A fuzzy logic enhanced bargaining model for business pricing decision support in joint venture projects/Fuzzy loginio pasikeitimu vertinimo metodo taikymas jungtines veiklos projektu vertei nustatyti.
Yan, Min-Ren
1. Introduction
As a response to the changing business environment and diverse
market demands, strategic alliances have been considered as effective
business models for creating competitive advantages. In recent decades,
project businesses are increasingly emerging and many companies
cooperatively participate in various projects by the manner of joint
venture (JV). The project-based short-term alliances are especially
popular in the construction industry (Norwood and Mansfield 1999). Since
construction projects have become larger and more complex, a growing
number of projects have exceeded the scope that can be handled by a
single company. The desire for and search for collaborators to achieve
synergistic competitiveness is the prime motive for companies to
collaborate (Xu et al. 2005). Through the manipulation of the
appropriate resources, a JV may bring about different kinds of benefits
to participating companies, such as risk sharing, resource
complementarities, reduced cost, knowledge sharing, and technology
transfer (Tam 1999; Munns et al. 2000; Nicolini et al. 2001; Proverbs
and Holt 2000; Simchi-Levi et al. 2001). JV has become an important
strategy for construction companies in response to the increasing
demands in the construction industry. The JV teams can also be
significantly competitive for the projects delivered by the
qualification-based selection system (Lo and Yan 2009).
To form a JV team, companies have to select partner(s), assign each
party's work scope, and especially, negotiate the sharing of
rewards, which is usually done by arranging separate amounts of the
expected total rewards or by sharing proportionally, depending on the
collaborating relationships among the JV teams. However, in a
negotiation, two parties may have different objectives and conflicts
(Saee 2008). Since each JV party is pursuing its maximum reward, the
conflicts of interest make the sharing of rewards always a challenging
task. Lai (1989) pointed out that bargaining is needed when a conflict
lies between participating parties, and communications and compromises
are required to reach an agreement. Raiffa (1982) proposed the concept
of "zone of agreement", which can be figured out by deducting
the lowest, acceptable price for each party from the total amount. As
each party strives for its maximum price, which is also acceptable to
the other party, in the "zone", bargaining usually is carried
out through numerous repetitions of offer-and-counteroffer until an
agreement is reached, or the bargaining is given up.
Bargaining in the construction industry is quite different from
other industries. The collaborations between JV parties are usually on a
short-term, project-to-project basis and the time allowed for bargaining
is strictly limited. Since time factor is crucial in this type of
negotiation, the JV parties may be forced to make a concession because
of the need to submit a bid on time. Thus, how to evaluate a bargaining
situation and offer a price acceptable to both parties in a timely
manner is critical for the success of a JV project. However, current
practices still lack a systematic tool or model for supporting a
company's pricing decisions. The research aim is to fill the gap.
There are many factors that could affect a company's pricing
on a specific project. However, previous research has pointed the
outcome of bargaining is highly influenced by the stakes of the
bargainers, the bargainer's level of dependence on the outcome of
bargining (Bacharach and Edward 1981). Accordingly, this research
focused on the variable, need for the revenue from the project, which is
used to represent company's level of dependence on the profit from
a JV project. A sequential bargaining model is developed, based upon
game theory, which is used to estimate acceptable prices in accordance
with each party's costs and needs. The game theory perspective
helps decision makers to take into account not only the current strategy
of the competitor, but his forthcoming responsive actions as well
(Ginevicius and Krivka 2008). Furthermore, fuzzy logic is used to
quantify a company's need for the revenue from the project, which
always features a certain degree of uncertainty. The applications of
fuzzy logic enhance the bargaining model to support quantitative
analysis and operational research of bargaining strategies.
2. The sequential bargaining model
Game theory has been defined as "the study of mathematical
models of conflict and cooperation between intelligent rational
decision-makers" and successfully applied to many important issues,
such as negotiations, finance, and imperfect markets. It allows
researchers to find mathematical solutions of conflict situations
(Peldschus 2008). Based on the concept of dynamic games, the bargaining
between two parties of a JV team is modeled as a sequential bargaining
process. In this model, the JV parties are termed as
"players".
2.1. Basic symbols and definitions
In the game theoretical analysis, the rationale of players'
behavior is to maximize their payoffs calculated based on quantified
considerations and both players are assumed risk neutral, while the
utility function can be used to modify this model in cases where the
players have other risk attitudes. Definitions of each basic symbol and
assumption in the model are as follows:
* k represents players in the bargaining, while a refers to player
A and b refers to player B.
* n represents round of bargaining. Each player's offer
accounts for a round.
* E represents total contract amount estimated based on announced
budget information and market price. The total contract amount is
assumed the award price. As agreement is reached, the total contract
amount is the sum of the payment obtained by player A (a*) and the
payment obtained by player B (b*).
* [a.sub.n] represents player A's quotation for its work scope
in the nth round. In this model, player A makes the first offer,
[a.sub.1], in the 1st round for its work scope. Further, since both
parties take turns to offer a price, only when the number of round is
odd (n = 1, 3, 5, ...) player A can offer its price.
* [b.sub.n] represents player B's quotation for its work scope
in the nth round. As assumed above, first player A offers [a.sub.1] in
the 1st round for its work scope, and then player B may make a
counteroffer, [b.sub.2], for its work scope. Since both parties take
turns to offer, only when the number of round is even (n = 2, 4, 6, ...)
player B can offer its price.
* [C.sub.k] represents cost estimated by the player k according to
individual work scopes. [C.sub.a] indicates player A's cost;
[C.sub.b] indicates player B's cost. Since information associated
with market prices of materials and labor is quite open, it is assumed
in this research that both parties in the bargaining can obtain clear
awareness of each other's cost.
* F represents total profit of the project (total profit plus total
cost of the project equals the total contract amount).
* P represents probability of failure in the bargaining.
* [L.sub.k(n)] represents the loss of potential profits when
agreement is not settled.
2.2. Sequential bargaining process
In this model, it is assumed that bargaining begins with the offer
proposed by player A in round 1 (n = 1), and there are three possible
reponses from player B: (a) accepts the offer, (b)rejects the offer and
closes the bargaining, and (c) makes a counteroffer. If player B makes a
counteroffer, then similarly, player A may accept, reject, or make a
counteroffer to player B. Usually the bargaining is an
offer-counteroffer process till the nth round, when an agreement is
reached, or the bargaining is given up. Accordingly, different rewards
or losses in each round are expected (as shown in Fig. 1). At the nth
round, it could be player A's or player B's turn to make the
offer. Nevertheless, in the bargaining model shown in Fig. 1, it is
assumed that it is player A's turn to propose the offer.
[FIGURE 1 OMITTED]
2.3. Equilibrium of sequential bargaining
In order to understand how players behave in the sequential
bargaining process, this research introduced the concept of "Nash
equilibrium", one of the most important concepts in game theory.
Nash equilibrium refers to a situation in which individuals
participating in a game pursue the best possible strategy while
possessing the knowledge of the strategies of other players. In Nash
equilibrium, each player's strategy should respond to the other
player's strategy, and no player wants to deviate from the
equilibrium solution (Myerson 1991). Thus, the equilibrium price of
sequential bargaining process is a best price for both parties under the
sets of information and bargaining situation.
The equilibrium of sequential bargaining can be solved through
"backward induction" (Gibsons 1992). According to the method,
whether a player accepts the counterpart's offer depends on his
expectation of rewards in the next round. Only when the reward offered
by the counterpart exceeds or equals what is expected would a player
accept the offer and settle the agreement. So, if player A offers the
highest price of [a.sub.n] at the nth round (n [greater than or equal
to] 3), a potential loss, [PL.sub.a(n)], may be incurred, thus the
expected payoff of player A in the nth round is as Eqn. (1):
[a.sub.n] - [PL.sub.a(n)]. (1)
Furthermore, since player B knows that, in the (n-1)th round, any
price higher than Eqn. (1) would be accepted by player A, player
B's best offer in the (n-1)th round is as Eqn. (2):
E - [a.sub.n] + [PL.sub.a(n)]. (2)
Similarly, for player B, in the (n-1)th round, the expected payoff
in the (n-1)th round is as Eqn. (3):
E - [a.sub.n] + [PL.sub.a(n)] - [PL.sub.b(n-1)]. (3)
In addition, since player A understands that, in the (n-2)th round,
any price higher than Eqn. (3) would be accepted by player B, and player
A's offer in the (n-2)th round is as Eqn. (4):
[a.sub.n] - [PL.sub.a(n)] + [PL.sub.b(n-1)]. (4)
As a summary of the aforementioned description, Table 1 shows the
prices acceptable to player A and player B in the last three rounds as
induced by backward induction.
Based on the concept of equilibrium, the player cannot produce a
price better than [a.sub.n]. Therefore, the equilibrium price can only
be solved when player A's offer in the nth and (n-2)th round is the
same as Eqn. (5):
[a.sub.n] = [a.sub.n] - [PL.sub.a(n)] + [PL.sub.b(n-1)]. (5)
Since bargaining between players is a repetitive process of
offer-counteroffer, when the round of bargaining n [right arrow]
[infinity], the P in each round will be very close. Thus, in this model,
the probabilities of failure in any bargaining round are assumed the
same and Eqn. (5) can be simplified as Eqn. (6):
[L.sub.a(n)] = [L.sub.b(n-1)]. (6)
2.4. Equilibrium price function
In this research, [L.sub.k(n)] is the loss of potential profits in
the JV project. However, bargaining theory (Bacharach and Edward 1981)
suggests that potential profits considered by a player in the bargaining
should be additional profit which can not be gained from other projects.
If a player has other opportunities that may earn the same amount of
profit, there is no potential profit for this project. Therefore, this
research developed a variable, need for the project ([S.sub.k]), to
encompass the above concept. Losses expected by player A and player B
are as Eqn. (7) and Eqn. (8) respectively.
[L.sub.a(n)] = (E - [b.sub.n-1] - [C.sub.a]/[C.sub.a])[S.sub.a],
(7)
[L.sub.b(n)] = (E - [a.sub.n-1] - [C.sub.b]/[C.sub.b])[S.sub.b].
(8)
It is common that player A and player B of the JV team may invest
on different scales. Thus, the [L.sub.k(n)] is evaluated on the unit
basis for the sake of fairness. Value of [S.sub.k] is assumed to fall
between 0 and 1; the higher the value, the higher the need for the
project, and vice versa. The value 1 indicates that the player has no
other opportunities, which can earn the same amount of profit as this
project. 0 indicates that the player can earn the same profit from other
opportunities and does not need the profit at all.
Since bargaining between players is a process of
offer-counteroffer, both players tend to gradually lower their offers to
reach an agreement. When the bargaining reaches n [right arrow]
[infinity], it can be inferred that the players' offers will
converge and players' offers in the last three rounds tend to be
the same. Thus, [a.sub.n-2], [a.sub.n], and a* can be considered equal
and the same principle applies to [b.sub.n-3], [b.sup.n-1], and b*. Eqn.
(9) can be derived by substituting Eqn. (7) and (8) given for
[L.sup.a(n)] and [L.sub.b(n)] in Eqn. (6):
[a.sub.n] = E - [C.sub.b] - (E - [b.sub.n-1] -
[C.sub.a])[C.sub.b][S.sub.a]/[C.sub.a][S.sub.b]. (9)
Based on the definitions of this research, the total contract
amount, E, is the sum of a* and b*, while total profit plus total cost
of the project equals the total contract amount. Thus, an equilibrium
price function can be derived from Eqn. (9) as Eqn. (10):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (10)
Eqn. (10) can be promptly used to suggest player A's offer as
an acceptable price for both parties. In most cases, the required
parameters of the equation, [C.sub.a], [C.sub.b], and F are already
established before bargaining, while [S.sub.a] and [S.sub.b] are not.
Thus, [S.sub.a] and [S.sub.b] are two key variables for determining the
price. Through Eqn. (10), the impacts of [S.sub.k] on company's
offers can be analyzed by using a fixed [S.sub.b] with different values
of [S.sub.a]. It is found that player A's suggested offer decreases
as the [S.sub.a] increases (see Fig. 2).
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
This scenario is more significant as the [S.sub.b] decreases.
Similarly, this research tests the suggested offers based on a fixed
[S.sub.a] with different values of [S.sub.b], and finds that the
suggested offer increases as the [S.sub.b] increases (see Fig. 3). This
scenario is more significant as the [S.sub.a] decreases. To summarize
these results, a company with relatively high need for the project is
likely to lose more of the profit of the JV project.
3. Fuzzy rule-based estimation of company's demand for the
project
Based on the aforementioned equilibrium price function, individual
company's demand for the project would have an impact on the
equilibrium price. Thus, quantitative analysis of the need for the
project is essential and it can be enabled by using fuzzy logic. In a JV
team, each party can obtain business information and speculate on its
partner's "need for the project" (S) through public or
private information channels. For example, the awareness that the
counterpart has not taken any construction project in the past six
months and opportunities for construction projects will be rare in the
following six months suggests that the counterpart's "S"
must be high. However, it is difficult to transform the above
information and linguistic variables into a specific value to facilitate
the decision-making. To the imprecise data or linguistic variables,
fuzzy logic is a widely used approach in helping decision making (Arslan
and Aydin 2009). Therefore, this research incorporates fuzzy logic to
quantify the "S" of each party and enable further quantitative
analysis.
3.1. Measure of need for the project
Carr (1987) proposed that a company's pricing should be
consistent with its status of business operation. If a company's
returns gained from business operations cannot cover its general and
administrative expenditures, this company will suffer loss. Thus, if a
company's total revenue is expected to fall behind its scheduled
revenue target, the company is in an urgent "S" and thus
forced to lower its offer for better opportunities. On the contrary, if
its scheduled revenue target has been reached, this company's
"S" is relatively low. In this research, the degree of
"S" is regarded in terms of the company's fulfillment of
scheduled revenue target. The lower the degree of scheduled revenue
target attainment, the higher the company's "S." The
degree of fulfillment of scheduled revenue target is closely related to
received revenues and potential business prospects in the future.
Moreover, future revenue is associated with future business
opportunities and the level of competition. Thus, this research assumes
that a company's "S" is influenced by three factors,
"received revenues"(R), "future business
opportunities"(O), and "level of competition"(L).
3.2. Fuzzy sets and membership functions
Both "R" and "O" are evaluated against the
company's degree of attainment of its scheduled revenue target. For
example, if "R"/scheduled revenue target yields a value of
0.95 (covering 95% of its scheduled revenue target), it is suggested
that this company's "R" is rather high. Both
"R" and "O" may exceed scheduled revenue target, so
values of these two items range between 0~2 and are further divided into
three degrees of "High", "Moderate", and
"Low". As for the variable of "L", the value is
represented by "number of competitors", which has been the
most frequently used criterion for measurement of competition level in
previous research. Note that the number of competitors is an adaptive
parameter, which is adjustable for specific cases in different
industries. Lo et al. (2007) have conducted a nation-wide study on the
traffic construction projects in Taiwan and proposes an estimation of
the number of competitors ranging from 3 to 13. In this research, we
took the estimation for the demonstration of the fuzzy membership
function. Therefore, this research ranges the value of "L"
from 3 to 15 so as to include some extremely competitive cases (3
competitors is the minimum requirement for open bids); higher values
indicate higher level of competition, which is also divided into three
levels of "High", "Moderate", and "Low".
"S" is defined in the range between 0 and 1, and further
divided into three levels of "High", "Moderate", and
"Low".
Membership functions commonly used include triangular functions and
bell-shaped functions (Yu and Skibniewski 1999). To demonstrate the
concept more efficiently, triangular functions are used in this research
(see Fig. 4). In a triangular membership function, each triangular fuzzy
number has linear representations on its left and right side such that
its membership function can be defined as Eqn. (11):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (11)
where s and l represent the smallest and the largest possible
values and m represents the most promising value that describes a fuzzy
event.
[FIGURE 4 OMITTED]
3.3. Fuzzy if-then rules
To effectuate the composition of the variables considered for
estimating a company's demand for the project, fuzzy inference
rules can be developed (Costantino and Gravio 2009). The company's
perceptions about the counterpart's need for the project can be
grouped into three rule categories as follows:
* If a company's "R" is high, and: (a) "O"
is high, then expected "S" will be low; (b) in other cases,
the expected "S" will be moderate.
* If a company's "R" is moderate, and : (a)
"O" is high while "L" is low, then the "S"
will be low; (b)"O" is not high, then a high "S" is
expected; (c) in other cases, the expected "S" will be
moderate.
* If a company's "R" is low, and : (a) "O"
is high while "L" is low, then the "S" will be
moderate; (b) in other cases, the expected "S" will be high.
* Twenty-seven If-Then rules are developed based on the
conbinations of the aforementioned three rule categories (see Table 2).
4. Illustrative case study
Two companies intend to form a JV, so as to bid for a project which
consists of 5.5 km of tunneling work and a substation. The assumed
amount of the winning bid is 3,229 million dollars. It is agreed that
company A handles the station portion and company B handles the tunnel
portion. Information for the JV project is summarized in Table 3.
For the company A, the highest price is cost ([C.sub.a]) +
estimated total profit (F) = 1,180 million dollars + 279 million dollars
= 1,459 million dollars. On the other hand, the highest price of company
B is [C.sub.b] + F = 1,770 million dollars + 279 million dollars = 2,049
million dollars. Since the total budget is limited, these prices are
hardly acceptable to both parties. Therefore, to expedite the bargaining
and make a rational bargaining strategy, both parties need to collect
information about each party's need for the project and estimate
the values of [S.sub.a] and [S.sub.b]. Based on the information implied
in each party's "received revenues", "future
business opportunities", and "level of competition",
[S.sub.a] and [S.sub.b] estimated by company A are 0.72 and 0.41,
respectively. Then the company A that used the equilibrium price
function may infer that it may earn 1, 256.77 million dollars while the
company B may receive 1, 972.23 million dollars.
If company B's recognition of each party's demand for the
project is similar to that of company A, the agreement can be reached
immediately. If both party's perceptions about their own and the
other part's need for the project differ, conflicts in the
bargaining may be incurred. In this situation, the accuracy of the
information received should be confirmed by both parties and as more
information is exchanged between both parties, the equilibrium price
function can be very helpful for both parties to adjust their pricing
policy in a timely and rational manner.
Considering a case that the company A can make sure that [S.sub.a]
is 0.72, while [S.sub.b] is not definite. By implementing a scenario
analysis, the acceptable rewards in different bargaining positions can
be estimated by the proposed model. Note that the estimation of high
[S.sub.b] represents that company A takes an optimistic bargaining
position and low [S.sub.b] for pessimistic bargaining positions. As
shown in Fig. 5, the suggested offer based on different sets of
[S.sub.b] can be easily obtained. Similarly, company B can lock
[S.sub.b] (suppose it is 0.41) and infer the company A's possible
offers based on different sets of [S.sub.a] (the rewards willing to
share by company B in Fig. 5). In this case, once the reward willing to
share by company B is more than the acceptable reward for company A, the
agreement can be made.
In addition to figure out the possible individual rewards in
various bargaining positions, the scenario analysis can turn to project
level by evaluating the total rewards needed with different bargaining
positions. As shown in Fig. 6, since the contract amount is fixed, the
possibility of agreement can be evaluated by comparing the contract
amount and the acceptable total reward. If both parties take too
optimistic bargaining positions, then the acceptable total reward might
over the contract amount to lower the possibility of agreement. Thus,
these objective evaluations give each company a clear guideline for
pricing. Irrational alternatives can be detected and eliminated with the
support of the proposed model and the functions can help making rational
decisions (Sarka et al. 2008).
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
5. Conclusions
During a business bargaining process, many interaction effects
might occur due to different levels of presentational and negotiation
skills or social psychological phenomena. A proper pricing strategy in
the dynamic bargaining process is important for an enterprise because it
can ensure right businesses when cooperating with other partners.
However, due to the lack of decision support models, business managers
tend to adopt a more intuitive and subjective approach to the bargaining
problem. Thus, a quantitative decision support model would help decision
makers to maintain their bargaining positions and contract price lines.
Irrational offers and alternatives can thus be detected and eliminated
during the bargaining process.
To solve bargaining problems, many researchers have theoretically
focused on the unique equilibrium price by assuming the information for
pricing is perfect. However, perfect information situation is not common
in real bargaining cases and companies inevitably continuously collect
information, evaluate bargaining situations, and repetitively make
pricing decisions in the bargaining process. Instead of finding a unique
equilibrium price, the approach of this paper is to propose a bargaining
decision support model, which can be used to assess the bargaining
situation and select a pricing strategy in a scientific and rational
manner. With the complementary use of game theory and fuzzy logic, the
research results are useful for JV parties to determine the best price
based on each party's cost and the estimated degree of need for the
JV project, thus can improve the possibility to reach an agreement. In
addition, this research provides a quantitative analytic framework for
objective business pricing and the framework enables further
developments of rational and quantitative bargaining models. With this
pilot study, the modeling assumptions can be improved for solving
specific bargaining problems and broader applications.
doi: 10.3846/16111699.2011.573281
Acknowledgement
Parts of the research were financially supported by the National
Science Council in Taiwan (NSC 99-2628-E-034-001).
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Min-Ren Yan
Department of International Business Administration, Chinese
Culture University (SCE), No. 231, Sec. 2, Jian-guo S. Rd., Da-an Dist.,
Taipei City 106, Taiwan E-mail: mjyen@sce.pccu.edu.tw
Received 29 September 2010; accepted 05 February 2011
Min-Ren YAN. PhD, Assistant Professor of the Department of
International Business Administration at Chinese Culture University
(SCE), Taipei, Taiwan. Dr Yan is concurrently the leader of the research
lab in Project Business Economics and Decision Models, the director of
Quality Centre for Business Excellence, and business consultant in web
technology, marketing, and services industries. His research interests
focus on strategic alliances, game theoretical analysis, project
business economics, and decision models.
Table 1. The acceptable prices in the last three rounds
Round Acceptable price for player A Acceptable price for player B
n-2 [a.sub.n] - [PL.sub.a(n)] E - [a.sub.n] + [PL.sub.a(n)]
+ [PL.sub.b(n-1)] + [PL.sub.b(n-1)]
n-1 [a.sub.n] - [PL.sub.a(n)] E - [a.sub.n] + [PL.sub.a(n)]
n [a.sub.n]
Table 2. The fuzzy if-then rules
Rule
code "R" is "O" is "L" is "S" is
1 IF High and High and High THEN Low
2 IF High and High and Moderate THEN Low
3 IF High and High and Low THEN Low
4 IF High and Moderate and High THEN Moderate
5 IF High and Moderate and Moderate THEN Moderate
6 IF High and Moderate and Low THEN Moderate
7 IF High and Low and High THEN Moderate
8 IF High and Low and Moderate THEN Moderate
9 IF High and Low and Low THEN Moderate
10 IF Moderate and High and High THEN Moderate
11 IF Moderate and High and Moderate THEN Moderate
12 IF Moderate and High and Low THEN Low
13 IF Moderate and Moderate and High THEN High
14 IF Moderate and Moderate and Moderate THEN High
15 IF Moderate and Moderate and Low THEN High
16 IF Moderate and Low and High THEN High
17 IF Moderate and Low and Moderate THEN High
18 IF Moderate and Low and Low THEN High
19 IF Low and High and High THEN High
20 IF Low and High and Moderate THEN High
21 IF Low and High and Low THEN Moderate
22 IF Low and Moderate and High THEN High
23 IF Low and Moderate and Moderate THEN High
24 IF Low and Moderate and Low THEN High
25 IF Low and Low and High THEN High
26 IF Low and Low and Moderate THEN High
27 IF Low and Low and Low THEN High
Table 3. Information of the JV project
Information Company A Company B
Estimated total amount 3,229 million dollars
of the project (E)
Work scope Station portion Tunnel portion
Estimated cost 1,180 million dollars 1,770 million dollars
([C.sub.a] and
[C.sub.b])
Estimated total profit 279 million dollars
of the project (F)
