The classical 1962 Benders decomposition scheme is a traditional approach for solving mixed-integer problems such as the uncapacitated facility location problem. Subsequent research has been focused on finding better cutting-plane generation schemes to reduce the solution process time. Pareto-optimal cuts are typically preferred because no other cut can dominate them. However, the Pareto-optim...

the planning of production and control of inventory problem is one of most important problems that companies are face with them. some times inattention to uncertainty in these problems causes to increase of costs of inventory control systems. one of the important ways encountering to uncertainty is the widespread of fuzzy sets instead of crisp numbers because in this approach, we can determine ...

This report constitutes the Doctoral Dissertation for Michael Perregaard and is a collection of results on the efficient generation of disjunctive cuts for mixed integer programs. Disjunctive cuts is a very broad class of cuts for mixed integer programming. In general, any cut that can be derived from a disjunctive argument can be considered a disjunctive cut. Here we consider specifically cuts...

In this article we found the solution of fuzzy linear controlled systemwith fuzzy initial conditions by using -cuts and presentation of numbersin a more compact form by moving to the eld of complex numbers. Next, afuzzy optimal control problem for a fuzzy system is considered to optimize theexpected value of a fuzzy objective function. Based on Pontryagin MaximumPrinciple, a constructive equati...

Gomory mixed-integer (GMI) cuts generated from optimal simplex tableaus are known to be useful in solving mixed-integer programs. Further, it is well-known that GMI cuts can be derived from facets of Gomory’s master cyclic group polyhedron and its mixed-integer extension studied by Gomory and Johnson. In this paper we examine why cutting planes derived from other facets of master cyclic group p...

Two-dimensional alphabetic trees have many applications in a wide variety of diverse fields. Although, a relatively fast algorithm that finds an approximate optimal alphabetic tree (OAT) does exist, yet, the only way to find the exact one is to use dynamic programming. In dynamic programming the (OAT) is found by simply examining all nodes in the two dimensional array of weights as possible roo...

A new approach is proposed for finding optimal cuts in hierarchies of partitions by energy minimization. It rests on the notion of h-increasingness, allows to find best(optimal) cuts in one pass, and to obtain nice ”climbing” scale space operators. The ways to construct h-increasing energies, and to combine them are studied, and illustrated by two examples on color and on textures.