A Quadratic Programming Algorithm for Deriving Efficient Farm Plans in a Risk Setting

Résumé du livre

The main focus was on developing an algorithm and supporting computer programs for use by extension personel to counsel farm managers on problems of enterprise choice. Investigation was initiated from the complete certainty viewpoint of linear programming. Upon introducing uncertainty, ramifications of changing expected income, variance and the correlation coefficient between enterprises were explored. This was extended to develop a quadratic programming algorithm which resulted in complete algebraic specification of the efficiency frontier through integration of the Lagrangian multipliers. The Von Neuman-Morgenstern utility analysis framework was posed for selecting the best alternative but dismissed as being cumbersome for practical application. A probability of loss function which places confidence intervals about the income level of each alternative was used since it is more amenable for application by extension workers. Data requirements were found to be no more difficult to satisfy in the quadratic programming model than in the presently used linear programming models. The triangular probability distribution was used in obtaining subjective estimates for the mean and variance of prices and yields. Subjective methods for deriving covariances between incomes from farm enterprises were discarded as being difficult to administer and subject to inconsistencies. A regional correlation matrix was used from which specific covariance estimates for individual decision problems were computed. Seven cases were studied as a test of the computer programs and the algorithm. Four of these cases were submitted from actual farm situations by an extension agent. Output from the computer provided each farmer with a report containing the composition of every efficient plan, the pattern of resource use, the shadow prices of limiting resources and confidence statements about achieving certain levels of gross margin. The report was presented in tabular form, in graphic form and as a set of algebraic equations. Although no extensive test of acceptance by farm decision makers was made, results with the four cases studied appeared encouraging.