Vector Combinatorial Problems in a Space of Combinations with Linear Fractional Functions of Criteria

The paper considers vector discrete optimization problem with linear fractional functions of criteria on a feasible set that has combinatorial properties of combinations. Structural properties of a feasible solution domain and of Pareto–optimal (efficient), weakly efficient, strictly efficient solution sets are examined. A relation between vector optimization problems on a combinatorial set of combinations and on a continuous feasible set is determined. One possible approach is proposed in order to solve a multicriteria combinatorial problem with linear- fractional functions of criteria on a set of combinations.

Matrix Power S-box Analysis

* Work supported by the Lithuanian State Science and Studies Foundation.

Realization of an Optimal Schedule for the Two-machine Flow-Shop with Interval Job Processing Times

Non-preemptive two-machine flow-shop scheduling problem with uncertain processing times of n jobs is studied. In an uncertain version of a scheduling problem, there may not exist a unique schedule that remains optimal for all possible realizations of the job processing times. We find necessary and sufficient conditions (Theorem 1) when there exists a dominant permutation that is optimal for all possible realizations of the job processing times. Our computational studies show the percentage of the problems solvable under these conditions for the cases of randomly generated instances with n ≤ 100 . We also show how to use additional information about the processing times of the completed jobs during optimal realization of a schedule (Theorems 2 – 4). Computational studies for randomly generated instances with n ≤ 50 show the percentage of the two- machine flow-shop scheduling problems solvable under the sufficient conditions given in Theorems 2 – 4.

Discrete Generalization of Gronwall-Bellman Inequality with Maxima and Application

Снежана Христова, Кремена Стефанова, Лиляна Ванкова - В работата са решени няколко нови видове линейни дискретни неравенства, които съдържат максимума на неизвестната функция в отминал интервал от време. Някои от тези неравенства са приложени за изучаване непрекъснатата зависимост от смущения при дискретни уравнения с максимуми.

N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

A Fast Algorithm for Weber Problem on a Grid

AMS subject classification: 90B80.

Optimization Problem in a Class of Linear System. Application to Multiple Drug Administration

2000 Mathematics Subject Classification: 62H15, 62P10.

A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.