FMS jobshop scheduling using Lagrangian relaxation method

This paper tackles a FMS jobshop scheduling problem with alternative routings. The objective function is to minimize the weighted flow time of jobs. We use Lagrangian relaxation method to relax the precedence constraints and propose a two-stage approach to solve the decomposed one-machine multi-operation problems. Three examples are tested and the computational results are compared to the Lagrangian relaxation method proposed by Hoitomt (1993). The comparison studies show that with the minimum weighted flow time of jobs as the objective of the scheduling problem the method proposed in this paper yields better solution with less computational time than the existing Lagrangian method