Taking account of uncertainty in demand growth when phasing the construction of a water distribution network

As is well known, water systems grow gradually over long periods of time, and the life of piping tends to be much longer than the planning horizon used for pipe sizing. Furthermore, the uncertainty about future demands grows with the length of the time horizon. The design of water-distribution systems should therefore be performed in phases, to follow the gradual network growth, and taking account of the uncertainty connected with demand growth. The design approach proposed in this paper to consider these aspects is able to identify, on prefixed time steps or intervals, the necessary upgrades of the construction where each upgrade consists of installing pipes in new sites or in parallel to pipes that already exist, in order to render the network able to satisfy user demand with acceptable service pressure over the different phases of its life. Uncertainty in demand growth is considered by expressing the growth rate by means of a discrete random variable with assigned probability mass function. Optimization of phasing of construction is then performed by considering two objective functions: present-worth cost of the construction (to be minimized), and minimum-pressure surplus over time (to be maximized), which is represented as a discrete random variable with a derived probability distribution as a consequence of the assumption made on the water demand, which randomly grows from phase to phase of the construction. Within this framework, a specific criterion to rank discrete random variables is presented here. The application of the methodology to a case study shows that optimizing phasing of construction while accounting for uncertainty in demand growth leads to the network being sized more conservatively, so that the network construction obtained turns out to be more flexible to adapt itself to various conditions of demand growth over time.