Economic development of groundwater in arid zones with applications to the Negev Desert, Israel

A mixed binary integer linear program is formulated to determine the economic development of marginal groundwater sources at local demand sites in an arid region. These marginal sources are required to augment the supply from an overloaded regional source. The model accounts for variable costs of supply, fixed investment costs, capacity constraints at the regional and local levels, and water quality requirements at the local sites. A Lagrangean relaxation reduces the model to a series of simple local problems, the solution of which provides an optimal sequence for developing the marginal groundwater sources while reducing the demands on the regional source. A heuristic and an exact procedure are also proposed to solve the problem for arbitrary levels of supply from the regional source. The exact procedure uses characteristics of the optimal solution to reduce the model to a series of knapsack-type problems. The theory is applied to a small case study taken from the Negev Desert in southern Israel.