Optimizing Fleet Composition and Size under Uncertainty in Urban Transit Systems

Project status


Start date: 01/01/16
End date: 01/31/18


Principal investigator:

About the research

The goal of this project was to study the fleet sizing problem in the context of an urban transit system with several unique features: (1) a fleet with a heterogeneous mixture of vehicles; (2) integrated decision support, including acquisition, retirement, and allocation decisions over multiple time periods; and (3) various uncertainties regarding demand for origin-destination (OD) pairs and vehicle efficiency. Over the course of a one-year grant effort, the researchers first developed a deterministic optimization model to minimize the total fleet acquisition and operation costs for all time periods within the planning horizon. Then, a two-stage stochastic programming (SP) model was devised to explicitly cope with uncertainty. The model minimizes the expected total costs by optimizing (1) the here-and-now fleet acquisition and retirement decisions in the first stage and (2) the allocation recourse decisions in the second stage after the random parameters are realized.

The research team collaborated with a local third-party logistics (3PL) company in St. Louis, Missouri, who provided real-world data for this project. Computational studies were conducted to show the benefit of the two-stage SP model by comparing it to the deterministic model using point estimates of random parameters. 


Report: Optimizing Fleet Composition and Size under Uncertainty in Urban Transit Systems (549.01 kb pdf) March 2018



  • Midwest Transportation Center
  • University of Missouri - Saint Louis