Fund allocation model for pipe repair maintenance in water distribution networks

Funds for repair maintenance operations of municipal water distribution networks are normally allocated to each predefined pipe section of the network. During the planning time period whenever pipe leaks are detected in a section, repair actions are udertaken until the funds assigned to the section are exhausted. In practice, funds are usually allocated to each pipe section based on the expected number of leak occurrences, leak size and leak duration or the expected leak volume. The allocation of limited repair funds to different pipe sections is however, frequently done without accurate quantitative analysis that carefully considers random events. In this paper, a mathematical model that considers explicitly the randomness of the time interval between leak occurrences and leak durations is developed and proposed for city authorities to ascertain the assignment of optimal funds for pipe repair maintenance operations. The objective of the proposed model is to maximize the net benefit, defined as the benefit gained from water saving due to repair fund allocation minus the allocated repair funds. The model is extended to determine the optimal allocation of the limited repair funds to different sections of the network by applying a Lagrangian relaxation method to find an optimal solution.