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

Sterna M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2007

Vol. 55, nr 1

59-69

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 wit h 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 suboptimal schedules of a good quality).

Generation of reducts and rules in multi-attribute and multi-criteria classification

Susmaga R., Słowiński R., Greco S., Matarazzo B.

Control and Cybernetics

2000

Vol. 29, no 4

969-988

The paper addresses the problem of analysing information tables which contain objects described by both attributes and criteria, i.e. attributes with preference-ordered scales. The objects contained in those tables, representing exemplary decisions made by a decision maker or a domain expert, are usually classified into one of several classes that are also often preference-ordered. Analysis of such data using the classic rough set methodology may produce improper results, as the original rough set approach is not able to discover inconsistencies originating from consideration of typical criteria, like e.g. product quality, market share or debt ratio. The paper presents the framework for the analysis of both attributes and criteria and a very promising algorithm for generating reducts. The algorithm presented is evaluated in an experiment with real-life data sets and its results are compared to those by two other reduct generating algorithms.