The proportionate flow shop (PFS) is considered as a unique case of the flow shop problem in which the processing times of the operations belonging to the same job are equal. A proportionate flexible flow shop (PFFS) is a machine environment with parallel identical machines at each stage. This study presents an effective hybrid approach based on constructive genetic algorithm (CGA) for PFFS sch...

In 1966, Graham showed that a simple procedure called list scheduling yields a 2-approximation algorithm for the central problem of scheduling precedence constrained jobs on identical machines to minimize makespan. To date this has remained the best algorithm, and whether it can or cannot be improved has become a major open problem in scheduling theory. We address this problem by establishing a...

We consider parallel machine scheduling problems with identical machines and preemption allowed. It is shown that every such problem with chain precedence constraints and release dates and an integer-concave objective function satisfies the following integrality property : for any problem instance with integral data there exists an optimal schedule where all interruptions occur at integral date...

This paper presents a Lagrangean relaxation approach for solving a parallel machine scheduling problem where the objective function is to minimize the weighted number of late jobs. The approach is an extension of an approach that has been successfully applied to the one-machine case. It is the first method that gives lower bounds to the problem when an exact solution cannot be found.