A Multiobjective Water Allocation Model for Economic Efficiency and Environmental Sustainability: Case Study

TL;DR

The paper addresses irrigation-water allocation under hydrological variability by extending the Lewis and Randall framework to enforce nonnegative pumping and surface-water use, while explicitly incorporating environmental-flow and canal-capacity constraints. It introduces three models: NB_max (maximize net benefit), EFD_min (minimize environmental-flow deficiency), and a multiobjective NB–EFD model, and tests them with a Rajshahi Barind Tract case study using SQP-based solution approaches. The study demonstrates economically and hydrologically consistent allocations across dry, average, and wet years and reveals Pareto-optimal trade-offs between farm income and ecological protection, offering a practical decision-support tool for water-scarce basins. The framework provides actionable insights for crop-area allocation, canal-scheduling, and groundwater use, while highlighting opportunities for future work in incorporating stochastic inflows, energy costs, and dynamic canal operations to enhance resilience.

Abstract

The management of irrigation water systems has become increasingly complex due to competing demands for agricultural production, groundwater sustainability, and environmental flow requirements, particularly under hydrologic variability and climate uncertainty. Addressing these challenges requires optimization frameworks that can jointly determine optimal crop allocation, groundwater pumping, and environmental flow releases while maintaining economic and hydrological feasibility. However, existing hydro-economic models, including the widely used Lewis and Randall formulation, may overestimate net benefits by allowing infeasible negative pumping and surface water allocations. We extend the Lewis and Randall framework by reformulating groundwater pumping and surface water use as non-negative, demand-driven decision variables and by explicitly incorporating environmental flow and canal capacity constraints. Three models are developed to maximize economic benefit, minimize environmental deficits, and a multiobjective model that evaluates the trade-offs between these two objectives. An illustrative test case examining optimal crop area allocation and environmental flow management across dry, average, and wet years, using data from the Rajshahi Barind Tract in northwestern Bangladesh, is presented. The results show that the proposed formulation produces economically and hydrologically consistent solutions, identifying optimal strategies when either net benefits or environmental protection is prioritized, as well as Pareto-optimal trade-offs when both objectives are considered together. These findings provide practical insights for balancing farm income, groundwater sustainability, and ecological protection, offering a robust decision-support tool for irrigation management in water-limited river basins.

Figures (13)

• Figure 1: Crop Calendar by Growth Stage in Rajshahi.
• Figure 2: Crop Production in Rajshahi (Tons/ha)
• Figure 3: Inflow and TEF in Dry, Avg. and Wet years
• Figure 4: Rainfall($R_m$) and Evapotranspiration($ET_m$) in Dry, Avg. and Wet years.
• Figure 5: Monthly Allocation of Environmental Flow and Water Requirement for Model 1 in Dry Year.