Minimizing the weighted sum of maximum earliness and maximum tardiness costs on a single machine with periodic preventive maintenance |
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| Affiliation: | 1. Université Lille Nord de France, LAMIH UMR CNRS 8201, Université de Valenciennes et du Hainaut Cambrésis, France;2. Université Lille Nord de France, Université d?Artois, France;1. School of Economics and Management, Anhui Normal University, Wuhu 241000, PR China;2. School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, Guangdong 518172, PR China;3. School of Management, Hefei University of Technology, Hefei 230009, PR China;4. Department of Industrial and Systems Engineering, Research Center on Digital Supply Chain and Operations Management, Khalifa University, Abu Dhabi, United Arab Emirates;5. Institute of Information and Computational Technologies, Almaty 050000, Kazakhstan;1. Instituto de Trasplante Multiorgánico, Hospital Universitario Fundación Favaloro, Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina;2. Servicio de Cirugía, Clínica “La Pequeña Familia”, Ciudad de Junín, Argentina;3. Servicio de Anestesiología, Hospital Universitario Fundación Favaloro, Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina;4. Unidad de Terapia Intensiva y Trasplante, Hospital Universitario Fundación Favaloro, Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina;5. Hepatología y Gastroenterología Pediátrica, Hospital Universitario Fundación Favaloro, Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina;1. Department of Industrial Engineering and Management, Taipei University of Technology, Taipei, 106, Taiwan, ROC;2. Department of Industrial Engineering and Enterprise Information, Tunghai University, Taichung City, 407, Taiwan, ROC |
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| Abstract: | We consider the problem of scheduling a set of jobs on a single machine against a common and restrictive due date. In particular, we are interested in the problem of minimizing the weighted sum of maximum earliness and maximum tardiness costs. This kind of objective function is related to the just-in-time environment where penalties, such as storage cost and additional charges for late delivery, should be avoided. First we present a mixed integer linear model for the problem without availability constraints and we prove that this model can be reduced to a polynomial-time model. Secondly, we suppose that the machine undergoes a periodic preventive maintenance. We present then a second mixed integer linear model to solve the problem to optimality. Although the latter problem can be solved to optimality for small instances, we show that the problem reduces to the one-dimensional bin packing problem. Computational results show that the proposed algorithm best fit decreasing performs well. |
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| Keywords: | Scheduling Earliness Tardiness Maintenance Due date |
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