ERIC Number: ED228274
Record Type: RIE
Publication Date: 1982-May
Reference Count: 0
Using a Polytope to Estimate Efficient Production Functions of Joint Product Processes.
Simpson, William A.
In the last decade, a modeling technique has been developed to handle complex input/output analyses where outputs involve joint products and there are no known mathematical relationships linking the outputs or inputs. The technique uses the geometrical concept of a six-dimensional shape called a polytope to analyze the efficiency of each constituent unit--department or university--within a higher education system. Farrell's method represents each institution as a point with multiple input and multiple output (joint products) coordinates. The institutions are plotted in six dimensional space, then joined by line segments to enclose the smallest possible convex region as a six dimensional polytope. If the surface of the polytope is the frontier productivity function, then the distance to the surface from each point measures the production efficiency of that point. The model and variations are largely explained by use of simple examples in two dimensions. Computer algorithms developed to handle the more realistic cases use higher dimensional polytopes. References to more detailed expositions, accounts of actual applications, and existing computer programs enlarge on this description of the methodology. (Author/CM)
Publication Type: Speeches/Meeting Papers; Reports - Research
Education Level: N/A
Authoring Institution: N/A
Identifiers: Joint Product Processes (Mathematics); Polytope (Geometry); Production Process Model
Note: Paper presented at the Annual Meeting of the Association for Institutional Research (22nd, Denver, CO, May 16-19, 1982). Some tables may be marginally legible due to small print.