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ABSTRACT
Tasks with long durations often face the requirement of having to periodically report their progress to process controllers. Under this requirement, working teams that simultaneously process multiple tasks need to schedule their work carefully in order to demonstrate satisfactory progress on each unfinished task. We present a single-machine scheduling model that reflects this requirement. Our model has multiple milestones at which the tasks are penalized if their progress is below a satisfactory level. We develop polynomial solution methods for the general case with convex nonlinear penalty functions and for the special case with linear penalty functions. Extensions of our model are also discussed.
Acknowledgements
The authors thank two anonymous referees for their helpful comments.
Funding
This research was supported in part by the Research Grants Council of Hong Kong under grant PolyU5195/13E.
Additional information
Notes on contributors
Chung-Lun Li
Chung-Lun Li is Chair Professor of Logistics Management at The Hong Kong Polytechnic University. He received his doctoral degree in Operations Research from Columbia University. His areas of interest are logistics, scheduling, supply chain management, and combinatorial optimization. His publications have appeared in IISE Transactions, Management Science, Naval Research Logistics, Operations Research, and Production and Operations Management.
Weiya Zhong
Weiya Zhong is an Associate Professor in the Department of Business Administration, School of Management, at Shanghai University. She received her doctoral degree from the Department of Mathematics at Zhejiang University, China. Her areas of interest are scheduling, combinatorial optimization, and operations management. Her publications have appeared in European Journal of Operational Research, Operations Research Letters, Journal of Combinatorial Optimization, and Journal of Scheduling.