Optimal replacement policy for single pipes in water distribution networks

In the actual operation of a distribution network, failure can occur in any component of the network, such as pumps, valves, junctions, and pipes. When a component is experiencing failure, the question raised is whether to replace or repair it. For the case of a pipe in the distribution network, which is one of the most frequently subject-to-failure components, there are some aspects that still remain unresolved in relation to practical operations of a maintenance program. In this research paper, a mathematical model is developed which aims to support a decision to repair or replace a main pipe in the state of failure. The objective of the model is to maximize the long-run availability of the pipe under some budget constraints. A semi-Markov process is used to depict the behavior of the pipe, and replacement ages of the pipe in each of its deteriorating stages are taken as the decision variables. The original nonlinear problem resulting from model formulation is converted to a linear problem by some simple transformations, and then numerical experiments are conducted to illustrate the applicability of the proposed model.