A Bi-level Formulation for Centralized Resource Allocation DEA Models
Subject Areas : International Journal of Mathematical Modelling & Computations
Mohammad Moghaddas
1
*
,
Ghasem Tohidi
2
1 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Keywords: Data envelopment analysis, Stability, Neural network, Centralized resource allocation,
Abstract :
In this paper, the common centralized DEA models are extended to the bi-level centralized resource allocation (CRA) models based on revenue efficiency. Based on the Karush–Kuhn–Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). A recurrent neural network is developed for solving this one-level mathematical programming problem. Under a proper assumption and utilizing a suitable Lyapunov function, it is shown that the proposed neural network is Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, an illustrative example is elaborated to substantiate the applicability and effectiveness of the proposed approach.