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Constraint satisfaction techniques in planning and scheduling: An introduction

100%

Bartak R.

Archives of Control Sciences

2008

tom Vol. 18, no. 2

141-158

Planning and scheduling are two closely related areas that, despite their similarity, deal with different problems. While the planning ask is to decide which actions are necessary to achieve a given goal, the scheduling task is to allocate known activities to scarce resources, such as machines, over time. Typically planning and scheduling problems are solved separately using different solving techniques. However, real-life problems require a more integrated approach. Constraint satisfaction seems to be such a unifying solving technology for both planning and scheduling problems. This paper describes how constraint satisfaction techniques can be applied to planning and scheduling problems.

An extended problem to Bertrand's paradox

100%

Ardakani M. , Wulff S.

Discussiones Mathematicae Probability and Statistics

2014

tom 34

nr 1-2

23-34

Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by careful examination of the probability space.