to a simple booking timeline. People buying their tickets 20 days or more in advance are offered a discounted low fare, while other passengers have to pay a higher price. Of course, the boat company will only find out how many high-fare passengers there are when they leave the harbour.
The trade-off between two risks
To maximise their profit, the boat company has to work out the optimal number of seat to sell to each group and faces a trade-off between two risks:
Proposing ‘too many’ seats at the lower price is risky because ‘too few’ seats are then available for passengers willing to pay the higher price, and you may lose out on those high value sales.
This risk is known as spill.
Proposing ‘too few’ seats at the lower price is also risky because ‘too many’ seats are then available at the higher price, and you may not sell all of them.
This risk is known as spoilage.
What this means is that a company must have an idea of the number of seats they should sell for each price proposed. Information on the demand is needed both for people buying in advance at the lower price and for the demand at the higher price in the last 20 days before departure. With this information, the company can put numbers on what is ‘too many’ or ‘too few’ and can work out the optimal quota of seats (Q) to offer at a discounted price. Since the capacity is fixed, the remaining capacity (100 – Q) is offered at the higher price. Working out the optimal Q involves dealing with the uncertainty of each demand, which involves calculating probabilities.
© By ENAC - Christophe Bontemps CC BY-NC-SA 3.0