Optimizing Fleet Composition and Size under Uncertainty in Urban Transit Systems

Project status

In progress

Start date: 01/01/16
End date: 12/31/16


Principal investigator:

About the research

Transportation fleets are capital-intensive assets of logistics/transportation companies or organizations. Optimizing the composition (types of vehicles) and size of a fleet is crucial for efficient and cost-effective operations. Fleet optimization in urban transit systems has additional complexities due to heterogeneous demand/customer types and uncertain demand, travel time, and vehicle productivity.

It is not uncommon for a logistics company to oversize its fleet with low utilization rates. And, all too often in paratransit (and regular bus service for that matter), we utilize larger vehicles than necessary due to those few occasions when they might be needed, or we use a larger vehicle due to the cost per seat per mile when the cost per trip of using the larger vehicle is not something the agency wants to show. All these call for proper methods for fleet sizing and optimization.

The fleet optimization problem addressed in this research can be described as follows. In each time period, the decision-maker determines the following: 1) how many vehicles of each type to acquire, to retire, thus the fleet size; 2) how many vehicles of each type to move between an origin-destination (OD) pair to satisfy the estimated demand; and 3) the total shipments made and delayed (if necessary). Each time period has an estimated demand to be satisfied through shipment made by the vehicles. Each vehicle has a limited capacity (e.g. amount of travel time) available. The objective is to minimize the total fleet operations costs, which include cost of owning, acquiring, and retiring a type of vehicle, operating cost for a type of vehicle to make a trip for an O-D pair, and penalty cost of delaying shipment. Uncertainties may be attributed to random customer demand, travel time and vehicle productivity (especially for aging vehicles). In this research, we will focus on addressing the uncertainty due to random customer demand.

The objectives of this project include the following: 1) develop an optimization model to address large-scale fleet composition and sizing decisions in a multi-period setting; 2) understand how random demand may impact the optimal fleet sizing solutions and costs; and 3) develop and implement stochastic optimization methods and compare with the deterministic approach based on point-estimates (mean) of random demand.

We plan to collaborate with a local logistics company or transportation agency in St. Louis, so that we may use their real life data to test and validate our models and solution methods.



  • Midwest Transportation Center
  • University of Missouri - Saint Louis