Distributing the production activities among the supply chain facilities with regard to the considered criteria can have a significant impact on the productive management. In this paper, a comprehensive mathematical model for Reentrant Permutation Flow Shop scheduling via considering a preventive maintenance and distributed jobs on different facilities is proposed. The uncertainty of the time of preventive maintenance operation is handled using robust optimization technique based on the uncertainty budget approach. Job assignment to production facilities and job scheduling are determined in the proposed model by considering multiple objectives include Cmax minimization, production cost minimization, and average tardiness. Due to the NP-hard nature of the proposed Flow Shop scheduling problem, a new hybrid meta-heuristic based on the novel adaptive large neighborhood search and the simulated annealing is adopted. The obtained results from an extensive numerical experimentation indicate the efficiency of the proposed model and solution algorithm to tackle the proposed problem.

The efficiency of metaheuristic algorithms has a direct relationship with their parameters setting, so that the incorrect selection of completely effective algorithmic parameters could make them inefficient. In this research, the combination of Taguchi approach and the Data Envelopment Analysis (DEA) method are applied to enhance the efficiency of the genetic algorithm to solve the Reentrant Permutation Flow Shop (RPFS) problem. Various scenarios are formed to select genetic algorithm’ s operators for units under evaluation. First, using the Taguchi method for each unit, the optimal parameters are specified with the goal of minimizing the objective function (maximum tardiness). Then the effective units are determined and ranked in order to specify the best operators of the algorithm according to the optimal objective function in the shortest possible time. This research can be used as a method for setting the parameters of other evolutionary and metaheuristic algorithms in order to avoid the disadvantages of the trial and error methods.

The deterministic Permutation Flow Shop scheduling problem with makespan criterion is not solvable in polynomial time‎. ‎Therefore‎, ‎researchers have thought about heuristic algorithms‎. ‎There are many heuristic algorithms for solving it that is a very important combinatorial optimization problem‎. ‎In this paper‎, ‎a new algorithm is proposed for solving the mentioned problem‎. ‎The presented algorithm chooses the weighted path that starts from the up-left corner and reaches the down-right in the matrix of jobs processing times and calculates the biggest sum of the times in the footprints of this path‎. ‎The row with the biggest sum permutes among all the rows of the matrix for locating the minimum of makespan‎. ‎This method was run on Taillard’s standard benchmark and the solutions were compared with the optimum or the best ones as well as 14 famous heuristics‎. ‎The validity and effectiveness of the algorithm are shown with tables and statistical evaluation‎.

Scheduling theory and Permutation therein are two important subjects in discrete operation research. In this paper, a new heuristic algorithm is proposed for solving Permutation Flow Shop problem by using regulations of columnar entries in the processing times matrix. There are  jobs to be processed on  machines with deterministic processing times and the object is obtaining the minimum of the total time to complete the schedule (makespan). This is not solvable in polynomial time. First, an initial suitable sequence of jobs is determined similar to many heuristics. For this, the matrix  is made such that every determines the measure of the fitness for the location of the th old row in the th new position. Thereafter, the Bellman Esogbue Nabeshima theorem is used. The presented algorithm is compared with the NEH (the best well-known existing method). This comparison is made by the Taillard’s standard test problems. Computational results demonstrate that the heuristic algorithm is better than some of the proposed heuristics known so far and it is superior with respect to others in a number of Taillard instances. As a result, it is almost as good as NEH and is very promising for the problem. On the basis of the structure of the proposed algorithm, it can perform a role as meta-heuristic.

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.

The problem of determining the sequence of a set of jobs with the objective function (OF) for minimizing the maximum earliness and tardiness, is studied. Since this OF is trying to minimizing and diminish the values of earliness and tardiness, it corresponds to different production systems, such as jIT. This OF is studied in problems associated with m machine and n jobs in Flow Shop case (n/m/P/Etmax).Several methods have developed for solving Flow Shop problems. Two quick heuristic methods, called HI and H2, with the aim of finding proper solutions in short time, are suggested. The branch and bound (BB) optimal method for solving n/rn/P/ETmax problems is applied. Offering fair upper and lower bounds results in obtaining optimal solutions in many problems. 400 n/rn/P/ETmax problems of small, medium and large sizes are randomly generated.For 83% of problems, optimal solutions are obtained, by BB method. The associated ranges for these problems are 4 to 75 machines and 4 to 50 jobs.

In industries machine maintenance is used in order to avoid untimely machine fails as well as to improve production effectiveness. This research regards a Permutation Flow Shop scheduling problem with aging and learning effects considering maintenance process. In this study, it is assumed that each machine may be subject to at most one maintenance activity during the planning horizon. The objectives aim to minimize the makespan, tardiness of jobs, tardiness cost while maximizing net present value, simultaneously. Due to complexity and Np-hardness of the problem, two Pareto-based multi-objective evolutionary algorithms including non-dominated ranked genetic algorithm (NRGA) and non-dominated sorting genetic algorithm (NSGA-II) are proposed to attain Pareto solutions. In order to demonstrate applicability of the proposed methodology, a real-world application in polymer manufacturing industry is considered.

Make-to-order is a production strategy in which manufacturing starts only after a customer's order is received; in other words, it is a pull-type supply chain operation since manufacturing is carried out as soon as the demand is confirmed. This paper studies the order acceptance problem with weighted tardiness penalties in Permutation Flow Shop scheduling with MTO production strategy, the objective function of which is to maximize the total net profit of the accepted orders. The problem is formulated as an integer-programming (IP) model, and a cloud-based simulated annealing (CSA) algorithm is developed to solve the problem. Based on the number of candidate orders the firm receives, fifteen problems are generated. Each problem is regarded as an experiment, which is conducted five times to compare the efficiency of the proposed CSA algorithm to the one of simulated annealing (SA) algorithm previously suggested for the problem. The experimental results testify to the improvement in objective function values yielded by CSA algorithm in comparison with the ones produced by the formerly proposed SA algorithm.

In this paper, we consider a Permutation Flow Shop scheduling problems with n jobs and m machines. The jobs have arbitrary processing times and due dates. Our objective is minimizing the total earliness and tardiness of all jobs. We develop a genetic algorithm to solve this problem. The performance of the algorithm is evaluated through computational experiments.