Linear programming system identification: The general nonnegative parameters case

By linear programming system identification, we mean the problem of estimating the objective function coefficient vector π and the technological coefficient matrix A for a linear programming system that best explains a set of input–output vectors. Input vectors are regarded as available resources. Output vectors are compared to imputed optimal ones by a decisional efficiency measure and a likelihood function is constructed. In an earlier paper, we obtained results for a simplified version of the problem. In this paper, we propose a genetic algorithm approach for the general case in which π and A are of arbitrary finite dimensions and have nonnegative components. A method based on Householder transformations and Monte Carlo integration is used as an alternative to combinatorial algorithms for the extreme points and volumes of certain required convex polyhedral sets. The method exhibits excellent face validity for a published test data set in data envelopment analysis.