Resource schedules play an important role in everyday life. Simply think of the airline schedules and bus and train schedules. This year the Franz Edelman award went to the Dutch Railways for their accomplishments in improving the schedules of the commuter rails system of the Netherlands. The Dutch Railways got the price for applying Operations Research to construct an improved timetable. As a result, the percentage of trains arriving within 3 minutes of the scheduled time increased from 84.8 % in 2006 to 87.0 % in 2007. This may not seem much, but it is a great achievement since the Dutch railway system is one of the worlds busiest. Even the public opinion changed because of the new schedules. The number of jokes on the trains arriving on time dropped significantly (now how can I proof that?)
Schedules like the ones used in railways are also present in other areas, for example in the Express market. Since Express services are all about on time delivery, they face the same challenge as the Dutch railways. In designing their schedules a much used approach is to start with an estimation of the amount of freight (parcels) that have to be moved between each origin and destination combination in the network. Based on the forecasted volumes the required schedules are than developed. Designing the network is not an easy task (see http://john-poppelaars.blogspot.com/2008/04/express-network-design.html) As you can imagine the data and parameters used in such a case are not fixed. For example think of vehicle capacities. How many parcels could a vehicle carry? This depends on the composition of parcels that have to be transported. These can be either bulky but light, but also compact and heavy (like a machine or engine). Normally a certain gross capacity is assumed for the vehicle, talking into account the freight profile of the past, assuming that that will be the same in the future.
A main cost driver in an Express network is the line haul cost, in road networks as well as air based networks. A network schedules consists of movements which designate the time of departure from the origin and the time of arrival at the destination and vehicle type. For trains it is exactly the same. Getting the vehicle type wrong (either to large or to big) is not efficient from a cost perspective. Since the Express market is a highly competitive one, you cannot effort to loose money that way. However, changing the vehicle in accordance with the actual volumes, most of the time, is impossible, as is the case with trains. Having a good estimate of the amount and composition of the parcels is therefore a must.
Obviously the amount and composition of parcels is not static but random over time. There are some characteristics of the time series that will repeat themselves, like the increase in number of parcels during the Christmas period. But estimating the amount and composition on a daily basis is really hard, if not impossible. How to address this issue than, because we still need reliable volume forecasts to construct the network. Trying to model the stochastic nature of the time series and incorporating it in the model to find the best line haul schedule will clearly complicate that model immensely. That under the assumption that an econometric model can be fitted to model both number, volume and weight of the parcels for each of the origin and destination combinations to be served by the network.
My way to deal with this random nature is to except it in designing the network and go for the average or some percentage of that average volume (say 90% or 110% of the average). Based on this static forecast the network can be designed. This works fine in practice, also because many times my customers are not able to supply my with the data to estimate a volume forecast model. To improve on this we do a sensitivity analysis based on volumes used using scenario’s that are discusses and approved by the customers.