Scalarization and convergence in unified set optimization

This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterizations for a unified preference relation and the corresponding unified minimal solution in terms of a generalized oriented distance function of the sup-inf type. We establish continuity of a function associated with the generalized oriented distance function and provide an existence result for the unified minimal solution. We establish Painlevé-Kuratowski convergence of minimal solutions of a family of scalar problems to the minimal solutions of the unified set optimization problem.

Economic Evaluation of Yield-Increasing Wheat Seeds Using a Distance Function Approach

New wheat-breeding techniques, such as hybridization and genetic modification, show increasing yield potential. This study involves estimating multi-output multi-input production technology by stochastic frontier techniques to evaluate the economic value of this yield potential. An input-oriented distance function is formulated and applied to European Farm Accountancy Data of 23 European countries. Based on the analysis, an average shadow value is derived for the increase in the marginal yield of wheat that corresponded to 18.87 €/ha. Further, technical change, technical efficiency, and returns to scale are measured for different European regions.