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MODELS AND AN ALGORITHM FOR MULTI-CRITERIA SYNTHESIS OF
CONTROL TECHNOLOGIES MANAGING INFORMATION SYSTEMS OF
VIRTUAL ENTERPRISES
Dmitry A. Ivanov
Chemnitz University of Technology
Department of Economics and Business Administration
Chair of Production and Industrial Management
D-09107 Chemnitz, Germany
E-Mail: idm@hrz.tu-chemnitz.de
Boris V. Sokolov, Dmitry N. Verzilin, Evgeniy M. Zaychik,
Russian Academy of Science,
Saint Petersburg Institute of Informatics and Automation
39, 14 Linia, VO
St.Petersburg, 199178, Russia
E-mail: sokol@iias.spb.su, verzilin@SV10100.spb.edu, EZaychik@beeline.ru,
KEYWORDS
Optimization, Planning, Dynamic Models, Simulation,
Information Systems, Virtual Enterprises.
ABSTRACT
Integrated information systems (IIS) of virtual
enterprises (VE) were considered as objects of control.
Two interrelated problems were jointly stated. The first
problem lied in program management of IIS and ranking
its structural states. The second one implied that control
functions regulating business processes should be
reallocated among elements and subsystems of IIS in a
real time mode. A formal multi-criteria description of
these problems was made and a combined (simulation-
based) algorithm of a solution was worked out.
INTRODUCTION
Virtual enterprises unite independent multi-business
partners (real enterprises) within a temporal task-
oriented technical-organizational structure through
information technologies and telecommunications
(Camarihna-Matos et al. 2004, Wang and Norrie 2001,
Ivanov 2003). Virtual enterprises are highly adaptive to
consumer needs and benefit juridical and physical
persons providing them with dynamic use of common
resources during remote collaboration within a business
project.
A virtual enterprise is a typical example of a modern
integrated transport, production and trading network
performing intensive structural dynamics. This issue
makes the structural synthesis of a VE more
complicated. In particular, the structure dynamics have a
complicative influence upon the following tasks: partner
selection (producers and suppliers of components,
retailers, etc); end products configuring; placement of
orders; configuring transport network and information
resources (Camarihna-Matos et al. 2004, Wang and
Norrie 2001).
An integrated information system is one of the main
subsystems of VE. It should be constructed through a
real-time configuring (structure-functional synthesis)
and interconnection of individual information systems
belonging to participants (real enterprises).
It is obvious that IIS run under conditions of structure
dynamics same as VE does (Okhtilev et al 2006).
Possible variants of structure dynamics involving
modern information systems are illustrated in fig. 1. Our
previous investigations confirmed that incrementation
(stabilization) of IIS potentialities and capacity for work
necessitates structures control (including the control of
IIS structures reconfiguration). There are many possible
variants of structure-dynamics control suitable for IIS.
The following variants are the most typical: alteration of
IIS functioning means and objectives; controlled motion
of CTS elements and subsystems; alteration of the order
of IIS tasks; redistribution of functions, tasks, control
algorithms and information flows among IIS levels;
reconfiguring of degraded structures; flexible use of
reduced technologies of IIS control.
As applied to IIS, the structure-dynamics control
belongs to the general discipline of structure-functional
synthesis and program construction, provided for IIS
development (Okhtilev et al 2006, Kalinin and Sokolov
1995, Zvirkun and Akinfiev 1993, Zvirkun et al. 1985,
Zimin and Ivanilov 1971).
Here we consider an important problem of structure-
dynamics control including interrelated business
processes (BP) planning and planning of IIS operations
aimed at BP improvements.
Proceedings 22nd European Conference on Modelling and
Simulation ©ECMS Loucas S. Louca, Yiorgos Chrysanthou,
Zuzana Oplatková, Khalid Al-Begain (Editors)
ISBN: 978-0-9553018-5-8 / ISBN: 978-0-9553018-6-5 (CD)
t
j
t
j+1
Business
Process
(BP)
Information
System
(IS)
Virtual Enterprise (VE)
B
1
VE (B
2
)
IS
2
IS
l
IS
1
IS
2
IS
n
Structure
State R
1
IS
l
IS
1
IS
2
IS
n
Structure
State R
2
IS
l
IS
1
IS
2
IS
n
Structure
State R
3
IS
1
IS
2
IS
n
Structure
State R
4
IS
l
IS
1
IS
n
Structure
State R
5
IS
l
IS
1
Structure
State R
6
IS
1
IS
2
Structure
State R
7
VE (B
n
)
IS
n
VE (B
l
)
IS
l
Telecommunicational
System (TS)
Figures 1: Variants of structure dynamics
PROBLEM STATEMENT
Modern IIS ought to reconfigure and adjust information
processes in order to agree with changeable business
projects and conditions of their execution.
Efficient functioning of IIS necessitates flexible
redistribution of tasks, functions and algorithms among
elements, subsystems and levels of the system.
Therefore following main tasks have to be redistributed:
receiving, transmission and processing of information,
planning and control of IIS and VE operation.
Moreover, different control technologies involve
different variants of IIS structures and different
information flows in control loops of IIS.
From a formal point of view a selection (synthesis) of
BP structure as well as a real-time structure-functional
synthesis of IIS implies joint multi-criteria optimization
of VE and IIS operation, selection of control functions
for business processes and redistribution of control
functions among nodes of IIS. Due to the real-time
mode of the IIS, the problem to be solved is more
complicated than the ones described in the works of
(Zvirkun and Akinfiev 1993, Zvirkun et al. 1985).
The problem of real-time distribution of control
functions can be solved at different stages of BP life
cycle. In our approach we consider the period of IIS
operation planning with simultaneous preliminary
distribution of control functions among main elements
of IIS and with construction of control programs for
these elements. The control programs can be corrected
at the stage of real-time control (implementation of the
plan). Program corrections can be accompanied by
reallocation of resources and by reconfiguration of IIS
structures.
Let us introduce some notation for problem definition.
Let A = {A
i
, i
∈
N={1,...,n}} be a set of business
processes (and corresponding control functions) to be
implemented at some node of IIS at a given time interval
T = [t
0
, t
f
]. To achieve the VE goals during the interval
T, the BPs have to be fulfilled. We distinguish between
the functions of goal definition, planning (long term and
operational planning), real-time control, VE states
analysis, external situation analysis and coordination.
The set A={A
i
, i
∈
N} is related to sets of informational-
technological operations
}},...,1{æ,{
)(
æ
)(
i
ii
sKDD =∈=
, that are
necessary for implementation of BP A
i
, i =1,...,n. Let
В={B
j
,j
∈
M={1,...,m}} be a set VE main elements and
subsystems. Each element B
j
can include technical
facilities
}},...,1{,{
)()(
lLCC
jj
=∈=
λ
λ
with
appropriate computer equipment and software.
Technical facilities are used for implementation of
control functions.
Let E(t) = ||e
i j
(t)|| be a known matrix function, with
e
ij
(t)=1 in case of the subsystem B
j
is carrying out the
function A
i
at time t in accordance with time-spatial,
technical and technological constraints, e
ij
(t)=0
otherwise.
Fig.1 presents an example of seven possible structural
states of IIS. The arrows show variants of
communication within the system. These variants
correspond to different control technologies (methods of
IIS application) and different spatial structures of VE.
Now the verbal description of a functions-distribution
problem can be presented as follows. It is necessary to
select the best variants of functions distribution among
the nodes of IIS for each structural state R
1
,R
2
,...,R
k
of
IIS (under known time spatial, technical and
technological constraints) and to find the best variants of
functions implementation. The structural states of IIS
should be sorted according to their preference. The
preference relation can be expressed through quality
functions characterizing efficiency of IIS and its
structural and technologic characteristics.
The described problem belongs to the class of multi-
criteria choice problems with finite sets of alternatives
(structural states of IIS).
ALGORITHM OF MULTI-CRITERIA PLANNING
OPERATIONS IN IIS
The general algorithm for the problem includes the
following steps.
Step 1. Models (analytical, simulation and combined
models) describing structural states R
1
,R
2
,...,R
k
are used
for optimal distribution of BP and control functions
among subsystems of IIS, for technological operations
planning and for evaluation of IIS efficiency. The
following characteristics of IIS efficiency can be used:
the total number of functions implemented in
subsystems during the interval Т, the total number of BP
in given macro-states, the total number of technological
operations executed over the time interval Т, the total
time of operations over the time period Т. The above-
mentioned characteristics can have stochastic or fuzzy
interpretation if uncertainty factors are present (Okhtilev
et al 2006, Orlovski. 1981).
The following dynamic model of functions distribution
can be used for evaluation of IIS efficiency (Okhtilev et
al 2006, Kalinin and Sokolov 1995, Zimin and Ivanilov
1971).
;;)(
)0(
æ
1
æ
)0(
æ
)(
1
)(
λ
λ
λ
φφ
ε
ji
l
jijiji
m
j
jii
ubxutx
∑∑
==
== &&
)()(
φφ
ν
jiji
y=
&
; (1)
( ) ( )
;0
1
)()()()()(
2
1
=
−+−
∑∏
∑
=Γ∈
Γ∈
m
j
ji
i
i
xaxau
β
φ
γ
φ
γ
α
φ
α
φ
α
φ
(2)
( ) ( )
0
1
)0()0()0()0()0(
æ
2æ
1æ
=
−+−
∑∏
∑
=Γ∈
Γ∈
l
jijijijiji
i
i
xaxau
λµ
µµ
ν
ννλ
;(3)
;;1)(;;1)(
1
)(
1
)(
itujtu
m
j
ji
n
i
ji
∀≤∀≤
∑∑
==
φφ
}1,0{)(
)(
∈tu
ji
φ
; (4)
,1)(æ;,,1)(
1 1æ
)0(
æ
1 1
)0(
æ
≤∀∀≤
∑∑∑∑
= == =
n
i
s
ji
m
j
l
ji
tuitu
λ
λ
λ
},0{)(æ;,
)()0(
æ
φ
λ
jiji
utui ∈∀∀
; (5)
(
)
}1,0{)(;0
)()0()0()(
∈=− txa
jijsijsiji
φφ
νν
; (6)
0)()()(
0
)(
0
)0(
æ0
)(
=== tytxtx
jijii
φφ
; (7)
(
)
;0)()(;)(
)(
æ
)0(
æ
)()(
=−=
fjifjijiifi
tytxaatx
φφφ
(
)
;0)()(;)(
)(
æ
)0(
æ
)()(
=−=
fjifjijiifi
tytxaatx
φφφ
(8)
;)(;)(
1
)()(
1
1 1
)(
0
∑∑∑
== =
==
m
i
fjn
n
n
i
m
j
fji
tJtJ
φφ
νν
;)(;)(
1
)()(
1
1 1
)(
0
∑∑∑
== =
==
m
i
fjn
n
n
i
m
j
fji
tJtJ
φφ
νν
(9)
where
)(
)(
tx
i
φ
is equal to total duration of the business
process Ai fulfillment in subsystem Bj as
1)(
)(
=tu
ji
φ
;
the variable
)0(
æ ji
x
express the current state of the
technological operation
)(
æ
i
D
;
)(
φ
ji
y
is equal to the time
passed after A
i
completion in B
j
until the time t = t
f
;
)0()0()0()0()(
,,,,
jiji
aaaaa
µνγα
φ
α
are given values setting end
conditions for
)(
)(
tx
i
φ
,
),(),(
)()(
txtx
φ
γ
φ
α
)(),(
)0()0(
txtx
jiji
µν
at time t =
t
f
;
)(
φ
ji
u
,
)0(
æ
λ
ji
u
,
)(
φ
ν
ji
are control inputs. Here
)(
φ
ji
u
(t)=1
if BP A
i
is being executed in the subsystem B
j
at time t,
)(
φ
ji
u
(t)=0 otherwise;
)0(
æ
λ
ji
u
(t)=1 if the technological
operation
)(
æ
i
D
is executed in the technical facility
)( j
C
λ
,
)0(
æ
λ
ji
u
(t)=0 otherwise;
)(
φ
ν
ji
=1 if BP A
i
was
implemented in the subsystem B
j
,
)(
φ
ν
ji
=0 otherwise.
Here the sets
1i
Γ
,
2i
Γ
include the numbers of
functions that are direct predecessors of the control
function Ai. The set
1i
Γ
indicates predecessors
connected by logical “and”, the set
2i
Γ
indicates
predecessors connected by logical “or”. The sets
1æi
Γ
,
2æi
Γ
include the numbers of technological operations
)(i
D
ν
and
)(i
D
µ
that are direct predecessors of the
operation
)(
æ
i
D
. The subscripts 1 and 2 express the type
of logical connection as stated above.
Therefore, constraints (2) and (3) define allowable
sequences of control functions and technological
operations. Constraints (4) and (5) specify that each BP
at each time can be carried out only in one subsystem B
j
(i=1,...,n; j=1,...,m) and conversely, each subsystem B
j
can carry out only one BP A
i
at the same time. Similar
constraints are used for technological operations
)(
æ
i
D
that are executed at the technical facility
)( j
C
λ
.
Expression (6) states switching-on conditions for the
auxiliary control input
)(
φ
ν
ji
(t). Expressions (7) and (8)
specify end conditions for the state variables at the time
t = t
0
, t = t
f
, R
1
is a set of positive real numbers. The
functionals J
0
, J
1
, J
2
are quality measures for distribution
of BP in IIS. Here J
0
is equal to total number of
functions by the time t = t
f
, J
1
is equal to the number of
subsystems the function А
i
is implemented in, J
2
expresses the elapsed time for implementation of all
necessary functions.
A simulation model of real-time control can be used
together with expressions (1)-(9) for taking into account
uncertainty factors. In this case special procedures of
inter-model coordination can be used (Okhtilev et al
2006, Kalinin and Sokolov 1995).
Extreme values of functionals characterizing IIS
efficiency can be determined via solution of optimal
control problem for finite-dimensional differential
system with mixed conditions. The solution algorithms
and different aspects of their programming are
considered in (Okhtilev et al 2006, Kalinin and Sokolov
1995).
Step 2. Structure-topological characteristics of IIS are
being evaluated (Zimin and Ivanilov 1971) including:
the coefficient of attainability J
4
, different measures of
structure compactness (radius J
5
of the structure,
diameter J
6
of the structure, integral measure J
7
of
structural compactness), measures J
8
of structure
centralization (decentralization).
The formulas for computation of measures are proposed
in (Zimin and Ivanilov 1971).
Step 3. The pairwise-comparison matrix Кc is
completed for measuring the IIS efficiency. Expert
appraisal is used for completion of the matrix.
Step 4. The weights of measures (significance
coefficients) are evaluated according to the matrix Кc.
The algorithm proposed in (
Orlovski 1981
) is used here.
The vector of coefficients is equal to the normalized
eigenvector
c
ω
r
corresponding to the maximal
eigenvalue Lmax of the matrix Kc. Thus the following
equation has to be solved:
(Кc –Lmax*I )
c
ω
r
= 0, (10)
where I is a unitary matrix.
Then a weight of each structural state (R
1
, R
2
,..., R
k
) of
IIS for each measure taken separately is evaluated.
These weights complete the matrix Кr. Each column of
the matrix Кr includes relative weights of the states in
respect of some measure. A weighted sum of measures
is received for each alternative R
1
, R
2
,..., R
k
. In other
words, total sets of weights are determined for each
structural state via the formula:
Кr
c
ω
r
=
*
ω
r
. (11)
Step 5. The structural states are sorted according to their
preference. The best one is characterized with the
maximal element of the vector
*
ω
r
. Each element of the
vector
*
ω
r
can be interpreted as a total weight of some
structural state.
CONCLUSIONS
Dynamic interpretation of operation planning in IIS let
thoroughly describe and investigate interrelation and
interaction of business processes and the processes of
information processing, storing and interchange.
The framework of integrated multi-criteria operations
planning in the context of IIS structure-dynamics control
results in the following advantages. The goals of IIS
planning can be directly interrelated with the goals of
business processes. Structure-dynamics operations (IIS
control technology) can be reasonably selected and
substantiated. Efficient compromise solutions can be
found for allocation of control functions among the
elements of IIS and for general programs (plans) of IIS
operation. The preliminary ordering of IIS structural
states let rapidly reconfigure it in case of failures
(Okhtilev et al 2006).
Several prototype versions of software were produced
for structure-dynamics control of IIS in different
application domains (cosmonautics, power industry,
management, etc, see http://www.spiiras-grom.ru). The
experiments with software confirmed efficiency of
models applied.
This work was supported by Russian Foundation for
Fundamental Investigations (grants 06-07-89242, 07-07-
00169, 08-08-00403), by Department of Information
Technologies and Computing of Russian Academy of
Sci. (Project 2.5).
REFERENCES
Camarihna-Matos, L., Kluwer (editors) et al 2004. Virtual
Enterprises and Collaborative Networks, Academic
Publishers, 610 p.
Wang L. and Norrie D. H. 2001. “Process Planning and
Control in a Holonic Manufacturing Environment.”
Journal of Applied Systems Studies, 2(1), 106–126.
Ivanov, D.A. 2003 Virtual Enterprises and Logistics Chains:
Integrated Approach to Organization and Control in New
Forms of Production Cooperation SPbSUEF, 120 p. (In
Russian)
Ohtilev, M.Yu., Sokolov, B.V., Yusupov, R.M. 2006.
Intellectual Technologies for Monitoring and Control of
Structure-Dynamics of Complex Technical Objects.
Moscow, Nauka, 410 p. (in Russian)
Kalinin, V.N. and Sokolov, B.V. 1995. “Multiple-Model
Approach to Description of Control Processes in Space
Systems.” Control Theory and Systems, No 1, 149-156.
(In Russian).
Zvirkun, A.D. and Akinfiev, V.K. 1993. Structure of the
Multi-Level Systems (Synthesis and Development).
Moscow, Nauka. (in Russian).
Zvirkun, A.D. and Akinfiev, V.K., Filippov, V.A. 1985.
Simulation Modeling in the Problems of Complex Systems
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Planning Problems via a Reduction to Optimal Control
Problems.” Journal of Calculus Mathematics and
Mathematical Physics. 11, No 3, 632-641 (in Russian).
Ore, O. Theory of Graphs. 1962. AMS Colloquium
Publications Vol. 38, AMS, Providence, RI, 270 p.
Orlovski, S.A. 1981. Decision Making under Fuzzy
Information. Moscow, Nauka, 208 p. (in Russian).
AUTHOR BIOGRAPHIES
DMITRY IVANOV is a researcher at the Chemnitz
University of Technology and Chair of the German-
Russian Coordination Office for Logistic. He studied
production management and engineering (2000). In
2002, he graduated in Saint Petersburg as a Ph.D. in
Economics on the topic of operative supply chain
planning and control in virtual enterprises. In 2006, he
received the Dr.rer.pol. degree at the Chemnitz
University of Technology. He is an author of six
scientific books and more than 70 papers published in
international and national journals, books and
conference proceedings. Since 2001, he has been
involved in research and industry projects on supply
chain management and virtual enterprises. Dr. Ivanov
received a German Chancellor Scholarship Award in
2005. His e-mail address is
:
idm@hrz.tu-chemnitz.de
.
BORIS V. SOKOLOV was born in Leningrad (now
Saint-Petersburg), Russia in 1951. He obtained his main
degrees in Mozhaisky Space Engineering Academy,
Leningrad. MS in Automation Control Systems of Space
Vehicles in 1974. Candidate of Technical Sciences
subject the area of planning automation and decision
making in 1982. Doctor of Technical Sciences subject
the area of military cybernetics, mathematical modeling
and methods in military research. Professional Interests:
Basic and applied research in mathematical modeling
and mathematical methods in scientific research, optimal
control theory, mathematical models and methods of
support and decision making in complex organization-
technical systems under uncertainties and multi- criteria.
At present he is a deputy director of St.-Petersburg
Institute for Informatics and Automation. His e-mail
address is:
sokol@iias.spb.su
and his Web-page
can be found at
http://www.spiiras-grom.ru.
DMITRY N. VERZILIN was born in Leningrad (now
Saint-Petersburg), Russia in 1960. He graduated from
Mathematical faculty of Leningrad States University in
1982. He obtained the degree of Candidate of Technical
Sciences in Mozhaisky Space Engineering Academy,
1992 and the degree of Doctor of Economics in St.-
Petersburg States University of Economics and
Finances, 2004. At present he is a leading researcher of
St.-Petersburg Institute for Informatics and Automation.
Professional interests lay in operations research,
simulation, and statistical analysis. His e-mail address is
verzilin@SV10100.spb.edu.
EUGENIY M. ZAYCHIK was born in 1962 in Rostov-
on-Don, Russia. He graduated from Military Academy
of Communication in 1992. He is a Candidate of
Technical Sciences (1994, Military Academy of
Communication). He is a specialist in simulation and
control of communication systems. At present he works
in St.-Petersburg Institute for Informatics and
Automation. His e-mail address is
EZaychik@beeline.ru.
