Structural rearrangement of the network system from an efficiency perspective: A silver lining of profit improvement

Previous studies on profit improvement mainly consider improving traditional profit efficiency including the technical, allocative, and price profit efficiencies. Few studies discuss profit improvement by optimizing the structural arrangement of the network system, which is about adjusting the combinations of upstream and downstream entities in the system. When achieving traditional efficiency, the system's profit can no longer be increased only by reducing inputs, increasing outputs, and adjusting prices. In this situation, structural rearrangement may provide a silver lining to profit improvement. In this study, we take the two-level supply chains as an example and address the research question of how to improve profit via structural rearrangement of the system containing several two-stage subsystems from the efficiency perspective. To answer this question, we view two-stage subsystems in each system as players and propose a data envelopment analysis permutation game method. Through this method, we find the optimal structural rearrangement plan, which is a new way to further improve the profit in addition to improving traditional profit efficiency. We propose a new efficiency measurement, the structural profit efficiency, and find overall profit efficiency is the product of structural profit efficiency and traditional profit efficiency. Finally, we conduct an experiment using the data of 27 supply chains to validate our proposed method and provide the optimal structural rearrangement plans for them.