A hybrid piecewise-linear/Newton approach to solve multi-period production and distribution planning problems in large water supply networks 

Efficient production and distribution planning of water is a challenging problem that many drinking water companies face. The development of effective tools to optimally supply this vital resource is therefore essential. Nowadays, many drinking water companies rely on simulation software packages (EPANET, InfoWorks) for the daily operation of their network. This software allows the user to make accurate and thus reliable simulations of the network for a chosen configuration. However, the user-defined scenario’s do not consider the lowest operating costs. Very often the pumps are working at a suboptimal point in their system curve and water production centers are not being used efficiently. This talk is concerned with the optimization of production and distribution operations in a large-scale mesh-structured water-supply network with multiple production centers and buffers that can re-inject water into the network. This planning optimization model involves complex hydraulic constraints, such as friction losses and pump curves and the relationships between pressure and flow in power terms, which are nonlinear equality constraints. Binary variables are also needed to model the free inflow or re-injection possibility of water at reservoirs. The resulting optimization problem is thus a nonconvex mixed-integer nonlinear program (MINLP). We propose an algorithm based on successive linearization steps to solve this model. We apply a piecewise linear approach with a (reduced) logarithmic number of binary variables. This approach provides us with estimates on the production totals and the stored quantities in buffers. Starting from this (slightly infeasible) solution, a feasible and economically acceptable plan is then derived using Newton’s method. Tests on an existing network operated by ‘De Watergroep’, a major drinking water company in Flanders, show that this approach leads to close to optimal solutions in short computational time