This study addresses the optimal pipe-sizing problem of a tree-shaped gas distribution network with a single supply source. An algorithm was developed with the aim of minimizing the investment for constructing a gas distribution network with a tree-shaped layout in which demands are fixed. The construction cost is known to depend on the pipe diameters used for each arc in the network. However, under the assumption that pipe diameters are continuous, we prove that it is possible to obtain the minimum construction cost directly and analytically by an iterating procedure that converts the original tree into a single equivalent arc. In addition, we also show that expanding the converted single arc inversely to the original tree computes the optimal continuous pipe diameter for each arc. Following this, we present an additional heuristic to convert optimal continuous pipe diameters into approximate discrete pipe diameters. The algorithms were evaluated by applying them to sample networks. The numerical results obtained by comparing the approximate discrete diameters with the optimal discrete diameters confirm the efficiency of our algorithms, thereby demonstrating their suitability for designing real gas distribution networks. 
Optimal pipe-sizing problem of tree-shaped gas distribution networks