Risk efficiency of optimal water allocation within a single and multi-stage decision-making framework
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The main objective of this research was to compare the results obtained from modelling irrigation water allocation decisions within a single-stage decision-making framework with the results obtained within a multi-stage sequential decision-making framework under a full water quota and a restricted water quota. A unified irrigation decision-making framework was developed to model the impact of the interaction between water availability, irrigation area and irrigation scheduling decisions as multi-stage sequential decisions on gross margin variability. An Excel ® risk simulation model that utilises evolutionary algorithms embedded in Excel® based on the Soil Water Irrigation Planning and Energy management (SWIP-E) programming model was developed and applied to optimise irrigation water use. The model facilitates the simulation of the economic consequences resulting from changes to the key decision variables that need to be optimised through gross margin calculations for each state of nature. Risk enters the simulation model as crop yield risk through different potential crop yields in each state of nature and stochastic weather which determines irrigation management decisions. Water budget calculations were replicated to include 12 states of nature within a crop rotation system of maize and wheat. The risk simulation model was applied in Douglas, a typical location of an irrigation farm. The results showed improved risk management within a multi-stage decision-making framework as indicated by higher gross margins and reduced variability due to improved irrigation scheduling decisions under both a full and restricted water quota scenario. Close to potential yields, if not full potential yields were achieved within both decision-making frameworks. However, a significant reduction in per state irrigation water use resulted within a multi-stage decision-making framework sequentially resulting in improved gross margins. A full irrigation strategy with reduced areas was followed under a restricted water quota with reduced gross margins resulting owing to lower gross incomes. The resulting impact of risk aversion on gross margin risk was insignificant within a multi-stage decision-making framework, whilst a more evident impact within a single-stage decision-making framework was indicated by a significant increase in minimum gross margins. The resulting monetary value of modelling irrigation decision within a multi-stage sequential decision-making framework was R11 149 and R14 413 under a full and restricted water quota respectively for a risk averse decision-maker. The resulting value of a multi-stage decision-making framework assuming risk neutrality was significantly lower at R4 261 and R7 019 for a full and restricted water quota respectively. Results indicate that the interaction between different decisions made at different times during the growing season as represented with a multi-stage decision-making framework, becomes much more important under restricted water supply conditions taking risk aversion into account. The cost of a water restriction within a single-stage and multi-stage decision-making framework of R218 319 and R215 561 respectively resulted under a risk neutral framework. Under risk aversion, a slightly lower cost of a water restriction of R212 513 and R209 249 was generated within a single-stage and a multi-stage decision-making framework respectively. The lower costs for a water restriction within a risk framework owes to the fact that risk averse decision-makers already make conservative decisions hence a water restriction will have a relatively limited impact on such a decision-maker. The overall conclusion is that, ignoring modelling irrigation decisions as sequential decisions within a multi-stage decision-making framework overlooks the risk reducing impact of the true nature of irrigation decisions. As a result, water use dynamics are not explicitly accounted for with the gross margin risk and the value of a water restriction over-estimated. The main recommendation from this research is hence that, agricultural water allocation policies should be formulated based on crop water optimisation models that consider the multi-stage decision-making framework within which irrigation decisions are made to ensure that the impact of any given policy on water use management is not over-estimated. Further research should focus on testing the global optimality of the solutions of the risk model with alternative evolutionary algorithm techniques and also reformulation of the model within a mathematical programming environment.
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