Fleet configuration subject to stochastic demand: An application in the distribution of liquefied petroleum gas

We study the problem of configuring a fleet, in which vehicles receive information on-line about the demand that they should fulfil while they are on the road. In each district it must be decided the number of vehicles and their capacity. The objective function is to minimise the operational cost subject to constraints for the minimum delivery capacity, the maximum vehicle size and the average waiting time for customers. The last constraint is modelled as a queuing system that is adjusted according to the simulation of the delivery process of a Chilean company that distributes liquefied petroleum gas in portable cylinders. We provide the analytical form of all the components of the model, so it can be solved using a standard non-linear programming package. We show that the fleet may increase its sales by 3% and reduce the waiting time of customers 10% by allowing a set of vehicles to share the buffer of orders rather than having vehicles to exclusively serve smaller sectors.