Fairness-guided design of water distribution networks for agricultural lands

Allocating finite resources (utility) among stakeholders in a fair manner is a nontrivial task. In this work, we provide an optimization framework to design water distribution networks that ensure fair allocations to multiple agricultural lands. Our formulation is a mixed integer nonlinear programming model that uses different schemes (social welfare, Rawlsian welfare, and Nash allocation) to guide water allocations to agricultural lands of varying sizes and over different seasonal periods. We demonstrate the applicability of our model by using a case study in the State of Sinaloa, Mexico. We find that the social welfare approach (the most widely used approach for social planning) yields allocations that are not unique and, as a result, the solution is ambiguous. Moreover, this approach fails to properly capture relative sizes of the stakeholders and tends to favor large stakeholders. We also demonstrate that the Rawlsian welfare approach favors smaller stakeholders but at the expense of more expensive designs; moreover, this approach also suffers from ambiguity due to solution multiplicity. Finally, we demonstrate that the Nash approach provides unique solutions that balance the utilities of large and small stakeholders in a more systematic manner.