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In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity , and items of different classes, each item with class and size . The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are packed consecutively. Moreover, items in consecutive shelves must be separated by shelf divisors of size . In...
In this paper we present a dual approximation scheme for the class
constrained shelf bin packing problem.
In this problem, we are given bins of capacity 1, and n items of
Q different classes, each item e with class ce and size
se. The problem is to pack the items into bins, such that
two items of different classes packed in a same bin must be in
different shelves.
Items in a same shelf are packed consecutively.
Moreover, items in consecutive shelves must be separated by shelf
divisors of size...
The purpose of this paper is to prove the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with positive price vector with nonsatiated utility functions of consumers by using variational inequalities. Moreover, the same technique is used to give an alternative proof of the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with nonnegative, nonzero price vector with nonsatiated utility functions.
The paper deals with the optimal inspections and maintenance problem with costly information for a Markov process with positive discount factor. The associated dynamic programming equation is a quasi-variational inequality with first order differential terms. In this paper we study its different formulations: strong, visousity and evolutionary. The case of impulsive control of purely jump Markov processes is studied as a special case.
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space are introduced....
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function.
The present paper generalizes these results to vector variational inequalities
putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced.
Under...
In the present note we consider the definitions and properties of locally pseudo- and quasiconvex functions and give a sufficient condition for a locally quasiconvex function at a point x ∈ Rn, to be also locally pseudoconvex at the same point.
When a system of one-sided max-plus linear equations is inconsistent, its right-hand side vector may be slightly modified to reach a consistent one. It is handled in this note by minimizing the sum of absolute deviations in the right-hand side vector. It turns out that this problem may be reformulated as a mixed integer linear programming problem. Although solving such a problem requires much computational effort, it may propose a solution that just modifies few elements of the right-hand side vector,...
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