J. Service Science & Management, 2010, 3, 363-368
doi:10.4236/jssm.2010.33042 Published Online September 2010 (http://www.SciRP.org/journal/jssm)
363
Decision-Making Optimization of TMT: A
Simulated Annealing Algorithm Analysis
Yueming Chen, Yuhui Ge, Zhiqiang Song, Mingyang Lv
School of Management, University of Shanghai for Science and Technology, Shanghai, China.
Received May 14th, 2010; revised June 19th, 2010; accepted July 26th, 2010.
ABSTRACT
The decision-making of Top management team (TMT) has been a hot point in academic. The paper find out annealing
algorithm method can effectively solve the decision-making optimization problem. Through considering the quality and
efficiency of decision-making, applying the annealing algorithm, the optimal decision preference sequence is found.
Finally, an application case is proposed. Through determining the initial solution, and choosing the solution neighbor-
hood, and setting the cooling function and temperature, with the simulated annealing algorithm, the optimal solution of
the decision is achieved.
Keywords: Top Management Team, Simulated Annealing Algorithm, Decision-Making
1. Introduction
Upper Echelons Theory is the theory which has profound
impact in the academic circles. It is proposed in 1984 by
Hambrick and Mason who suggested that researching
into top management team (TMT) decision-making in-
stead of individual decision-making would decrease the
decision fault caused by the individual of limited ration-
ality [1]. As a result, problems about decision-making of
TMT become popular and stimulate a lot of research.
Most part of the research has focused on TMT demo-
graphic characteristics and their heterogeneity. The re-
searchers suggested that the demographic characteristics
and their heterogeneity could reflect the decision-making
of TMT and predict organization outcome. There is ad-
vantages in this static analysis which can evaluate and
predict performance of a company to some degree, how-
ever, the demographic characteristics are not the exact
reflection of TMT decision-making [2], and cannot an-
swer the question of decision-making optimization of
TMT. In this case, we propose two dimension which is
decision efficiency and decision quality to analyze deci-
sion-making optimization of TMT and find out the opti-
mal decision preference sequence.
2. Literature Review
In the violent changing society, decision effect is directly
influenced by decision efficiency. Ensley (2000) suggest-
ed that decision efficiency and cohesion are two core
factors influencing team performance [3]. In fact, team
cohesion is a kind of condition and display of decision-
making quality. To improve the decision-making quality
is one of the key factors which prompt the top manage-
ment research changing from individual level to team
level. Decision-making quality of TMT has important
influence on decision-making effect despite of the chang-
ing environment. Therefore, the decision-making effect
depends on decision-making efficiency and decision-ma-
king quality. Higher level of decision-making efficiency
and decision-making quality will result in better deci-
sion-making effect.
2.1. Measurement of Decision-Making Efficiency
How can we achieve high decision-making performance?
Economist Heyek once pointed out that decision-making
efficiency depended on the matching degree of decision-
making power and key decision knowledge [4]. He sug-
gested to combine the power and the knowledge. Only
combining the two can it achieve high efficient decision-
making. However, Heyek’s saying is too obscure that he
didn’t point out how power and knowledge combined. In
fact, decision-making efficiency can be measured by the
weighted preference of all the alternative choices from
all decision-makers, that is to say, base on the considera-
tion of all decision-makers’ decision-making preference,
comprehensively consider the “preference distance” be

Decision-Making Optimization of TMT: A Simulated Annealing Algorithm Analysis 364
tween the final and the original preference sequence of
decision-making which is the difference of the two. If the
“preference distance” between the two is bigger, the effi-
ciency will be lower.
2.2. Decision-Making Quality
To improve decision-making quality of individual execu-
tives is the primary idea of introducing the theory of TMT
[1]. Although the substitution of group rationality for indi-
vidual rationality can’t completely eliminate the negative
influence of limited rationality in improving decision qual-
ity, it can validly reduce the bounded rationality in deci-
sion-making which comes from the interactions between
team members [5]. However, interaction is only the nec-
essary condition in improving decision-making not the
sufficient condition, so the decision quality evaluation
should be done by other factors. Reviewing the related
past research on quality of decision-making, the decision-
making quality evaluation is mainly done by the subject
idea of the TMT members which mainly using psycho-
logical scale to investigate TMT’s opinion to every deci-
sion-making quality, such as Wang Guofeng [6]. The inner
logic lies in the feasibility of decision-making quality eva-
luated by satisfaction degree of TMT. This rooted in the
posterior characteristic which TMT decision-making qua-
lity should be evaluated by the objective decision imple-
menting effect, however, in the real setting, it is not feasi-
ble. One reason is that it will take quite a long time to see
the actual effect, when the time past, the uncontrollable
factors influenced decision will increase. So, the ineffec-
tive of decision can not attribute to the bad quality of deci-
sion-making; another reason is that it won’t be good for
the improving of decision process if the decision-making
factor be evaluated by the decision implementing effect.
Therefore, this paper uses the satisfaction of top manage-
ment team with the decision-making process to evaluate
the decision-making quality. When the degree of TMT
members’ satisfaction in decision-making with the deci-
sion-making quality is higher, the decision-making quality
is higher.
3. Optimization Model of TMT Cognitive
Integration
Based on above findings, the optimization model of top
management team cognition integration is built. Suppose
in every decision process, TMT faces a decision-making
program set, set it as A = {aj}, j = 1, 2, …, n, TMT mem-
bers set K = {ki}, I = 1, 2, …, m. First, TMT members
form preference sequence of the program set A based on
their own information sources, set the sequence as X =
{xij}. The principles of optimization of cognitive integra-
tion are high decision making efficiency and high quality.
3.1. High Efficiency of Decision-Making
Based on the consideration of the weight of every deci-
sion-maker, when the “preference distance” between final
and original preference sequence of TMT decision-making
is smaller, the efficiency of decision-making will be higher.
For the “preference distance” measurement, some schol-
ars (such as Zhang Lin et al, 2004) proposed to use the
Mahalanobis distance [7]. However, in fact, compared to
the Euclidean distance, Mahalanobis distance gets its
advantages in the correlated sample. In this study, the
primary preference based on their own discretion rather
than on the idea of intercommunication. It depends more
on the inter independence rather than the inter correlation.
So, it is more easy and effective to use Euclidean dis-
tance than Mahalanobis distance. As it is known that
Euclidean distance dE(x, y) between two point (or vectors)
x, y is:
 
2
,
E
dxy xy
 (1)
To simplify the calculations, the “preference distance”
will take the square of Euclidean distance, which is
“preference distance” di:
2
1
(
n
iij
j
dxe


)
j
(2)
The shorter of Euclidean distance means the higher of
decision-making efficiency. Considering different weights
Wi of each decision-maker in decision-making, the fol-
lowing model can be established to represent the deci-
sion-making efficiency optimization:
2
111
1
min( )()
. .1,01,01,0
mmn
iiiij j
iij
m
ijiji
i
Exwdwxe
st wexw


 
 







(3)
3.2. High Quality of Decision-Making
The quality of decision-making can be measured by TMT
members’ satisfaction degree with the decision quality.
Zhang Lin et al [7] proposed the concept of using rela-
tive entropy to measure the quality satisfaction with de-
cision-making. The so-called relative entropy is an im-
portant concept in information theory which measures
the fitness degree of two messages. As to variable X, Y,
when X = (x1,,……xn); Y = (y1,……yn), 0 ≤ x
n
≤ 1,
0 ≤ yn ≤ 1, and
11
1
nn
ii
ii
xy



 , the relative entropy of
X compared to Y is
1
(, )
n
i
hxy

ln 0
i
i
i
x
xy  . Obviously,
i

, if and only if ii
x
y

, get its minimum. In (, )hxy
reverse, the lower of , the more closer between (, )hxy

Decision-Making Optimization of TMT: A Simulated Annealing Algorithm Analysis 365
i
x
and i, So can be use to measure the fit-
ness degree between
y(, )hxy
i
x
and .
i
When the fitness between final optimal solution sets de-
cided by TMT after discussion and the preference sequence
of every TMT is higher, the overall satisfaction is higher
thus with the decision-making higher as well. So the deci-
sion-making quality of TMT can be measured by :
y
i
q
1
ln
nij
iij
j
j
x
qx
e

 (4)
Considering different weight Wi of every TMT mem-
ber in decision-making, a model can be established to
simulate the optimization of decision-making quality:
111
1
min( )ln
. .1,01,01,0
mmn ij
iii ij
j
iij
m
ijiji
i
x
Qxwqw x e
st wexw



 







(5)
Integration of the various members of TMT preference
was based on the consideration of both decision-making
quality and decision-making efficiency, that is either to
find the fittest preference set to ensure the decision-
making efficiency or make every TMT member satisfy to
ensure the decision-making satisfaction. So, the optimi-
zation model of TMT decision-making process can be
express by following equation set:
 
2
111
1
min
() ln
.. 1,0,
01,0 1,
1, 0
jj
mn nij
iijj ij
j
ij j
jij
m
ii
i
decisionE eQ e
x
wxex
e
st
ex
ww
 

 






 



 










1
1
(6)
In Equation (6), is the dependent variable of
object function, α, β are the weight factors of deci-
sion-making efficiency and decision-making quality,
represent the importance of efficiency and quality of
TMT decision-making. When the value of α is bigger
representing that TMT laid more emphasis on deci-
sion-making efficiency; when the value of β is bigger
representing that TMT laid more emphasis on deci-
sion-making quality. The object of TMT cognition inte-
gration optimization is to find out the optimize prefer-
ence sequence set E(ej). As can be seen from the equation
set, this problem is a NP-hard problem, and is a kind of
continue optimization problem which is hard to get over-
all optimal solution by ordinary methods. Even if the
optimal solution can be achieved, the solution efficiency
is low enough. So, we use the Simulated Annealing (SA)
Algorithm to solve the problem.
decision
4. Problem Solving
Simulated annealing algorithm (Simulated Annealing
Algorithm, SA algorithm) is inspired by the phenomenon
of annealing process in thermodynamics which will
achieve equilibrium ultimately. SA can search for the
optimal solution simulating the annealing process. The
algorithm can achieve an approximate global optimal
solution in polynomial time through the selection of rela-
tively small state in target areas in certain probability [8].
In this paper, the reason to use SA is as follows.
1) SA likewise intelligent optimization algorithms is
“problem dependent”, and its research focus is on the
application of algorithm in various complex problems [8].
However, in the research of TMT, seldom application
researches of SA can be seen.
2) Compared to genetic algorithms and other intelli-
gent optimization algorithm, SA is more effective in
finding the global optimal solution as it accept second-
best solution in certain probability through the rules of
Metropolis which greatly enhance the capacity of global
searching.
The solving step of this problem can follow several
steps:
Step 1: Each TMT member has their own preference to
the program set, to put them all we can get the initial
preference sequence of TMT , randomly choose an initial
solution Ei = {e1
i,……, en i },0, l = 1, 2,…, n.
Given initial temperature T0 and ending temperature Tf,
let iteration index k = 0, Tk = T0.
i
l
e
Step 2: In the neighborhood of initial solution, ran-
domly generate a neighbor solution E
j = {e1
j,……, en j},
l
0
j
e

, l = 1, 2…, n, calculate the incremental value
of the objective function:
() ()
j
i
ll
decisiondecision edecisione (7)
Step 3: If 0decision


ξ(0,1U
, let i = j and go to step 4;
otherwise, generate)

, if exp ξ
k
decision
T





,
let E i = E j.
Step 4: If the thermal equilibrium (i.e. frequency of
inner cycle become greater than the frequency of setting
cycle n(Tk)), then go to step 5; otherwise go to step 2.
Step 5: According to Tk + 1 = r·Tk lower the temperature,
(r generally values from 0.95 to 0.99 with two decimal
places, otherwise the cooling rate either too fast or too
slow), k = k + 1, if Tk < Tf the algorithm stops, otherwise
go to step 2.

Decision-Making Optimization of TMT: A Simulated Annealing Algorithm Analysis 366
5. Application Examples
A TMT of one firm with five members which one is
CEO while the others are vice presidents in charge of
each functional department. In one decision-making con-
ference, there are 6 decision programs for discussion and
decision. Before the decision debate, the preference se-
quences to the decision program of every TMT member
are listed in Table 1.
Suppose the decision weight of CEO is 0.4, each vice
president is 0.15, the weight factor α, β of decision-
making quality and decision-making efficiency are both
0.5. That is, the decision-making quality and efficiency
are the same important.
5.1. According to the Problem Characteristics to
Determine the Initial Solution
If randomly generate an initial solution, high temperature
annealing process would be relatively long. CEO noted
that the weight is high, the initial solution can be shilling
for the CEO’s preference sequence, that is, E0 = (0.5, 0.4,
0.8, 0.3, 0.1, 0.3). Considering the decision weight of
CEO is the highest, we can choose the CEO’s preference
sequence as initial solution, that is, E0 = (0.5, 0.4, 0.8, 0.3,
0.1, 0.3).
5.2. The Choice of Neighborhood
The choice of neighborhood plays a very important role
in problem solving efficiency, but the choice methods
closely linked to specific issue. Because the solution of
this problem is in the (0,1) interval, and the computer
will treat the solution closed to 0 as 0 as limited by the
computer precision, the program running would occur
error as the calculation has exceeded the definition do-
main. So, it is not suitable to have a random search
around the neighborhood of the previous solution. In
order to ensure not only the solution is in the definition
domain, but also ensure a relatively wide search range,
we carried out the following neighborhood search
method as follows to determine the new solutions: First,
code the preference sequences exactly from the original
sequence, such as (0.5, 0.4, 0.8, 0.3, 0.1, 0.3), then swap
the preference value in the sequence itself. As the size of
Table 1. Initial decision preference order of TMT.
program
TMT 1 2 3 4 5 6
CEO 0.5 0.4 0.8 0.3 0.1 0.3
VP1 0.4 0.5 0.7 0.8 0.2 0.5
VP2 0.7 0.2 0.3 0.7 0.2 0.4
VP3 0.6 0.7 0.2 0.6 0.4 0.5
VP4 0.6 0.6 0.1 0.5 0.8 0.1
neighborhood is = 15, so the number of inner loop is
15 times.
2
6
c
5.3. The Choice of Cooling Function
There are many setting of cooling function. According to
the characteristics of this problem, we use moderate cool-
ing rate, the cooling function is defined as Tk + 1 = r·Tk, r
equals 0.97, that is Tk + 1 = 0.97·Tk.
5.4. The Initial Temperature and the to be
Determined Temperature
According to the scale of this problem, the initial tem-
perature T0 equals 50, final temperature Tf equals 0.1.
5.5. The Retention of Good Solution
Although in theory, the probability of a simulated an-
nealing algorithm will converge to global optimal solu-
tion at a probability of 1, but it is far from the reality [9],
it is greatly related to the actual problem solving. In this
study, as neighborhood search is random exchange with-
in the old solution, the search process is random, so the
global optimal solution may appear in the iterative proc-
ess but the end. As a result, in order to prevent missing
out the optimal solution, all solutions must be retained
per iteration, and then filter them where the optimal solu-
tion can be determined.
5.6. Results
According to the above algorithm and parameter setting
step, using VB language for programming, after 20 times
iteration, removing repetitive solution, obtain the follow-
ing results shown in Table 2:
As the minimum function value is 0.0942 is, so re-
spectively (0.4, 0.5, 0.3, 0.3, 0.8, 0.1) is the optimal TMT
decision-making preference sequence, and thus program
5 with the weight 0.8 is the optimal program. This is the
solution under 20 iterations calculation. According to SA
algorithm, this solution is the global optimal solution of
this problem.
Obviously, optimal solution (0.4, 0.5, 0.3, 0.3, 0.8, 0.1)
is quit different from the mean value of preference se-
quence (0.56, 0.48, 0.42, 0.58, 0.34, 0.36) which repre-
sent that it would not achieve high efficient and high
quality decision-making through simple averaging. This
may attribute to the mean value which represents a
“compromise” program, and this simple “compromise”
approach may put the choice of the program into two
problem: on one hand, it can not take into account the
interests and preferences of all decision-maker which a
simple “compromise” program can not be accepted by
everyone very quickly; on the other hand, the “compro-
mise” preference program is different from most mem-
ber’s preference which more or less make TMT members

Decision-Making Optimization of TMT: A Simulated Annealing Algorithm Analysis 367
Table 2. Calculation result.
Program
Iteration 1 2 3 4 5 6
Function
value
1 0.8 0.3 0.1 0.3 0.5 0.4 0.1666
2 0.4 0.5 0.3 0.3 0.8 0.1 0.0942*
3 0.3 0.4 0.1 0.3 0.8 0.5 0.1626
4 0.1 0.4 0.3 0.3 0.5 0.8 0.3661
5 0.8 0.4 0.3 0.5 0.1 0.3 0.3299
6 0.8 0.1 0.3 0.3 0.5 0.4 0.279
7 0.3 0.3 0.1 0.8 0.5 0.4 0.1481
8 0.5 0.3 0.4 0.3 0.8 0.1 0.1308
9 0.4 0.8 0.1 0.3 0.3 0.5 0.222
10 0.3 0.3 0.1 0.5 0.8 0.4 0.1481
11 0.4 0.1 0.3 0.5 0.3 0.8 0.4071
12 0.3 0.5 0.1 0.8 0.4 0.3 0.174
13 0.1 0.8 0.3 0.5 0.4 0.3 0.2703
14 0.3 0.4 0.1 0.5 0.8 0.3 0.1131
15 0.3 0.1 0.4 0.3 0.5 0.8 0.4027
16 0.5 0.3 0.1 0.4 0.8 0.3 0.1068
17 0.3 0.3 0.1 0.4 0.8 0.5 0.1699
18 0.5 0.3 0.1 0.3 0.4 0.6 0.2664
19 0.3 0.1 0.3 0.4 0.8 0.5 0.2823
20 0.8 0.5 0.4 0.3 0.3 0.1 0.1902
unsatisfied which result in overall deny of this program.
Therefore, a simple compromise decisions is inappropri-
ate. It should take into account the preferences of all de-
cision-makers with in-depth exchanges and discussions
and the consideration of decision-making efficiency and
all parties’ satisfaction, thus comes out the optimal deci-
sion.
6. Conclusions and Discussions
This study found that:
First, taking into account both the quality of decision-
making and efficiency of decision-making, the TMT, the
average decision-making preference sequence is not the
optimal sequence. TMT decision-making therefore can
not simply choose the mean preferences of all team mem-
bers. When choosing decision-making program with “mean
highest” method should also taken the quality and effi-
ciency of decision-making factors into account, using
more advanced algorithms such as simulated annealing
algorithm to find out the optimal decision sequence.
Second, simulated annealing algorithm can success-
fully solve the optimization problem of TMT decision-
making, and it is an effective tool in complex issues in
TMT decision-making optimization.
The shortcomings of this study are:
First, this study only intercept two variable—the qual-
ity and efficiency of decision-making—to search for the
optimal sequence of cognitive preferences, we need fur-
ther investigation to find out whether there are better
variables. At the same time, the usage of Euclidean dis-
tance and relative entropy to measure these two variables
has not been empirical investigated but only two hy-
potheses based on theoretical derivations.
Second, this study did not take limited rationality into
account. In fact, although the group is relatively rational
than individual, it is difficult to avoid the rational bias,
especially when group thinking exist [10]. Although the
satisfaction degree of team member is high, the quality of
the overall decision-making from external perspective
may not so high. How to reduce the group’s limited ra-
tionality and to improve group performance is worth stu-
dying.
Third, the application of simulated annealing algo-
rithm will be quite different as the problem changed. So
the application techniques play an important role. In this
study, the using of inter-switch method in neighborhood
searching greatly improve the calculation efficiency but
discretize the search of new solution which makes some
potential solutions cannot be searched which eliminate
the advantage of stimulate annealing algorithm. This
problem still needs to further investigate to find out bet-
ter neighborhood search method.
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