We study a single machine scheduling problem, where the objective is minimum total early work. In this setting, a job is penalized according to the duration of the parts of the job completed prior to its due-date. First we prove that the problem is NP-hard. Then, based on a number of properties of an optimal schedule, we introduce a pseudo-polynomial dynamic programming algorithm, verifying NP-hardness in the ordinary sense. Our numerical tests indicate that the dynamic programming solves problems of hundreds of jobs in very reasonable time.
Bibliographical noteFunding Information:
This research was supported by the Israel Science Foundation (Grant no. 1286/14 ). The second author was supported in part by the Recanati Fund of The School of Business Administration, and Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem, Israel.
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- Dynamic programming
- Single machine
- Total early work