Routing field channels through a tertiary unit with heterogeneous fields

The extensive irrigation systems of South Asia are predominately a hierarchy of canals delivering water to a tertiary unit. A network of field channels transfers water within the tertiary unit to the field where it is applied using surface irrigation. The network of field channels within a tertiary unit is often left to the farmers/farmer associations to construct, maintain, and operate. This paper develops a mathematical model/algorithm for routing the field channel along the existing field boundaries such that every field is serviced by a field channel and minimizing the total length of the field channel as a proxy measure of the cost of construction of field channels. The models developed in this paper are formulated as integer programs, implemented in a general-purpose solver. The model is applied to a tertiary unit of the Gomal Zam Irrigation System in Pakistan and shows that for this particular application, the optimized total length of field channels is 9,463 m compared with 11,313 m when an expert judgment is used, a reduction of 1,850 m (20%).