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Single-machine rescheduling with outsourcing allowed and a limit to maximum time deviation

Liu Le;Business School, University of Jinan;  
This paper considers the single-machine rescheduling addressing an unexpected arrival of new jobs with outsourcing of any jobs to a single subcontractor allowed, where the objective is to minimize the weighted sum of the total outsourcing cost and total completion time, while both the total outsourcing cost and the maximum time deviation are subject to an upper limit. Problem-specific 0-1 programming model, nondeterministic polynomial(NP) hardness, and several optimality properties are first established. Subsequently, by using dynamic programming technique and two different ways of deciding the set of outsourcing jobs, two heuristics are designed to solve this problem, i.e., job addition-related heuristic(JA-H) and job removal related heuristic(JR-H). In the simulation experiments, by systematically generating plenty of test instances, performances of the two heuristics in solution quality and computational times are comparatively analyzed. Experimental results show that JR-H algorithm outperforms JA-H algorithm in terms of both optimization quality and efficiency.
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