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On minimizing resource consumption with constraints on the makespan and the total completion time
Institution:1. School of Management Science and Engineering, Dalian University of Technology, Dalian 116023, China;2. Faculty of Science, Kunming University of Science and Technology, Kunming 650093, China;3. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China;4. Department of Healthcare Management, Yuanpei University, Hsinchu, Taiwan;5. Graduate Institute of Business Administration, Cheng Shiu University, Kaohsiung, Taiwan;6. Department of Statistics, Feng Chia University, Taichung, Taiwan;1. Department of Statistics, Feng Chia University, Taichung 40724, Taiwan;2. Business Administration Department, Fujen Catholic University, Hsinpei City, Taiwan;1. Department of Computer Science and Engineering, Indian Institute of Technology Madras, India;2. Indian Institute of Information Technology Sricity, India
Abstract:We investigate a single machine scheduling problem where the resource consumed depends on the release times of jobs. The objective is to minimize the total consumption subject to a constraint on the makespan or the total completion time. Results by Li are extended to the case where the consumption function is convex decreasing. A further extension to multiple consumption functions is shown. Conditions for feasibility are developed in each case.
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