Abstract
Optimising crop planning in conjunction with intra-seasonal water allocation necessitates the use of daily water budget calculations to determine the timing and amount of irrigation events, which complicates the solution of the problem to global optimality. The main objective of this research was to compare the intra-seasonal water allocation of a mixed integer nonlinear programming (MINLP) model with that of differential evolution (DE), to allocate a limited amount of water while considering irrigable area and the irrigation schedule that will maximise the total gross margin. Results show that both solution procedures adhere to economic theory of water allocation under limited water supply. The conclusion is that the MINLP model most likely achieved very near global optimality as the solutions of the two models were very close to each other. DE holds promise to solve more complex models involving risk and multiple crops.
Highlights
Dealing with increasing water scarcity will be an important research topic during the decade, in the midst of producing enough food for a growing population (Paly et al, 2010)
The results show that the mixed integer nonlinear programming (MINLP) solver outperformed the differential evolution (DE) algorithm in terms of achieving a higher total gross margin
Maize productivity plateaued at the maximum potential maize yield of 17 t/ha when water allocations exceeded 525 mm/ha for the 30 ha listed for both MINLP and DE
Summary
Dealing with increasing water scarcity will be an important research topic during the decade, in the midst of producing enough food for a growing population (Paly et al, 2010). According to Garg and Dadhich (2014), there is a shift in research from maximising crop yield per unit area to increasing productivity of water through deficit irrigation under limited water supply conditions. Transpiration is reduced when the root zone soil water content drops below a crop specific threshold (Allen et al, 1998) and, the water deficit reduces crop yield. The onset of water deficit will only be known if the soil water content is tracked on a daily basis and the impact thereof on crop yield is determined by the sensitivity of a specific growth stage to the water deficit (Doorenbos and Kassam, 1979). Even if the allocation per hectare is known, the irrigator still needs to schedule water allocation to minimise electricity costs
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