Technion, IEM faculty - Operations Research seminar

Speaker: Lea Kraiskaia
 
Title: PROBLEMS AND EXTENSIONS OF EFFICIENCY MODELS IN QUASI-CONCAVE ENVIRONMENT
 
Date: 14/03/2011
 
Time: 12:30
 
Place: Bloomfield-527
 
Abstract:
 
 <http://ie.technion.ac.il/seminar_files/1299404645_Lea_seminar.doc>
 
But here it is also:
 
abstract: The process of production is defined directly by the technology T, which is defined by collection of
possible pairs of inputs x and outputs y. In a case of a single output the technology is defined by the production
function, which expresses the level of output y that can be achieved by given input x. The technology defines the
following sets: the set of possible inputs, and the sset of possible outputs. The common assumption is that those two
sets are convex. In many cases it is assumed that the technology is concave. The term ^”concave technology" is
derived from the special case where there is a single output and the production function is concave. Similarly, we
will define quasi-concave technology, in which the production function is quasi-concave. Certainly in both of those
cases the sets are convex. The necessary conditions to convexity of these sets are unknown, the conditions which are
defined above are sufficient. The present research consists of two parts. The first problem is linear formulation for
output radial efficiency of quasi-concave model for multiple inputs and multiple outputs. Previous researches
concerning efficiency in quasi-concave model presented calculation of input efficiency, since it^“s a simple linear
programming. Also, output efficiency was calculated for one output only. The analysis of the output efficiency
quasi-concave model indicates that coefficients are always between concave model coefficients and the FDH
coefficients. The quasi-concave model has lower separation ability than the concave model. Also, the more outputs are
used, the lower the separation ability. The results of this research demonstrate that just like the concave model,
the quasi-concave model for multiple outputs is a useful and applicable, especially since it can be difficult to
aggregate multiple outputs into one. The second problem is an attempt to calculate production function in conditions
of error existing in the output and uncertainty in the input. In this research a new heuristic algorithm was
developed. It doesn^“t necessary give optimal solution but it always returns efficient outputs.
 
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