Abstract
This paper considers two-person cooperative games on scheduling problem which is motivated by the medication dispensing at outpatient pharmacies. We prove that two-person cooperative games on minimizing the number of tardy jobs is NP-hard, and two-person cooperative games on minimizing the total weighted number of tardy jobs and on minimizing the total weighted completion time are NP-hard even if the jobs have the same processing times. We develop dynamic programming algorithms for problems of two-person cooperative games on minimizing the total (weighted) number of tardy jobs and on minimizing the total (weighted) completion time respectively, which run in pseudo-polynomial time and indicate that they are binary NP-hard.
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Acknowledgments
This research is supported by National Natural Science Foundation of China project “Study of the operational mechanism and its optimization of resource management in surgical operations” (No. 71371120). The first author is also supported by the key discipline “Applied Mathematics” of Shanghai Second Polytechnic University (No. A30XK 1322100).
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Liu, L., Tang, G., Fan, B. et al. Two-person cooperative games on scheduling problems in outpatient pharmacy dispensing process. J Comb Optim 30, 938–948 (2015). https://doi.org/10.1007/s10878-015-9854-1
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DOI: https://doi.org/10.1007/s10878-015-9854-1