Optimal Design of Gravity-Fed Sewer Lines Using Linear Programming

Abstract

The cost of a sewerage system is mainly governed by the size of the sewer pipe, excavation depth and manhole spacing. A linear programming model is developed to minimize the total cost comprising of the pipeline cost, excavation cost and manhole cost of the sewer line. The constraints of the optimization model are related to the distance between two consecutive manholes, and slope of the sewer line to maintain the self-cleansing velocity. The nonlinearity due to the pipe size is eliminated by considering only those available diameters that satisfy the self-cleansing velocity constraint. The model selects the combination of pipe sizes and slope of the sewer line between different manholes maintaining the self-cleansing velocity, which results in the minimum value of the total cost of the entire sewer line. The application of the developed model is illustrated with the help of an existing design problem, and the results are compared with the available solution using forward recursive dynamic programming. It is found that the linear programming model results in lesser value of the total cost of the sewer line.