Abstract
We consider a production planning problem with two planning periods. Detailed planning occurs in the first period, when complete information is known about a set of orders that are initially available. An additional set of orders becomes available at the start of the second planning period. The objective is to maximize the number of on-time orders. We derive an upper bound on the competitive ratio of any deterministic online algorithm, relative to the performance of an algorithm with perfect information about the second set of orders. This ratio depends on the relative lengths of the two planning periods. We also describe an efficient algorithm that delivers a solution which asymptotically achieves this upper bound ratio as the number of jobs becomes large.
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Acknowledgements
This research is supported in part by National Science Foundation Grant DMI-0421823, and by the Summer Fellowship Program of the Fisher College of Business, The Ohio State University, to the first author.
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Hall, N.G., Posner, M.E. & Potts, C.N. Online production planning to maximize the number of on-time orders. Ann Oper Res 298, 249–269 (2021). https://doi.org/10.1007/s10479-018-2928-6
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DOI: https://doi.org/10.1007/s10479-018-2928-6