Nash-equilibrium algorithm and incentive protocol for a decentralized decision and scheduling problem in sustainable electroplating plants

This paper addresses a decentralized production decision and scheduling problem in smart electroplating plants considering environmental sustainability. Due to the characteristics of the electroplating process, part processing times are confined to time-window constraints and controlled by independent autonomous agents with the support of multi-agent and distribution manufacturing technologies. It is shown that part processing times in chemical/physical tanks not only determine the productivity but also affect the environmental cost. Hence, two essential issues should be addressed: (a) how to find equilibrium strategies of agents (i.e., part processing times) in such a decentralized manufacturing setting; and (b) how to design an incentive protocol inducing the equilibrium strategies towards the optimal ones concerning the productivity and the environmental cost simultaneously. To deal with the first issue, this paper establishes a non-cooperative sequential game model, which simulates the evolution process of the strategies from an unstable state to an equilibrium one. Then, an iterative algorithm is developed to find Nash equilibrium strategies based on a cyclic bi-value graph. To address the second issue, a novel heuristic rule is proposed for the incentive protocol by exploring the characteristics of time-window constraints and environmental cost functions. The results of numerical experiments validate the performance of the Nash-equilibrium algorithm and the effectiveness of the heuristic rule.