This investigation considers a reentrant PERMUTATION FLOWSHOP scheduling problem whose performance criterion is maximum tardiness. The reentrant FLOWSHOP (RFS) is a natural extension of the classical FLOWSHOP by allowing a job to visit certain machines more than once. The RFS scheduling problem, in which the job order is the same for each machine in each layer, is called a reentrant PERMUTATION FLOWSHOP (RPFS) problem. In this paper, a mathematical model is extended to solve the given problem minimizing the maximum tardiness on an m-machine RPFS problem. This problem is solved by three meta-heuristic algorithms, namely genetic algorithm, simulated annealing and tabu search. The results of these algorithms are compared to the optimal solutions obtained by the integer programming approach. The experimental results show that the genetic algorithm has a better performance than the others tested.

In this paper, we consider the problem of scheduling on two-machine PERMUTATION FLOWSHOP with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim to tighten the models’ representations. One of them is based on dominance rules from the literature. Then, we provide the results of extensive computational experiments used to measure the performance of the proposed MILP models. They are shown to be able to solve optimally instances until the size 40-job and even several larger problem classes, with up to 60 jobs. Furthermore, we can distinguish the effect of the minimal time lags and the inclusion of the valid inequalities in the basic MILP model on the results.

The aim of this paper is to determine an upper bound for the number of non-co-spectral PERMUTATION graphs in terms of automorphism group of a graph G. As a corollary, we determine the eigenvalues of all PERMUTATION graphs P (Cn), where  2 Aut(Cn).

In this paper, a review of Multiple objective FLOWSHOP Scheduling Problems is introduced. Different version of the problem are classified according to different multi objective optimization approaches, FLOWSHOP assumptions, solving methods, and also objective functions terms. This paper can be considered as a complete and valuable reference for researchers in the field of scheduling, especially multiple objective ones.

The aim of this paper is to propose a new particle swarm optimization algorithm to solve a hybrid FLOWSHOP scheduling with sequencedependent setup times problem, which is of great importance in the industrial context. This algorithm is called diversified particle swarm optimization algorithm which is a generalization of particle swarm optimization algorithm and inspired by an anarchic society whose members behave anarchically to improve their situations. Such anarchy lets the algorithm explore the solution space perfectly and prevent falling in the local optimum traps. Besides, for the first time, for the hybrid FLOWSHOP, we proposed eight different local search algorithms and incorporate them into the algorithm in order to improve it with the help of systematic changes of the neighborhood structure within a search for minimizing the makespan. The proposed algorithm was tested and the numerical results showe that the proposed algorithm significantly outperforms other effective heuristics recently developed.