A model for conjunctive use of ground and surface water with opportunity costs

In this study, we develop a multi-stage decision model for the conjunctive use of ground and surface water with an artificial recharge. We assume a certain supply and a random demand. We explicitly integrate opportunity costs for the unsatisfied demand. We also incorporate in the model the importance weight attributed by the decision-makers to the final groundwater level at the end of the planning horizon. We show, under some mild assumptions, that the problem can be formulated as a convex program with linear constraints. We illustrate the methodology through a hypothetical example, and discuss the optimal decision policy and its sensitivity to a number of factors.