A neurodynamic scheme to bi-level revenue-based centralized resource allocation models

This paper presents a new bi-level centralized resource allocation (CRA) model based on revenue efficiency which extends the classical revenue efficiency models to a more general case. In real world, there are large organizations like restaurant chains in which all the decision making units (DMUs) operate under the supervision of a central decision maker. In such intraorganizational scenario, the proposed bi-level model attempts to maximize the total revenue produced by all the DMUs and to minimize the reallocation cost in a hierarchical order under a centralized decision-making environment. Using the Karush-Kuhn-Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program with complementarity constraints (MPCC). According to optimization theory and some concepts of ordinary differential equations, a capable neural network is then developed to solve this one-level mathematical programming problem. Under proper assumptions and utilizing a suitable Lyapunov function, the proposed neural network is analyzed to be Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, some illustrative examples are elaborated to substantiate the applicability and effectiveness of the proposed approach.