Water Planning and Management: An Extended Model for the Real-Time Pump Scheduling Problem

Abstract

This work deals with the modeling of a water distribution system with a view to optimizing real-time pump schedules through the use of an integer linear programming (ILP) tool. We describe a number of different constraints that need to be modeled, and we provide mathematical models for each of them. Along with the more familiar capacity and demand satisfaction constraints, we consider specific constraints related to requirements such as water quality and maximum power consumption. Problems include taking the discrete behavior of pumps into account and modeling hydraulic phenomena. Solutions must be applicable to very large networks (about 100 pumps and 50 storage tanks in our example), and available computation time is limited in practice (30 min maximum in the application in hand) because of the real-time scheduling constraint. This problem is not new, but there are very few studies in the literature that address these various aspects of the problem at the same time, which implies a significant number of variables. We present as exhaustive a panorama as possible of the constraints and elements that have to be considered when modeling a water distribution system, and then describe our own model and computational work.