No abstract

SUMMARYAn econometric methodology is developed for nonparametric estimation of concave production technologies. The methodology, based on the principle of maximum likelihood, uses entropic distance and convex programming techniques to estimate production functions. Empirical applications are presented to demonstrate the feasibility of the methodology in small and large datasets.

No abstract

We develop an efficiency measurement framework for systems composed of two subsystems arranged in series that simultaneously computes the efficiency of the aggregate system and each subsystem. Our approach expands the technology sets of each subsystem by allowing each to acquire resources from the other in exchange for delivery of the appropriate (intermediate or final) product, and to form composites from both subsystems. Managers of each subsystem will not agree to "vertical integration" initiatives unless each subsystem will be more efficient than what each can achieve by separately applying conventional efficiency analysis. A Pareto Efficient frontier characterizes the acceptable set of efficiencies of each subsystem from which the managers will negotiate to select the final outcome. Three proposals for the choice for the Pareto efficient point are discussed: the one that achieves the largest equiproportionate reduction in the classical efficiencies; the one that achieves the largest equal reduction in efficiency; and the one that maximizes the radial contraction in the aggregate consumption of resources originally employed before integration. We show how each choice for the Pareto efficient point determines a derived measure of aggregate efficiency. An extensive numerical example is used to illustrate exactly how the 2 subsystems can significantly improve their operational efficiencies via integration beyond what would be predicted by conventional analysis.

SUMMARYA cutting plane algorithm for the solution of generalized geometric programs with bounded variables is described and then illustrated by the detailed solution of a small numerical example. Convergence of this algorithm to a Kuhn-Tucker point of the program is assured if an initial feasible solution is available to initiate the algorithm. An algorithm for determining a feasible solution to a set of generalized posynomial inequalities which may be used to find a global minimum to the program as well as test for consistency of the constraint set, is also presented. Finally an application in optimal engineering design with seven variables and fourteen nonlinear inequality constraints is formulated and solved.