Single machine group scheduling with resource dependent setup and processing times |
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| Institution: | 1. Institute of Engineering Cybernetics, Technical University of Wroclaw, Wroclaw 50372, Poland;2. Belarus State University, and United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk 220012, Belarus;3. MACSI team of INRIA-Lorraine and LORIA-INPL, Ecole des Mines de Nancy, Parc de Saurupt, Nancy Cedex 54042, France;1. University of Mercu Buana, Indonesia;2. University of Haute Alsace, France;1. College of Mathematics Science, Chongqing Normal University, PR China;2. Key Laboratory for Optimization and Control, Ministry of Education, Chongqing, PR China;3. Department of Statistics, Feng Chia University, Taichung, Taiwan;4. Department of Industrial Engineering and Management, Nan Kai University of Technology, Nantou, Taiwan;1. Department of Business Administration, Eastern Connecticut State University, 83 Windham St., Willimantic, CT 06226-2295, United States;2. LIAAD – INESCTEC LA, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464 Porto, Portugal;1. School of Business Administration, The Hebrew University, Jerusalem, Israel;2. School of Industrial Engineering, Jerusalem College of Technology, Jerusalem, Israel |
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| Abstract: | A single machine scheduling problem is studied. There is a partition of the set of n jobs into g groups on the basis of group technology. Jobs of the same group are processed contiguously. A sequence independent setup time precedes the processing of each group. Two external renewable resources can be used to linearly compress setup and job processing times. The setup times are jointly compressible by one resource, the job processing times are jointly compressible by another resource and the level of the resource is the same for all setups and all jobs. Polynomial time algorithms are presented to find an optimal job sequence and resource values such that the total weighted resource consumption is minimum, subject to meeting job deadlines. The algorithms are based on solving linear programming problems with two variables by geometric techniques. |
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