-
Yu.
A. Zack
SOLUTION OF THE
GENERALIZED JHOHNSON PROBLEM WITH CONSTRAINTS ON THE SCHEDULE AND TIME
OF THE MASHINE. PART 1. EXACT SOLUTIONS
METHODS
(Control
Sciences / Problemi
upravlenija, 2010, № 3, P. 17-25)
The
problem of finding of optimal permutation which determines the
sequence of a set of
tasks in a fixed and equal of all tasks sequence of execution of
certain works of different machines, is generalized to the case when
the restrictions on the start and end time both for the execution of
individual tasks, and the time of equipment work a set. The
properties of admissible and optimal sequence of tasks are studied.
The formulas calculating the lower limit of the total length schedule
are presented. Exact and approximate methods for solving the problem
are developed.
-
Yu.
A. Zack
SOLUTION
OF THE GENERALIZED JHOHNSON PROBLEM WITH CONSTRAINTS ON THE SCHEDULE
AND TIME OF THE MASHINE. PART 2. APPROXIMATIVE METHODS OF SOLUTION
(Control
Sciences / Problemi
upravlenija, 2010, № 4, P. 12-19)
The
complex algorithm of the flow-shop problem solution using heuristics
based on various hypotheses and preference rules is developed. The
rules of construction of the tasks
performance sequences that allow analyzing various areas of
attraction of local minima an offered. The paper shows that
efficiency of the constructed schedules increases due to the local
variation algorithm offered. Comparison with earlier received
solutions is given, the numerical example is made.
-
Yu.
A. Zack
CONSTRUCTION
OF
POSSIBLE AND OPTIMALE SCHEDULE
OF IMPLEMENTATION OF WORKS ON ONE MACHINE
(Cybernetics
and Systems Analysis/ Kibernetika
i
sistemny analiz, 2011, № 2)
Properties
of feasible and optimum solutions of task of the construction
races-limning of implementation of tasks are certain on one machine
in the conditions of limits on partial orders and terms of completion
of tasks. The new are developed, not examined in literature exact and
close methods and algorithms decisions of the formulated task, which
carry out approaching to the optimum time-table from below and allow
decisions to set the fact of unjointness of the initial system of
limitations, and also list of tasks on the initial stages, the
temporal range of implementation of which must be extended. The
offered algorithms are illustrated numerical examples and can find
application at the decision of wide class of the applied tasks.
-
Yu.
A. Zack
MATHEMATICAL
METHODS
IN THE TASKS OF PROCESSING RESULTS OF PROFESSIONALS AND
APPLICANTS QUALIFICATIONS TESTING PROFESSIONAL AND ENTRANTS
(Informationnije
technologii, 2010, № 9, P.
57-64)
Problem
solving for the test results evaluation tasks is offered by vector
optimization techniques. Techniques of developing and calculating the
values of complex compromise criterion of evaluating of testing
results are offered. It allows presenting the results of test set as
a certain real number. Recommendations are given for tests
design.
The results obtained here might be used for scoring in
computer training systems, as well as in the procedure of employee
and student selection, when the number of available working and
training places is not enough for all the applicants.
-
Yu.
A. Zack
THE
METHODS OF RISK ASSESSMENT IN THE TASKS OF THE SELECTION
OF THE EFFICIENTS PORTFOLIO SECURITIES AN THE DECISION MAKING OF ENT
SET OF ALTERNATIVES
(USiM,
2010, № 4, P. 84-92)
A
problem of forming an efficient portfolio
of securieties is considered in a multiobjektive formulation and in
the terms of a system of constraints. Some particular reformance
criteria and limitations specifed in the form of the probality of
obtaining some capital gains are not below a specifed set level. The
method for solving the formulated problems in conditions od selecting
the most efficient solution from a set of alternatives are suggested.
(Figs.:
1,
Tables: 7)
-
Yu.
A. Zack
OPTIMIZATION
OF THE PLANNING OF PRODACTION AND THE GATTING OF PAPER PRODUCTS
(USiM,
2010, № 5, P. 82-93)
A
n integrated mathematical model of planning the loading of paper
making machines an the multi-step cutting of paper as a task of
linear progamming of a big size is suggested. All real restrictions
in the production are taken into account. The algorithms of
constructing the optimal time-tables of the technological equipment
are singled out.
(Figs.:
2)
-
Yu.
A. Zack, S. V. Rotin
Mathematisches
Modell und Algorithmen der Termin und Reihenfolgeplanung
Mathematisches
Modell und exaktes Lösungsverfahren für das Job-Shop-Problem
mit
zusätzlichen Restriktionen auf Beginn und Abschluss einiger Jobs
Mathematical
model
and algorithms of the appointment and scheduling
(http://www.optimorum.de/doc/J_II_Cmax.pdf)
Summary
The
temporal
and capacity planning in the form of job-shop problem with
additional restrictions on the initiation and completion of several
jobs is considered. On the base of determined properties of the
earliest and latest possible times for the initiation of scheduling
operations we succeed in obtaining of effective low bounds for the
project duration. Using these we can cut off the plans with wittingly
inadmissible order of operations from the first steps of the
algorithm, and determine conflicts in the resources and/or in the
prescribed periods for completion of certain jobs. Accurate and
approximate numerical methods are developed, based on the successive
approximations to the feasible set "from below", which
permit on each iteration to control efficiently the compatibility of
the arising constraints, which include the iteratively refined common
temporal restriction on the completion of all jobs. The first
compatible solution, found in the process of progressive relaxation
of the common temporal restriction, has to be optimal.
-
Yu.
A. Zack
Mathematical
models of trade-off schemes in multicriteria mathematical programming
problems with fuzzy constraints
(Cybernetics
and
systems analysis, 2010, Volume 46, № 5, P. 755-771.)
Abstract
Single-
and multicriteria mathematical programming problems with fuzzy
constraints are formulated as vector optimization problems. The
formulations of such problems, their mathematical models, trade-off
schemes, efficiency criteria, and solution methods are considered.
Fuzzy logic membership functions are proposed to represent losses due
to violations of some boundary conditions. Methods for the
normalization of local criteria are given. Algorithms and
computational schemes are proposed to solve these problems where the
solutions are chosen from a finite set of alternatives. A numerical
example is given.