A linear programming model to optimize cropping pattern in small-scale irrigation schemes: an application to Mekabo Scheme in Tigray, Ethiopia
Abstract
Selection of a viable irrigation cropping system, while considering all agronomy and extension constraints , has always been a scientific and professional challenge for agricultural scientists and practitioners. However, this prevailing challenge c an be scientifically addressed using optimization techniques among them linear programming model. The model could take in the initially introduced percentage of crops as an entry point for optimization subjected to all introduced constraints while maximizing the farming income. Favorably, Microsoft Excel program includes a linear programming solver tool, which could be utilized for this purpose. The solver tool could easily be accessed from Excel program Data menu after activating the Add -Ins part of the Excel Options.
Accordingly, a simple and low input linear model was developed applying the Excel Solver tool to optimize the irrigation cropping pattern for the Mekabo small -scale irrigation scheme currently under construction in the Tigray region in Ethiopia. The input parameters were collected from field survey s and an assessment of the on-farm agronomic conditions. The objective function was subjected to agronomy and extension constraints as well as minimum required crop levels to comply with food security strategy. The model could find a viable solution while all constraints and optimality conditions were satisfied. A sensitivity analysis was also performed to analyze all other likely development scenarios. This paper will introduce the developed model and will discuss the processes led to the attainment of an optimized cropping pattern.
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Introduction
Sustainable development of small-scale irrigation schemes has been the cornerstone of food security programs supported by government and external donors in Ethiopia since the 1980s. Many landmark strategies have been introduced to address the ongoing demand for food security, including the development of new small-scale irrigation projects. One of the principle challenges during initial stages of development of a new irrigation project is the selection of a viable cropping system that can be effectively implemented by farmers. This is usually addressed during the feasibility study where engineers attempt to identify a system which optimizes the farmers’ income while considering agronomic conditions and farmers’ knowledge and experience. To determine a right cropping pattern, designers have to discreetly consider various agronomy and extension constraints including crop water consumption, nutrition values, disease and pest resistance, market demand, fertilizer input, labor requirement, capital input, post harvest processing necessity, crop production level, and market prices.
Although, the selection of optimum cropping system is a scientific and professional challenge, it is believed that it can be scientifically addressed using optimization techniques such as a linear programming model. The linear programming model quantifies an optimal way of integrating constraints to satisfy the objective function to optimize crop production and profits for irrigation farmers. The linear programming model, as a reliable optimization technique, has been known in many engineering fields for years. It has also extensive application as an optimization module in several complex engineering software. However, the complex software usually require heavy license fees for installation and operation, which in most cases is beyond the financial reach of many small-scale irrigation projects. Favorably, Microsoft Excel program includes a linear programming Solver, which could be utilized for simple optimization scenarios like optimization of cropping pattern in small-scale irrigation projects. This Solver tool could easily be accessed from Data menu after activating the Add-Ins part of Excel Options. The model analyzes the cases where the existing limitations must be satisfied in a way to maximize the profit or minimize the cost (Frizzone et al., 1997). Birhanu et al. (2015) successfully used linear programming model to obtain an optimized cropping pattern for the Koga Irrigation Dam project in Ethiopia. Aparnathi and Bhatt (2014) introduced surface and ground water as constraints to their linear programming model to optimize the cropping pattern for a project under study in their region. Bertomeu and Gimenez (2006) utilized a simple linear programming model to optimize the allocation of farmers' resources and lands for maximum benefit. Frizzone et al. (1997) employed this technique for optimizing the use of water resource in the Senator Nilo Coelho irrigation project in Brazil.
The principal objective of this study is to develop a low input simple technique approach to maximize farming benefits, considering the agronomic, economic and social constraints facing a typical small-scale irrigation project in Ethiopia. Accordingly, a linear model was developed using the Microsoft Excel Solver tool to determine an optimized cropping system for the Mekabo small-scale irrigation scheme currently being developed in the Tigray region of Ethiopia. The project is located about 50 km north of the city of Mekelle. The input parameters were collected from field surveys and an assessment of on-farm agronomic factors, as well as the expertise and operational constraints of the new irrigation farmers. The objective function (Maximizing farming benefits) which includes decision variables (percentage of crops in the cropping pattern) was subjected to agronomy and extension constraints as well as minimum required crop levels to comply with the food security strategy. After inputting data in Excel sheet and running the Solver, the linear programming tool could successfully find a solution while all constraints and optimality conditions satisfied. A sensitivity analysis was also performed to analyze all other likely development scenarios. This paper will discuss the processes that led to the development of an optimized cropping system for Mekabo small-scale irrigation scheme.
Conclusion
a. The linear programming model for Mekabo scheme successfully optimized the cropping pattern for maximum income while satisfying all of the imposed constraints.
b. With the current sets of constraints and input data, the model showed a high level of sensitivity to the changes in the percentage of vegetables as well as vegetables and cereals combined.
c. The model exhibited low sensitivity for the imposed changes to cereals and cash crops.
d. During sensitivity analysis the model could not find a feasible solution in some circumstances because the conditions of one or more constraints could not be satisfied during the optimization process. Achieving a feasible solution in these cases may mean that the assessment values for constraints need to be improved. This could be achieved by reconsidering a better on -farm water management, increased fertilizer, additional pesticide inputs, improved seed varieties, increased labor, additional capital input, and increased post harvesting management.