An evaluation of quadratic programming and the MOTAD model as applied to farm planning under uncertainty

The objective of this thesis was to study the efficiency of three methods used in farm planning under uncertainty. The first method considered was the QP-VAR method which minimizes the variance of activity returns subject to a minimum income level using a quadratic programming algorithm. The second method is the MOTAD method which minimizes the mean absolute deviation of activity returns subject to a minimum income level using a linear programming algorithm. The third method is the Semivariance method which minimizes the negative 'semi variance of activity returns subject to a minimum income level. The main elements used to evaluate the efficiency of these methods were the magnitude of the biases and the dispersion of the estimates of the income-risk frontier obtained using each method. In order to achieve this objective, a research procedure comprising a theoretical and an empirical study was developed. The theoretical study included an analysis of the measures of risk used by each method and of the assumptions underlying the use of such measures. Furthermore, the plausibility of these assumptions was thoroughly discussed. Using the conclusions drawn from the theoretical study, a set of experiments (the empirical study) was designed to test the efficiency of the methods as estimators of income-risk frontiers. The purpose of these experiments was to test the performance of the methods when applied using sample data of relatively small size rather than complete frequency distributions of activity returns. Two trivariate normally distributed populations (one with high and the other with low degrees of correlation among activity returns) and two trivariate gamma distributed populations (one with high, the other with low degrees of correlation among activity returns) representing activity returns data were generated using a random number generator. Using these populations as data bases, three points on the "true" income-risk frontiers were determined applying the appropriate method in each case. Estimates of the income-risk frontiers were obtained using randomly drawn samples from the populations and the mean risk estimates obtained using each method were compared to establish bias. The degree of dispersion of the estimates as provided by each method was also compared. If two methods were unbiased, the method with the smallest dispersion of its estimates was considered more efficient. A general conclusion drawn from this thesis was that there is not an optimal method to be used in all cases. In order to choose the best method, it is necessary to consider the nature of the farm decision- maker's utility function and the frequency distribution of activity returns. However, the QP-SEMIV method appears to be appropriate under a wider range of empirical situations than the QP-VAR and MOTAD methods.Land and Food Systems, Faculty ofGraduat