Fertilizer Purchase Optimization as a Problem of Mixed Integer Nonlinear Programming

Purpose: This paper aims to introduce a model of fertilizer purchase optimization - an improvement of the one originally developed for supporting African farmers. The improvement takes into account necessity of purchasing fertilizers in bags of fixed weight instead of arbitrary amounts. Design/Methodology/Approach: A fertilizer purchase optimization model expressed as a nonlinear programming problem and its implementation in Microsoft Excel, once developed for a project named Optimized Fertilizer Recommendations in Africa (OFRA), were analysed. An extension of the above model in the form a mixed integer nonlinear programming problem and its implementation in Microsoft Excel were developed. Findings: The model of fertilizer purchase optimization developed for OFRA omits an important issue – availability of fertilizers in fixed-sized “portions” only (50 kg bags). An improved model which includes the inevitable purchases of fixed-sized “portions” of fertilizers into the optimality criterion is introduced. Practical Implications: The improved model is much more compliant with the conditions of the fertilizer market than the original one whereas performing the optimization remains unchanged from the point of view of the user. Originality/Value: Creating a fertilizer purchase optimization model taking into account real market conditions (sale of fertilizers in fixed-sized “portions) handles an issue which is disregarded in many existing models despite its influence on the final financial output.