Optimal Recovery From Disruptions In Water Distributions Networks

Abstract

: In this study, we develop a bi-level optimization model for recovery of a disrupted water distribution system. The model minimizes the total cost of recovery of the system. The cost includes the repair cost of the system and systemic impact of disruption on the system during the repair process. The systemic cost is calculated in terms of the unmet demand while the system is still damaged. The upper level problem is to schedule the repair tasks, and the lower level problem is to optimize the supply of water (optimal mitigation) given the schedule from upper level problem. The upper level problem is solved using Simulated Annealing, and the lower level problem uses a Generalized Reduced Gradient algorithm. We first apply and validate the model on a small water distribution system with only three elements damaged due to disruption. In this case, the recovery process requires tasks that can be performed in only one mode. We later apply the model to a larger and more complex water distribution system with eight elements damaged due to disruption. We perform three different experiments on this system . In the first experiment, limited resources are available at each time period. In the second experiment, the resources are increased by 50%, and in third experiment, some tasks are provided with an additional mode. The results show that the availability of resources has a significant impact on total cost of recovery of systems. Adding modes to a few tasks can help in reducing the total cost of disruption on the system.