A classical single machine minmax common due-date assignment (CON) problem is studied. The problem is extended (independently) to the following settings: (1) general position-dependent job processing times are assumed, and an efficient O(n 4) solution procedure is introduced; (2) the option of job rejection is allowed, and this case is shown to be solved in O(n 5); (3) a deterioration effect is considered, and an O(n 2) solution algorithm is proposed; (4) parallel uniform machines are considered; and (5) the machine setting is that of a permutation flowshop. The last two settings are known to be NP hard, and efficient heuristic procedures are introduced and shown numerically to produce very small optimality gaps.
Bibliographical noteFunding Information:
This work was supported by Israel Science Foundation [grant number 2505/19]. The first 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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- job rejection
- position-dependent processing times
- uniform machines