Optimum pipe network of tofu and tempe wastewater distribution using multiple sources single sink network model

The purpose of this research is to find the optimum route to flow wastewater from multiple sources to a single facility of wastewater treatment in Mojosongo, Surakarta, Indonesia. The sources are 11 small enterprises of tofu and tempe producing 1000 litres wastewater everyday on average from each location. Local government of Surakarta want to bulid a pipe network to flow the waste from those locations to a single sink facility with minimum distance. There are several feasible paths from each node of 11 sources of waste to the treatment facility. We propose a multiple sources single sink network model to solve this problem. The distance of each link of pipe network connecting two nodes is the only parameter. We assume the total cost to build the pipe network is proportional to the total distance and the pipe at each link to is capable to flow the waste water produced by sources flowing waste to the link. We introduce one dummy node to represent the origin of pipe network where there is no wastewater source at the node. The problem is formulated as a single objective integer linear programming model and branch-and-bound algorithm is used to solve the model.