In this paper, an exact geometric algorithm is presented for solving two-JOB sequencing and SCHEDULING problems in FLEXIBLE flow SHOP and JOB SHOP environments while the resources are (un)available in some time periods and processors (un) availability is the same in all work centers. This study seems utterly new and it is applicable to any performance measure based on the completion time. The investigated models are very close to the actual SCHEDULING problems, because they envisage the FLEXIBLE JOB SHOP environments, heads, set-up times, arbitrary number of unavailability periods on all resources, arbitrary number of work-centers, any kind of cross-ability, any kind of resume-ability and several types of performance measures. The proposed model is presented to solve two-JOB problems because it is a graphical approach. However, it is concluded that the idea can be extended to n-dimensional problems as well.

In this paper FLEXIBLE JOB-SHOP SCHEDULING problem (FJSP) is studied in the case of optimizing different contradictory objectives consisting of: (1) minimizing makespan, (2) minimizing total workload, and (3) minimizing workload of the most loaded machine.As the problem belongs to the class of NP-Hard problems, a new hybrid genetic algorithm is proposed to obtain a large set of Paretooptimal solutions in a reasonable run time. The algorithm utilizes from a local search heuristic for improving the chance of obtaining more number of global Pareto-optimal solutions. The solution method uses from a perturbed global criterion function for guiding the search direction of the hybrid algorithm. Computational experiences show that the hybrid algorithm has superior performance in contrast to previous studies.

FLEXIBLE JOB SHOP SCHEDULING problem )FJSP( is an extension of the classical JOB SHOP SCHEDULING problem which allows an operation to be processed by any machine from a given set .FJSP is NP-hard and mainly presents two difficulties .The first one is to assign each operation to a machine out of a set of capable machines, and the second one deals with sequencing the assigned operations on the machines .However, it is quite difficult to achieve an optimal solution to this problem in medium and large size problems with traditional optimization approaches .In this paper a memetic algorithm (MA) or FLEXIBLE JOB SHOP SCHEDULING with overlapping in operation is proposed that solves the FJSP to minimize makespan time and obtain the optimum solution for small problem and best solution for medium and large scale problems .In this paper we also used preemption to improve the results of memetic algorithm and reduce the makespan.

In this paper, Multi-objective FLEXIBLE dynamic JOB SHOP SCHEDULING with maintenance constraints is investigated. In the recent researches the single objective models were assessed. Whereas in competitive conditions, decision makers encountered with simultaneous multi-objective problems that could be conflict with each other. In this research, the objectives are makespan, mean flow time and mean tardiness. These objectives are adaptable to the concept of just-in-time and supply chain management. In real world, machines may be unavailable for various reasons, such as maintenance. In this paper deterministic machine availability as a non-fixed availability is studied. Therefore a mathematical model and improved genetic algorithm with dynamic control parameters that changed through the algorithm is proposed to reducing the probability of early convergence and local optimum. Moreover a heuristic algorithm is proposed to solve maintenance sub-problem. Computational experiments for the three flexibility levels show that the best result of proposed algorithm without maintenance have 3.9%, 4.9% and 4.55% improvement and mean results have 4.9%, 5.33% and 4.6% improvement compared with existing methods. And with considering one, two and three maintenance, the mean of objective function have increased 4.68%, 9.48% and 11.75%. The results show the superiority of the proposed algorithm.

Introduction: The FLEXIBLE JOB SHOP system is one of the most widely used SCHEDULING systems in production environments, consistently attracting researchers' attention due to its diverse applications. Many studies in this field assume fixed and predetermined processing times. However, processing times can increase due to the deterioration effect, and after implementing rate-modifying activities (RMA), these times return to their original values. This study examines the FLEXIBLE JOB SHOP SCHEDULING system, considering JOB rejection policies, dual resource constraints (human and machine), and RMA maintenance activities.Methods: The objective of FLEXIBLE JOB SHOP SCHEDULING is to assign each operation to a machine and a worker from a set of eligible machines and workers in a way that optimizes the sequence of operations on the machines. A mathematical model based on the mixed-integer linear programming approach was developed for this purpose. Literature review classifies the problem with the stated assumptions as NP-hard, making the use of meta-heuristic methods essential for finding near-optimal solutions. Thus, Variable Neighborhood Search (VNS), Simulated Annealing (SA), and a combined VNS-SA algorithm were employed to solve the problem.Results and discussion: Twenty sub-problems were analyzed, categorized into small, medium, and large-sized problems. The characteristics of each problem were defined by parameters such as the number of JOBs, machines, workers, total operations, and buckets. Meta-heuristic methods, including VNS, SA, and their combination, were utilized to solve the problem. Seven neighborhood structures based on changes in assigned machines and workers, operation and JOB replacements, execution of RMA activities, and JOB acceptance/rejection were developed to enhance solution space exploration. The solution generation structure ensures feasibility within the FLEXIBLE JOB SHOP system's requirements. The parameters of the meta-heuristic methods were tuned using the Taguchi method. Parameters related to the combined VNS-SA algorithm, such as initial temperature, number of neighborhood searches, and shake procedure counter, were reported. The results of the meta-heuristic methods were compared, and for small-sized problems, they were also compared with exact solutions.Conclusion: The results of the twenty sub-problems solved using the three meta-heuristic approaches were compared statistically. The combined method of simulated annealing and variable neighborhood search showed superior performance in solving the problem.