A COLLABORATIVE OPTIMIZATION MODEL FOR

STRATEGIC PERFORMANCE

Zhang Hao, Cui Li, Zhou Yong-sheng and He Ming-ke

School of Business, Beijing Technology and Business University, Beijing, China

zhhaozhhao@126.com

Keywords: Strategy, Performance, Collaborative optimization, Chaos optimization.

Abstract: The logical framework formed by enterprise strategic performance which designed from the dimensions of

structure, capability and the culture is what we used to refine the key points of strategic performance. To

construct a collaborative optimization model for strategic performance, it should be based on the overall

optimization framework of collaborative optimization technology with the chaotic optimization method.

The objective of system-level optimization is strategic performance optimization. The optimization goal of

the subsystem-level is to make the difference between the designed subsystems and the subsystems

provided by system-level optimization as little as possible. The numerical simulations show that the model

is scientific and feasible.

1 INTRODUCTION

The operation of the enterprise consumes a variety of

resources. Both the external resources and the

internal resources are factors that affect the

enterprise strategic objectives. Allocation of

resources is the key content of strategic

development, strategy implementation and strategic

control. It is in the process of being continuous

optimized. The optimization of strategic

performance can be achieved by allocating the

limited resources so as to maximize the performance,

and create cost-effective for companies, so that the

limited resources can get into the most lucrative

returns. How to effectively optimize the performance

of the strategy is an important task both in theory

and practice community. Based on the concept of

collaborative optimization, this paper forms the

strategic synergy mechanism operation framework

with the sub-systems coupling by structure,

capability and culture, and composes collaborative

optimization model for strategic performance

combined with chaos optimization method and

makes numerical simulation.

2 THE LOGICAL FRAMEWORK

OF THE FORMATION OF

ENTERPRISE STRATEGIC

PERFORMANCE

Strategy performance optimization is to

comprehensively and dynamically adjust the

input-output relations between the financial elements

and non-financial elements which will influence

strategy performance, so as to achieve the enterprise

overall strategy performance optimization. Strategic

system consists of the structure, capacity and cultural

composition, as shown in Figure 1. The three

dimensions are coupling with one another,

interrelated and mutually supporting. The strategic

system adjusts the relationship between the three

dimensions according to changes in the internal and

the external environment of the enterprise. It will

adjust the configuration of resources and the extent

of influence in order to make sure the strategic

performance optimization. Cooperating the sectors

of enterprises and the resource allocation, making

the strategy performance always maintain the

optimal status, adjusting the disharmony factors

between enterprise and its business environment, and

correcting deviations in time will help enterprise

adapt to the external environment better. After all the

strategic business units are aware of the stimulation

645

Hao Z., Li C., Yong-sheng Z. and Ming-ke H..

A COLLABORATIVE OPTIMIZATION MODEL FOR STRATEGIC PERFORMANCE.

DOI: 10.5220/0003573306450649

In Proceedings of the 13th International Conference on Enterprise Information Systems (MMLM-2011), pages 645-649

ISBN: 978-989-8425-56-0

Copyright

c

2011 SCITEPRESS (Science and Technology Publications, Lda.)

from the external environment, they will achieve

information sharing by initially screening and

analyzing the information then communicating with

each other. Thus, the strategic business unit formed a

coupling relationship. However, the coupling

manner and extent are not determined by the

strategic business units. They pass the information to

the strategy system, and then the strategy system

calculates and balances the internal and external

environment status and the development trend

comprehensively. On one hand it will pass the

amended information to the strategic business units,

on the other hand it will export the strategic

collaborative performance. The strategic business

unit adjusts the coupling relationship between each

other according on the instruction passed by the

strategic layer, so that to achieve a dynamic

optimization strategy and to ensure that the

companies can adjust their strategies timely.

Figure 1: Logical Framework Which Strategy Performance

Formed.

3 PRINCIPLES OF

COLLABORATIVE

OPTIMIZATION FOR

STRATEGIC PERFORMANCE

This paper uses the idea of collaborative

optimization for reference to design the principles of

collaborative optimization for strategic performance.

Collaborative optimization is method proposed by

Braun which decomposing, coordinating and

integrated optimizing according to one discipline to

multidisciplinary designed optimization. Each

discipline’s calculations have a very good degree of

autonomy, without taking into the account of the

impact of other disciplines. The basic framework of

collaborative optimization consists of optimization

of system-level and subsystem level. In sub-system

optimization, design variables are only related to the

design parameters of the discipline involved with

and coupling variables of other related disciplines. If

it meets the requirement of the internal constraints of

the subsystems, the optimization objective is to make

the difference between the optimization solution of

the subsystem and system level as minimum as

possible. The task of system-level optimization is to

make the best overall objective of the system, and

coordinate activities of the various subsystems so

that the variance between each sub-system’s

optimization results will gradually decrease. Taking

strategic system as the system-level of optimization,

structure, capability, culture as a subsystem (which

can also be divided from other aspects), the coupling

relationship between subsystems will be determined

by the system level optimization.

Definition I. During the process of designing and

operating the enterprise strategy system,

collaborative optimization for enterprise strategic

performance must analyze the extent of the

interaction between subsystems, and adjust the

models and methods of enterprise system

optimization by taking advantage of these

interactions.

Definition II.

Co

i

SubsystemSystem

Δ+Δ=Δ

∑

)( (1)

In equation (1),

System

Δ means the overall

system performance,

∑

Δ

i

Subsystem

is the sum

performance of subsystem, and

Co

Δ

means the

increment calculated the interaction between the

various subsystems after collaborative

optimization.

Definition III. Subsystem: The basic module in

enterprise system which are independent in functions

but keeping mutual exchange of information and

material as well. Such as: sales department and

production department, finance department and sales

department.

Definition IV. Design variables: A group of

independent variables used to describe the

characteristics of the strategic system, and can be

controlled in the design process.

Definition V. State variables: A set of parameters

Strategy System

Framework

Capabilit

Culture

Strategy Performance

External environment

Stimulation

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

646

used to describe the function or characteristics of the

system or subsystems.

Definition VI. Constraints: The constraints needed

to be met during the operation of system or

subsystems.

Definition VII. System Collaborative Optimization:

In collaborative optimization for strategic

performance, the subsystems coordinate for their

common strategic goal - the best of the overall

enterprise systems. The relationship of each

subsystem is more cooperative. System layer is

responsible for planning, coordination and leading

the overall direction of optimization; subsystem is

responsible for the compatibility optimization, and

study the feasibility of the direction of optimization.

The mathematical description of collaborative

optimization for strategic performance as:

System layer:

)(min xf

..t

s

0)( =xC

i

Sub-system layer

： )(min

∗

xC

i

..t

s

)(xg

i

)()()(

∗∗∗∗

−−= xxxxxC

T

i

)()()( xxxxxC

T

i

−−=

∗∗∗

ni ,,3,2,1 "=

In the equation above:

x

is the system level

design variables,

)(xf

is the objective function,

)(xC

i

is the compatibility constraint of subsystem

i

,

∗

x

is the design variables of sub-system layer,

∗∗

x

is the design variables’ optimization results of

subsystem, )(

∗

xC

i

is the objective function for the

subsystem

i

,

n

is the number of the variables.

4 THE COLLABORATIVE

OPTIMIZATION MODEL FOR

STRATEGIC PERFORMANCE

The structure of Collaborative optimization model

can be designed according to the logical framework

of strategic performance. It can be divided into two

levels: system level and subsystem level. System

layer is responsible for the overall strategic systems

optimization; the sub-system layer is responsible for

the optimization of the subsystem itself. The system

level and subsystem layer have got a close coupling

relationship. The subsystem-level’s optimization

goal is to make the difference between the designed

subsystems and the subsystems provided by

system-level optimization as little as possible.

Figure 2: Framework of Collaborative Optimization for

Strategic Performance.

Figure 3: Function for Collaborative Optimization for

Strategic Performance’s Framework.

The strategic elements of structure dimension

contain capital structure, product structure,

organizational structure and personnel structure. The

strategic elements of capacity dimension include

marketing capability, management capability,

innovation and decision-making capability. The

strategic elements of culture dimension consist of

values, cohesion, entrepreneurship, enterprise

learning. Standardized the value of the performance

elements of the strategy, making

i

x

represents the

performance value of the

i

strategic element,

)(xf

for the system level performance value,

1

f ,

2

f ,

3

f

for performance value corresponding to the

System level strategic optimization

Optimization：System objective

Constraint ： The coupling variables

b

etwee

n

subsystems and shared variables are same

Optimization of subsystem

1

Optimization：

Collaboration

between

subsystems

Constraint：Constraint of

subsystem 1

Optimization of subsystem

n

Optimization：

Collaboration

between

subsystems

Constraint：Constraint of

subsystem 1

Analysis module of

subsystem 1

Analysis module of

subsystem

n

System level strategic optimization

)(min zf

..t

s

0))((),(

2

=−=

∑

∗∗

zxPzxJ

iii

Optimization of

subsystem 1

2

1

))((

)(min

zqx

xJ

ii

i

−

=

∑

..t

s

0)(

1

≤

id

xh

0)(

1

=

ie

xg

Optimization of

subsystem

n

2

))((

)(min

zqx

xJ

ii

in

−

=

∑

..t

s

0)( ≤

ind

xh

0)( =

ine

xg

A COLLABORATIVE OPTIMIZATION MODEL FOR STRATEGIC PERFORMANCE

647

three subsystems respectively. As enterprise systems

with the feature of complexity, chaos and

collaboration, so combined the collaborative

optimization with chaos optimization, collaborative

optimization model for strategic performance is

shown below. In this model

∗

x

is the optimal

solution calculated by the system,

∗∗

x

is the

optimal solution returned by the subsystem,

α

is

for the weight. Strategic performance is the bigger

the better, therefore, in the design of system level,

we take

)(xf

as the reciprocal of the value of

strategic performance.

(1) System layer：

i

i

i

xxf

∑

=

=

12

1

/1)(min

α

(2)

..t

s

10 ≤≤

i

x

)12,,2,1( "=i

0)()(

)()()(

2

1212

2

1111

2

88

2

66

2

4

1

1

=−+−+

−+−+−=

∗∗∗∗

∗∗∗∗∗∗

=

∑

xxxx

xxxxxxf

i

i

i

0)()(

)()()(

2

1212

2

1010

2

22

2

11

2

8

5

2

=−+−+

−+−+−=

∗∗∗∗

∗∗∗∗∗∗

=

∑

xxxx

xxxxxxf

i

i

i

0)(

)()()(

2

77

2

66

2

33

2

12

9

3

=−+

−+−+−=

∗∗

∗∗∗∗∗∗

=

∑

xx

xxxxxxf

i

i

i

(2) Subsystem layer：

① Subsystem 1：

2

1212

2

1111

2

88

2

66

2

4

1

1

)()()(

)()(min

∗∗∗

∗∗

=

−+−+−+

−+−=

∑

xxxxxx

xxxxf

i

i

i

(3)

..t

s

9.05.0

1

≤≤ x

861

5.05.0 xxx +≥

95.0

3

≤x

12114

6.04.0 xxx +≥

②Subsystem 2：

2

1212

2

1010

2

22

2

11

2

8

5

2

)()()(

)()(min

∗∗∗

∗∗

=

−+−+−+

−+−=

∑

xxxxxx

xxxxf

i

i

i

(4)

..t

s

95.06.0

5

<

<

x

5102

5.05.0 xxx ≤+

1247

6.04.0 xxx +≥

6108

5.05.0 xxx +≥

③Subsystem 3：

2

77

2

66

2

33

2

12

9

3

)()(

)()(min

∗∗

∗∗

=

−+−+

−+−=

∑

xxxx

xxxxf

i

i

i

(5)

..t

s

9.0

9

≤x

4.0

10

≥x

10119

7.03.0 xxx ≤

+

5.0

11

≥x

10712

xxx ≤

If

i

x

generated by the chaotic sequence cannot

satisfied the constraints, then transformed

i

x

,take

1,

)(

+

+=

niiii

xdckx ,

i

c

is the lower limit for the

constraint,

i

d

is the absolute value of the

difference between the upper and lower limit

constraints.

5 MODEL SIMULATIONS

Standardize the performance evaluation of strategic

elements of the enterprise, each evaluation value is

somewhere in between

]1,0[

. The weight of each

index, initial value, final value, function values are

shown in Table 1.

Table 1: Simulation Data.

i

x

i

α

i

x

initial

value

i

x

final

value

)

(min xf

(min

x

f

∗∗

1

x

0.092 0.946 0.527

3.106 1.145

2

x

0.105 0.173 0.351

3

x

0.067 0.146 0.864

4

x

0.057 0.909 0.569

5

x

0.112 0.195 0.746

6

x

0.085 0.591 0.023

7

x

0.073 0.139 0.459

8

x

0.096 0.109 0.814

9

x

0.064 0.188 0.870

10

x

0.095 0.161 1.000

11

x

0.078 0.241 1.000

12

x

0.076 0.210 0.026

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

648

Figure 4: Alternation curve with

50=n

.

The value of each index of current enterprise’s

performance is the initial value. Through optimized,

each index can obtain its relative optimum value in

the strategic systems. When the time f alternation is

50, the optimization curve is what’s shown in Figure

4. When the initial function value is 3.106, the

corresponding value of the strategic performance is

0.322. After iterations, the optimal function value is

1.145, the corresponding optimal value is 0.873.

That’s optimal value is the theoretical value, the state

it corresponds to is ideal, which may have got some

difference with the reality. For example, the optimal

value which corresponds to the management ability

6

x and the corporate learning

12

x is too small. The

deviation with the actual situation is the result of the

constraint set. The relative optimal value is

theoretical. In practice, there may be a variety of

uncontrollable factors. In theory, if we can express

each influential factor by function scientifically and

reasonably, and set the corresponding constraints,

then the method can offer useful ideas for enterprise

strategy collaborative optimization.

6 CONCLUSIONS

This paper designs principle and structure about

strategic performance collaborative optimization the

bases on the concept of collaborative optimization,

composes operation collaborative optimization model

combined with chaos optimization method and makes

numerical simulation. Taking strategic system as the

optimization system-level, analyzing strategic

elements from dimensions of structure, capability and

cultural, the coupling relationship between

subsystems is determined by the system-level

optimization. Strategy system calculates and balances

the internal and external environment status and the

development trend comprehensively. On one hand it

will pass the amended information to the strategic

business units, on the other hand it will export the

strategic performance. The strategic business unit

adjusts the coupling relationship between each other

according on the instruction passed by the strategic

layer, so that to achieve a dynamic optimization

strategy, which reflects the consistency and

collaboration of the internal and external environment.

The model is feasible in theory proved by numerical

simulations, in practice, it still needs to set more

comprehensive and specific data conditions.

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