Chance Constrained Model for Storm-Water System Design and Rehabilitation

Abstract

A mixed integer chance constrained optimization model was developed to determine design and rehabilitation management strategies for storm-water drainage systems conditioned on the likelihood of exceeding the system's conveyance capacity. The model is multiobjective in nature and capable of considering multiple design or rehabilitation alternatives. Model objectives include the minimization of cost and probability of system failure. The probability that storm-water flows exceed the conveyance capacity of any network segment within the system is expressed as a chance constraint. The model combines kinematic wave routing methods and second-moment analysis to formulate the chance constraint. In this manner, only the mean, variance, and form of the distribution of the storm-water flows are needed to formulate the deterministic equivalent optimization model. To illustrate the model, an example is presented using an existing storm-water drainage network at Duke University, Durham, North Carolina. Results of this example specify the most cost-effective storm-water network design at varying system reliabilities. These results define trade-off relationships between total system cost and the probability of system failure.