On the minmax common-due-date problem: extensions to position-dependent processing times, job rejection, learning effect, uniform machines and flowshops

Abstract

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(n⁴) solution procedure is introduced; (2) the option of job rejection is allowed, and this case is shown to be solved in O(n⁵); (3) a deterioration effect is considered, and an O(n²) 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.

KEYWORDS:

• Scheduling
• position-dependent processing times
• job rejection
• uniform machines
• flowshop

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

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.