Optimizing Cropping Pattern Using Chance Constraint Linear Programming for Koga Irrigation Dam, Ethiopia

Optimal cropping pattern decisions without consideration to water supply uncertainty would result in yield/benefit that is less than expected and probability of system failure in meeting a given irrigation demand. In this study, a chance constraint linear programming (CCLP) model was used for optimizing cropping pattern for major crops grown at Koga Irrigation scheme, Ethiopia. The model incorporated uncertainty of inflow at exceedance probability of 90%, 80%, 70%, 60% and 50%. The model objectives were yield and benefit maximizations subject to land and water availability constraints. Each objective function has four scenarios. The models were solved using LINGO14. The cropping patterns under yield and benefit maximization models were found to be identical under all scenarios. However, the cropping patterns of each model varied among scenarios. The study showed that the possibility of irrigating 5904.3 to 8051.0 hectares of land at 80% by optimizing cropping patterns at irrigation efficiency of 48%. This could increase the yield by 108 to 153%, benefit by 153 to 208% and physical water productivity by 132% to 186% and economic water productivity by 205% to 241% of the actual values. In conclusion, the irrigated land in 2012/13 was below the optimal value and the irrigation water was mismanaged. Therefore, with optimal crop planning and water management, the design command area of 7000 ha could be irrigated. Finally, a study should be made to determine optimal levels of crop water deficit that maximize water productivity.