Polyhedral Assurance Regions with Linked Constraints

Abstract

The duality between efficiency and zero profit maxima has long characterized the theory of perfect competition in economics. Similarly, Data Envelopment Analysis (DEA) models in ratio and convex form imply zero profit maxima under the normalizations required for the linear programming (LP) reductions. Such zero profits are implied both in the absence and in the presence of cone-ratio (CR) assurance region (AR) bounds on the multipliers. However, if the AR input-output bounds on the multipliers are linked (linked-cones - LCs), which is precluded with CRs, then the normalizations required for the LP reduction must be dispensed with; and the DEA problem must be reformulated to be meaningful. This LC reformulation, as developed here, shows efficiency and profitability are separate concepts; and it gives new absolute profitability and non-linear efficiency measures. Both measures are relative to the full (m + s)-dimensions of the multiplier spaces, in contrast to the (m + s - 2)-dimensions of the LP normalized multiplier spaces. For the multiple output, multiple input problem, LP computational procedures may be used to find the maximum profit solutions; for the one-output problem, a non-linear programming procedure is suggested to find the efficiency solutions. Additional research is required to find the efficiency solutions for multiple output problems.

Working Paper No.92