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.

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.

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.

This paper addresses a new mixed integer nonlinear and linear mathematical programming economic lot sizing and SCHEDULING problem in distributed PERMUTATION FLOW SHOP problem with number of identical factories and machines. Different products must be distributed between the factories and then assignment of products to factories and sequencing of the products assigned to each factory has to be derived. The objective is to minimize the sum of setup costs, work-in-process inventory costs and finished products inventory costs per unit of time. Since the proposed model is NP-hard, an efficient Water Cycle Algorithm is proposed to solve the model. To justify proposed WCA, Monarch Butterfly Optimization (MBO), Genetic Algorithm (GA) and combination of GA and simplex are utilized. In order to determine the best value of algorithms parameters that result in a better solution, a fine-tuning procedure according to Response Surface Methodology is executed.

Purpose: This paper aims to propose a FLOW SHOP SCHEDULING problem for equipment overhaul. This problem consists of three stages, the separation of the components of an equipment is done in the first stage. Repairs and overhaul operations are carried out on the separated parts of the first stage in the second stage. Finally, the overhauled parts of the previous stage are mounted on each other in the third stage. In the third stage, operations are performed in parallel workSHOPs. The objective function of the problem is the maximum time to complete jobs, and the sequence of processing jobs should be done in such a way that the value of the objective function is minimized. Design/methodology/approach: To solve the problem, a mixed integer programming model has been proposed for small size, which determines the processing sequence of jobs based on the position of each job. A genetic algorithm has been used to solve the problem in large dimensions. By increasing the size of the problem and in different sizes, the results have been examined and analyzed, which shows the efficiency of the model and the proposed algorithm. Findings: To check the accuracy of the model's performance and also the effect of the presence of parallel machines in the third stage, an example was presented in this paper. Accordingly, while the accuracy of the model's performance was checked, the effect of the presence of more machines was determined in the third stage. As the number of machines increased in the third stage, the value of the objective function did not deteriorate. The performance of GAMS in solving the problem in a small size was investigated. Considering that solving the problem for large dimensions is not possible in a reasonable time and the problem is NP-hard, then solving the problem in large dimensions was done using a genetic algorithm. Therefore, solving the problem on a large dimension has been done using the genetic algorithm. According to the obtained results, the efficiency of the genetic algorithm was shown. Due to its low average value, it indicated the convergence of the genetic algorithm. Research limitations/implications: Considering that there are not many published papers in the field of equipment overhaul, it is difficult to access related models and papers. Therefore, in this paper, the model and solution method have been written with many reviews. Also, to check and reduce costs, the number of third-stage machines has been determined using sensitivity analysis. Practical implications: The problem of equipment overhaul is used in many fields in reality. For example, the operations related to the maintenance, repair and overhaul of the aircraft engine have been investigated. Since the planning of maintenance and maintenance operations is difficult, the focus of research has been on improving maintenance operations by finding suitable SCHEDULING for job SHOP operations in maintenance operations. They emphasized that SCHEDULING can improve maintenance operations and presented a simulation model. Social implications: The purpose of creating a space to start an activity is to reduce costs, earn money and achieve profit. To examine the cost-effectiveness of the equipment overhaul issue, we can refer to the number of third-stage machines. According to the amount of equipment to perform an overhaul on them, the number of third-stage machines can be determined. Therefore, extra machines can be removed to reduce the cost. On the other hand, if the related equipment to the customers is different, to reduce the storage costs or increase customer satisfaction, different goals should be considered. Here, the objective function of maximum completion time is considered for this purpose. If the equipment must be available at a certain time, goals such as the total time to complete the job can be considered. In line with the application of the social implications in the investigated problem in this paper and considering that the investment costs, as well as the ability to respond to the applicants' requests, are related to the number of third-stage machines, the value of the objective function is analyzed based on the number of third-stage machines and analysis has been done. Originality/value: In this paper, a three-stage FLOW SHOP SCHEDULING problem in the overhaul industry was studied. Accordingly, a new mathematical model based on the job processing position was proposed, which dealt with the exact solution of the problem in small dimensions. According to the type of problem in the overhaul environment, the combined FLOW SHOP problem for equipment overhaul was investigated. Also, the use of parallel machines in the third stage of the equipment overhaul problem is one of the new issues under investigation.

Although several papers have studied no-idle SCHEDULING problems, they all focused on FLOW SHOPs, assuming one processor at each working stage. But, companies commonly extend to hybrid FLOW SHOPs by duplicating machines in parallel in stages. This paper considers the problem of SCHEDULING no-idle hybrid FLOW SHOPs. A mixed integer linear programming model is first developed to mathematically formulate the problem. Using commercial software, the model can solve small instances to optimality. Then, two metaheuristics, based on variable neighborhood search and genetic algorithms, are developed to solve larger instances. Using numerical experiments, the performance of the model and algorithms are evaluated.