Competition and Evaluation of Two-Stage Systems with Fixed-Sum Outputs

Fixed-sum outputs are widely found in fields and lead to fierce competition among individuals or organizations. While competition strategy and efficiency evaluation for single-stage or black-box systems with fixed-sum outputs are discussed, few concerns the network systems with fixed-sum outputs that prevail in practical production and should not be neglected. In this study we analyze the competition and evaluation of network systems with fixed-sum outputs. First, we propose a data envelopment analysis (DEA) method searching a competition equilibrium that all basic two-stage systems are relatively efficient, by simultaneous adjustment of their intermediate outputs and fixed-sum outputs simultaneously, rather than only adjusting fixed-sum outputs, then proposing models for evaluating system competition efficiency and intervals of stage efficiencies based on the equilibrium frontier. Second, we focus on the normal case in which systems’ intermediate outputs may be excessive or inadequate for the uncertain capacity of final outputs, which are determined by competition instead of personal preference in the condition of fixed-sum outputs. To balance the excess and shortage in achieving the competition equilibrium, a method that allows external transfer of intermediate outputs is developed. An illustrative example indicates that the competition equilibrium can be achieved with less adjustments in some situations, when intermediate outputs are allowed to be externally transferred.