Application of Stochastic Dynamic Programming (SDP) for the optimal allocation of irrigation water under capacity sharing arrangements

This study attempts to arrive at an optimal allocation of irrigation water using capacity sharing (CS) as an institutional arrangement, and stochastic dynamic programming (SDP) as an optimisation model. It determines the value of an additional unit of water under a crop enterprise mix of lucerne-maize-wheat (LMW). SDP is an improvement on linear programming (LP) under stochastic conditions. The SIM-DY-SIM Model was used to simulate optimal returns, decision and policy variables under varying conditions of capacity share. LP results show that wheat has the highest MVP of R0.39/m3, with maize exhibiting the lowest value of R0.09/m3. The MVPs generated with SDP range between R0.06/m3 and R0.35/m3 on the whole farm basis, with revenue to the farmer increasing with an increase in CS content and increased percentage water release. However, the MVP of water decreased with the increased supply of the resource - a phenomenon that follows the general rule of decreasing marginal utility of a resource as more of it is used