We study single machine scheduling problems. Generalised due dates are assumed, i.e. job due dates are specified according to the positions of the jobs in the sequence, rather than their identity. Thus, assuming that due dates are numbered in a non-decreasing order, the jth due date refers to the job assigned to the jth position. In addition, we allow the option of job rejection, i.e. not all jobs must be processed. In this case, the scheduler is penalised for each rejected job, and the total rejection cost becomes part of the objective function. Two objective functions are considered: maximum tardiness plus rejection cost, and total tardiness plus rejection cost. Both problems are proved to be NP-hard. Pseudo-polynomial dynamic programmes and efficient heuristics are introduced and tested numerically.
Bibliographical noteFunding Information:
This work was supported by the Israel Science Foundation [grant number 1286/14]. The second author was also supported by the Charles I. Rosen Chair of Management and by The Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.
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- dynamic programming
- generalised due dates
- job rejection
- single machine