Research Article Hybrid Metaheuristics for Solving a Fuzzy Single Batch-Processing Machine Scheduling Problem S. Molla-Alizadeh-Zavardehi, 1 R. Tavakkoli-Moghaddam, 2 and F. Hosseinzadeh Lotfi 3 1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran 2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran 3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Correspondence should be addressed to S. Molla-Alizadeh-Zavardehi; saber.alizadeh@gmail.com Received 14 February 2014; Accepted 30 March 2014; Published 22 April 2014 Academic Editors: P. Agarwal, V. Bhatnagar, and Y. Zhang Copyright © 2014 S. Molla-Alizadeh-Zavardehi et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper deals with a problem of minimizing total weighted tardiness of jobs in a real-world single batch-processing machine (SBPM) scheduling in the presence of fuzzy due date. In this paper, frst a fuzzy mixed integer linear programming model is developed. Ten, due to the complexity of the problem, which is NP-hard, we design two hybrid metaheuristics called GA-VNS and VNS-SA applying the advantages of genetic algorithm (GA), variable neighborhood search (VNS), and simulated annealing (SA) frameworks. Besides, we propose three fuzzy earliest due date heuristics to solve the given problem. Trough computational experiments with several random test problems, a robust calibration is applied on the parameters. Finally, computational results on diferent-scale test problems are presented to compare the proposed algorithms. 1. Introduction A batch-processing machine (BPM) is a special variant of a scheduling problem, in which several jobs can be simulta- neously processed in such a way that all the jobs in a batch start and complete their processing at the same time. Te main advantage is to reduce setups and/or facilitation of material handling. Te problem of BPM scheduling is ofen encountered in real industries. Te industrial application of these machines can be found in semiconductor burn-in operations, environmental stress-screening (ESS) chambers, chemical, food, and mineral processing, pharmaceutical and construction materials industries, and so forth. Te BPM scheduling problem is important because the scheduling of batching operations has a signifcant economic impact. It is mainly motivated by an industrial application, namely, the burn-in operation found in the fnal testing phase in semiconductor manufacturing [1, 2]. In the semiconductor manufacturing, the jobs have diferent processing times and sizes that are both required by the customers. Te jobs are grouped in batches where a batch means a subset of jobs. Te BPM can process a batch of jobs as long as the sum of all the job sizes in the batch does not violate the capacity of the machine. Te processing time of a batch is equal to the longest processing time of all the jobs in that batch. Ikura and Gimple [3] were the frst researchers who studied the BPM problem and Lee et al. [4] frst presented a detailed description for burn-in operation. As reported in the studies, the exact algorithms have a slow convergence rate and they can solve only small instances to optimality. As this study addresses SBPM with fuzzy due dates using metaheuristics, the review on SBPM scheduling under a fuzzy environment and the application of metaheuristics to these problems is carried out. For an extensive review on BPM scheduling problems, we refer to Potts and Kovalyov [5] and Mathirajan and Sivakumar [6]. In BPM scheduling problems, Wang and Uzsoy [7] frstly proposed a metaheuristic algorithm. Considering dynamic Hindawi Publishing Corporation e Scientific World Journal Volume 2014, Article ID 214615, 10 pages http://dx.doi.org/10.1155/2014/214615