Stochastic Optimization Model for Short-term Planning of Tanker Water Supply Systems in Urban Areas

Tanker-based water distribution systems are amongst one of the most prevalent methods to supply water in many developing countries facing water crisis and intermittent piped water supply. These tanker water supply systems need tighter coordination between the water sources, treatment facilities, consumers and tanker suppliers to efficiently manage timely delivery and quality water. Furthermore, accounting for the uncertain nature of customer demands while making the planning decisions would not only aid in achieving minimum operational cost but is also important in reducing the water wastage. This paper proposes a two-stage stochastic recourse programming model for an optimal planning and scheduling of tanker water supply system under daily demand uncertainty. The main objective is to supply water to maximum number of consumers with minimum total operating costs. A solution strategy combining Sample Average Approximation (SAA) and Monte-Carlo Simulation (MCS) methods, to generate an equivalent deterministic MILP (mixed integer programming problem) model with multiple scenarios of demand uncertainty realization, is adopted for problem solving. The proposed model is applied to an example tanker water supply system and the benefits of two-stage stochastic modelling in making agile decisions incorporating the effect of uncertainties are illustrated. The results also demonstrate the efficacy of adopting stochastic programming models and methods in such real-world application cases.