Individualized time-dependent water pricing for residential consumers

Abstract

We consider a water supplier that provides water to residential consumers. The supplier desires the ability to control the consumption and the funds to protect, maintain, upgrade and expand the available infrastructure. To do so, the supplier implements individualized dynamic pricing that maximizes the weighted sum of the total supplier profits and the total consumer convenience. The supplier has the constraint of providing water cheap enough to allow consumers to fulfill their basic needs, but expensive enough to discourage them from consuming too much, depleting the reserves and congesting and deteriorating the available infrastructure. Our work contributes to the literature by providing the mathematical formulation and solution of an individualized time-dependent pricing problem, so the supplier can determine the optimal individualized time-dependent pricing for any given consumer group and any given time interval. This work integrates the allocated reserve and unit cost of the supplier, the ideal consumption, minimum required consumption and price sensitivity of each consumer and the price cap imposed by the government. The behavior of the results to parameter value deviations is observed through computational experiments and explained. The ideal consumption and price sensitivity of each consumer for these experiments are provided by the largest water supplier of Greece. An increase of up to 3225% in the objective function the supplier wishes to maximize is achieved, compared to uniform pricing.