Risk-Based Two-Step Optimization Model for Highway Transportation Investment Decision-Making

Abstract

A new methodology is introduced for project selection that explicitly addresses issues of achieving maximized overall project benefits by selecting a subcollection of candidate projects for possible implementation at a given budget level while controlling the total risk of the expected project benefits within an acceptable lower bound. The covariance value is utilized to denote the risk of the expected benefits of jointly implementing two projects, in which each project maintains a range of possible benefits and a probability distribution. The summation of all covariance values corresponding to all possible project implementation combinations represents the total risk of the expected benefits. The methodology contains two-step optimizations. First, the Markowitz mean-variance model is employed to establish the lower-bound risk of project benefits for a given budget level. Second, the conventionally accepted zero/one knapsack model for project selection is augmented to incorporate the lower-bound risk established from the first-step optimization as one additional chance constraint. In this way, the overall benefits of projects selected for implementation are maximized while controlling the total risk of the expected project benefits within a lower bound for a certain percentage of time. The proposed model is applied for a 6-year statewide interstate highway project selection and programming. Cross comparisons are made in the consistencies of project selection results generated from the basic knapsack model, proposed two-step enhanced knapsack model, and current state highway programming practice.