Lagrangian Relaxation Technique for Solving Scheduling Problems by Decomposition of Timed Petri Nets

In this paper, we propose Lagrangian relaxation technique for solving scheduling problems by decomposition of timed Petri nets. The scheduling problem is represented by the transition firing sequence problem to minimize a given objective function. The timed Petri net is decomposed into several subnets so that the subproblem for each subnet can be easily solved by a shortest path algorithm. The optimality of solution can be evaluated by the duality gap derived by Lagrangian relaxation method. The performance of the proposed method is compared with the conventional optimization algorithm with penalty function method. The results show that the duality gap within 1.5% can be derived for AGVs routing problems. The effectiveness of the proposed method is demonstrated by comparing the performance between the conventional method.