A new approach for achievement of the equilibrium efficient frontier with fixed-sum outputs
提出一个线性规划模型，能一步实现固定和产出下的共同均衡有效前沿，解决现有算法计算负担大的问题，并引入权重限制和二次目标以获得唯一前沿。
In a recent paper, Yang et al developed an algorithm based on the extended minimal adjustment strategy and the equilibrium competition strategy to achieve a common equilibrium efficient frontier. However, the computational burden of their algorithm is challenging when a sample contains many inefficient decision-making units (DMUs). In this paper, we propose a linear programming model that can achieve a common equilibrium efficient frontier in a single step, regardless of the number of inefficient DMUs. Furthermore, we demonstrate the existence and the non-uniqueness of the equilibrium efficient frontier and identify its shortcomings through an example. Next, we extend our approach to incorporate weight restrictions to indicate the relative importance of the different inputs and outputs and introduce the secondary goal of minimizing the maximal relative deviation for each fixed-sum output, which can result in a unique equilibrium efficient frontier.