BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 55, Issue 1, March 2007

Analysis of Dynamic Systems and Mechanical Engineering

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pp 59 - 69

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Dominance relations for two-machine flow shop problem with late work criterion

M. STERNA
The paper concerns the two-machine non-preemptive flow shop scheduling problem with a total late work criterion
and a common due date (F2|dj = d|Y ). The late work performance measure estimates the quality of a solution with regard
to the duration of late parts of activities performed in the system, not taking into account the quantity of this delay. In the
paper, a few theorems are formulated and proven, describing features of an optimal solution for the problem mentioned, which is
NP-hard. These theorems can be used in exact exponential algorithms (as dominance relations reducing the number of solutions
enumerated explicitly), as well as in heuristic and metaheuristic methods (supporting the construction of sub-optimal schedules
of a good quality).
Key words: 

scheduling, flow shop, late work criterion, dominance relation


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