A numerical and an analytical method for optimum planting date determination

Apart from number and size of machines in a farm, operations scheduling can also affect timeliness costs. In this study a new equation was presented for determination of timeliness costs and it was proven that the new equation is a generalization of the well-known ASABE standard equation. Based on the new equation, a parameter namely, timeliness index was defined that indicates the distribution of an operation around the optimum time of performing the operation. By minimizing the index, the whole timeliness cost is minimized. Since the planting operation is highly sensitive to its time of accomplishment, timeliness cost was determined accordingly. In this study the optimum planting starting date (opls) regarding the concept of timeliness costs, was determined. If for any reason, the planting operation cannot be performed in the minimum planting period, an optimization method is required to determine opls. For this, a numerical approach and an analytical method were presented for determination of opls and a computer model was developed based on the numerical method. opls was determined for the Research Farm of the University of Tehran in Karaj–Iran and both methods showed good agreement with each other.