This study considers scheduling in Hybrid flow shop environment with unrelated Parallel machines for minimizing mean of job's tardiness and mean of job's completion times. This problem does not study in the literature, so far. Flexible flow shop environment is applicable in various industries such as wire and spring manufacturing, electronic industries and production lines. After modeling the problem as a mixed integer programming model, three heuristics named Cluster, H1 and H2 is proposed for solving it. The first heuristic (Cluster) algorithm utilizes clustering methods for determining sequence of jobs. The second and third heuristics (H1 and H2) determine sequence of jobs with using SPT and EDD rules, respectively. The experimental results of study show that Cluster algorithm outperforms H1 and H2. 

In this paper the problem of job shop scheduling with Parallel machines in each stages is discussed. The objective is to minimize the maximum completion time (makespan). This problem is a combination of two classic problems of job shop and Parallel machines which in this case Parallel machines has been used as kind of flexibility in the job shop problem. The review of literature has shown that this problem has not been discussed yet. After presenting the mathematical mode, heuristic algorithms are used for solving this NP-hard problem. Regarding this, five algorithms are presented and a lower bound is developed. Finally all these algorithms have been analyzed. According to results the proposed algorithm of H2 works better than the others when there are few jobs. As the number of jobs increases H1 is more efficient than H2 asymptotically. Also the efficiency of H3 algorithm is the worst among the rest.

This article addresses a multi-stage flowshop scheduling problem with equal number of unrelated Parallel machines. The objective is to minimize the makespan for a given set of jobs in the system. This problem class is NP-hard in the strong sense, so a hybrid heuristic method for sequencing and then allocating operations of jobs to machines is developed. A number of test problems are randomly generated and results obtained by proposed heuristic are compared with optimal solutions reported by the Lingo 8.0 package applying the branch & bound approach. The results show that the proposed hybrid method is more efficient when the problem sizes have been increased.

scheduling of jobs and maintenance activities is a vital problem in a production system. In the current business environment, the competitiveness of manufacturing companies is based on their ability to response the rapid changes in demand with high quality and low costs. Therefore. in this paper, the scheduling of jobs and maintenance activities in an unrelated Parallel machines environment is studied. By considering the controllable processing times, a multi-objective mathematical programming model is presented to minimize the sum of the compression and expansion of processing times and maintenance costs, makespan, tardiness, and earliness. The multi-choice goal programming (MCGP) is applied. The problem is NP-hard, therefore, the NSGA-II algorithm is developed to solve the medium and large size instances. The obtained results from solving the proposed model with NSGA-II and comparing with the results from MCGP demonstrates that the proposed algorithm is presented a non-dominated solution set in a short time.

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