A mission in this chapter is to extend previous mathematical programming problems using historical data to stochastic and fuzzy programming problems under uncertainty, particularly considering the risk-management. In the practice decision making, it is necessary to take various constraints and assumptions into consideration as well as uncertainty, such as the probability derived from the statis...

Verifying that a piece of software has no bugs means proving that it has certain desired properties, such as an array index not taking values outside certain bounds. Abstract interpretation is used in the static analysis of code to establish the inclusion-wise smallest set of values (numerical invariant) that the program variables can attain during program execution. Such sets can be used to de...

This paper describes a narrative-oriented approach to the design and the analysis of a computational system and a set of activities for mathematical learning. Our central contention is that programming can offer a key to resolving the tension between the different representational structures of narrative and mathematical formalism. In the course of describing our approach, we make a distinction...

The ntd>mensiond veotor, &, 1s selected from E+-=I&. &bQ]. ,1 solution to P i s at hand hexh hen the solution to E satisfies the complementary alackness mnditlon gwen by. ?*#(?*) =&*bO and g(z*i s b 0 , ?\-here ?* eolves E far &=?* B n o o ~ s .WD C:EOFFAIOY'~' hare related this to the elsssical rork of K m m o Tucx~n's"" raddle-pomt erloivalenee by sholring thst. if &* exists, then (s? &'i 1s ...

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by  many researchers. Considering the quantity discount in  purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In  this paper, stochastic dyn...

Facets for the polyhedron of two-connected networks with bounded rings Abstract. We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a \ring") does not exceed a given length K. We present here a new formulation of the problem and derive facet results for di...