Nash equilibria and the price of anarchy under SPT-LPT mixed coordination mechanism in distributed manufacturing

In the distributed manufacturing of new energy vehicle components, achieving a balance between the self-interested behaviors of individual production departments and the factory’s overall objectives is critical. This paper addresses this challenge by developing game-theoretic models to analyze the impact of a mixed coordination mechanism — specifically, those combining Shortest Processing Time (SPT) and Longest Processing Time (LPT) rules — on the existence of Nash equilibria (NE) and the Price of Anarchy (PoA). We propose different algorithms tailored to the parallel and uniform equipment-models, each capable of producing NE; and provide upper bounds of the PoA from the perspective of both equipment utilization and operational efficiency in theory. We conduct simulation analyses based on randomly generated instances to evaluate the average PoAs of our algorithms, which are consistent with the theoretical results. Our findings offer valuable managerial insights by elucidating how technological parameters, such as equipment number, type, and the degree of coordination, influence production performance in distributed manufacturing systems.