Mark-up Decision Model: Evaluating the Profit Ranges of International Construction Projects with

Support of Case Based Reasoning

Woo Yong Jeong

University of Yonsei, Korea (email: trust-jeong@hanmail.net ) Du Yeon Kim

University of Yonsei, Korea (email: cagebird@yonsei.ac.kr ) Seung Heon Han

University of Yonsei, Korea (email: shh6018@yonsei.ac.kr ) Yeon Il Jeong

Industrial Bank, Korea (email: yeonil@ibk.co.kr )

Abstract

Not only competitive but also decent level of profitable mark-up size is essential in establishing a bidding strategy to successfully capture the project opportunities while securing more chance to gaining profit. For this purpose, there have been numerous researches to present either quantitative or qualitative models to provide an optimal level of mark-up. However, to a certain extent, current approaches have been challenged in that they are set up largely depending either on unrealistic subjective data or insufficient data on the actual profit performance. More often than not, useful previous cases are not well incorporated in making a rational mark-up decision. In order to solve this limitation, this study begins with analyzing the 1,563 international construction projects performed by Korean global contractor during the last decade. These data contain the objective information such as actual profit, variation of the exchange rate, contractor’s capability, country’s finance reliability, etc. Then, this paper adopts a case based reasoning (CBR) to properly investigate the previous performances of real overseas projects so making a modest mark-up based on realistic data is possible. CBR enables mark-up decision model by retrieving the similar previous project set, which is used to calculate the average previous profit and its variance. This statistical baseline makes it possible to predict the mark-up competitiveness as well as to evaluate the possibility of a project failure (bad profit) of a given project. Particularly, this model shows the possible scenarios of how much mark-up size can be lowered while considering the probability of a project loss. Although, this model is developed based on the Korean contractor’s experiences, the proposed method and results can be applicable to international construction bidders to reasonably decide the make-up level.

Keywords: mark-up size, profit, profit ranges, probability, case based reasoning

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1. Introduction

As economically emerging and oil-producing countries have been booming with the respective economic growth as well as uprising oil price, corresponding construction contracts have also increased, which enables international construction companies to increase their bidding opportunities. However, this opportunity does not always secure the chance of profitability. Han et al. [1] argued that actual performance of international companies are not promising, showing a higher rate of project loss than that of domestic market because the level of risk exposure is gradually expanding and the bid competition also becomes more highly intensive. Therefore, of much more importance is that the contractors should estimate an appropriate bid mark-up size not only to capture a bid opportunity but also to have a higher chance of earning a positive profit.

The bid mark-up estimation entails uncertainties and complexities that make difficulty to analyze and model in a quantitative way. In this regard, Hegazy and Moselhi [2] stated that the ability of experts to derive reliable decisions of mark-up estimations primarily relied on the partial cues, which implied that the principal act and rule for solution is not either computational or deep reasoning, but rather some form of pattern recognition and an analogy with previous situations. Li [3] also indicated that mark-up decisions simply ‘emerge’ in a single step from a mixture of experience, intuition and gut feeling, without going through a sequence of discourses or thoroughly reasoning steps.

In order to overcome this problem by the way of quantitative approaches, many researchers have suggested artificial intelligence tools and other reasoning models. Tavakoli and Utomo [4], and Ahmad [5] develop an expert system. Hegazy and Moselhi [2], and Dias and Weerasinghe [6] used artificial neural networks. In addition, Chua et al. [7] and Dikmen. et al. [8] adopted a case based reasoning (CBR) to support the decision of mark-up size. These previous researches have contributed to extending the understanding of what factors attribute to the determination of a mark-up size, how important each factor is and what measures of mark-up size are. However, current approaches, particularly conducted by Chua et al. and Dikmen. et al. have some challenges, summarized as follows:

(1) The most of the key input data was constructed from subjective opinions or relative ratings surveyed by the experts’ individual responses. Data such as level of experience, financial capability, technical capability, and potential profitability are likely to be elicited differently and easily biased based on their personal background and perceptions to the specific level of risk exposures.

(2) The previous CBR research built on models based on the insufficient amount of data to determine a reliable mark-up size, which lacked the consideration of numerous conditions and different scenarios. For example, suppose that the prediction algorithm of CBR is composed of just 10 features for the estimation (i.e., provision of the advanced payment) and each feature constitutes the two types of text options (i.e., yes or no), the required data would easily exceed the 1,024 cases for a perfect matching

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between previous data set and a given project. However, most of the CBR model for mark-up estimation was simply based on the cases below 200, even where they entail more than 20 features requiring significant large scales of data for case reasoning.

(3) The targets of previous studies were focusing on the average mark-up size or the maximum/ minimum mark-up size. However, actual competitive bid mark-up is usually determined under the desired mark-up size. In other word, profit distribution and profit variance of the actually performed cases are required to fit in order to estimate the risk of searching the desired mark-up size. Previous studies did not sufficiently investigate solutions for this situation.

To suggest a resolution for these issues, this study used the 1,563 international projects actually completed from 1997 to 2006, which have been reported to the International Contractors Association of Korea (ICAK). These registered projects encompass the objective figures or characters including actual profit performances, claimed cost, schedule performance, type of bidding and type of alliance. In addition, other objective data were also obtained collected by the third institutes, including such useful data as fluctuations of currency exchange rate, estimation of the contractor’s capability, and contractor’s financial capability. On this basis, the mark-up prediction model was developed by the adoption of CBR tool and profit distributions fitted from the previous cases and their performances. Out of the total of 1,563 projects, 1,413 projects were used in developing a CBR model, and 150 projects were left for testing the accuracy of a proposed model.

Criteria Previous studies Current study

Estimation criteria of feature Mainly subjective opinions by experts Objective data from real projects’ performances

Classification criteria of feature

Mainly qualitative classification

(ex: low, normal, high) Character or numeric

Project type Specific type All types

Project number Almost below 200 cases 1563

Profit Variance Not applied Applied

Table 1. Differences between previous studies and current study in estimating mark-up size

2. Method

2.1 Mark-up Decision Model

The bidding process of international construction projects portrays less information while involving more uncertainty than is the case of domestic projects. This normally makes the decision of bid price more difficult and less profitable. Figure 1 and 2 show that the decision of a mark-up size can potentially be determined by the variables of expected cost as well as

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variance of profit distribution of previous similar projects. At first, the expected project cost is to be estimated by the bidder’s capability and domain-specific knowledge of cost estimation. This paper does not deal with the exact method of how to assess the expected project cost because it is commonly and widely developed practice in construction industry. Secondly, the previous similar examples out of really captured bids are to be retrieved by the use of CBR. Utilizing these data enables to quantitatively define the profit distribution of previous similar group and to presume the mark-up competitiveness of a probable project. If there exist sufficient number of previous similar cases under the assumption that the bidder who has performed these projects frequently participates in lots of bid opportunities and consistently determines the mark-up size with a consideration of the profit of previous similar projects, it can be reasonably hypothesized that the pattern of profit distribution is almost coinciding with that of mark-up distribution. However, if this is not the exact case, it should be noted that the difference in figure 1 between the actual bid mark-up and the average profit of previous similar cases is not the real winning probability associated with a mark-up size, rather is the just mark-up competitiveness. As well, the gain or loss probability of a given project can be derived based on the profit distribution of the previous similar cases.

Thirdly, if previous similar cases are collected from the same company, both expected profit and profit distribution of these data can be applicable to other potential projects pursued by the same firm, and this guideline enables to evaluate the gain or loss probability of a given project. On the other hand, if these data are driven from other companies, it would not be reasonable to apply the same standards to the future projects. Therefore, these standard values drawn from other companies’ performance should be tailored based its own characters and capabilities of doing projects. Otherwise, it would be better to be referred as a simple comparison even while it can be useful to guess other bidders’ average profit and their relevant distributions regarding the previous similar projects, to a certain extent, executed differently.

Figure 1. Principle of Mark-up Decision Model

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Figure 2. Basic Procedures of Mark-up Decision Model

2.2 Case Based Reasoning

CBR means the process of solving new problems based on the solutions from previous ones [9]. CBR is analogous to Artificial Neural Network (ANN) in the way that they both grasp relevant information from previous cases. However, while ANN suggests the most suitable case based on a rule that is hidden from the users or decision makers, CBR retrieves the most similar case or several representing cases through prioritizing by the weighted features that are pre-defined by the decision maker. For this reason, ANN is often difficult to explain the reason why it is exactly right, whereas CBR explains the results and procedures of how they are determined. As such, ANN is more difficult to define model’s contexture as the structure of data is becoming more complicated and unstructured. By contrast, CBR can convey the most similar cases no matter how complicated it could be. The mark-up decision of overseas projects is so complicated and unstructured such that it is difficult to draw a clear definition; thus this paper applies CBR under the condition of obtaining sufficient sets of data that is essential ingredients in making the CBR-based decision model for deriving a desirable mark-up size.

The general procedure of CBR comprises three steps: retrieve, reuse or revise, and retain. Retrieving indicates that, at the outset, the decision maker finds a previous similar case or cases in order to solve the given problem. The previous cases enclose several features that have weights associated with the importance of each feature. If there exists a previous case that exactly matches the same features of a given project, the decision maker can simply use it as to

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solve the problem, thus called ‘reusing.’ If it is not the case, the decision maker can resolve the problem in a different way, as follows: (1) If several specific features of a given project are the same with a previous case, it gains a mark; (2) After comparing all the features, the highest marked case or relevant case set is selected; (3) Then, decision maker unravels the given problem using this retrieved case or case set, which is called ‘revising’; and (4) Finally, this solution on a given project is accrued again into a data set for the future usage; thus called ‘retaining.’

2.3 Determining Factors on Profitability

Many studies on the evaluation or prediction of profitability have been performed. Zhi [10] suggested 60 risks of international construction projects under the structures with partitioning into three hierarchical levels. Han et al. [11] drew 64 factors of causes of bad profit in overseas construction projects based on the Korean contractors’ real performances. Also, Mochtar and Ardit [12] proposed 11 important factors as a pricing strategy for the U.S. construction industry. Chua et al. [7] and Dikmen. et al. [8] utilized the 30 and 44 factors, respectively, aiming at providing a CBR-based mark-up size.

* ICAK, International Construction Association of Korea; CAK, Construction Association of Korea; KEIB, Korea

Export-Import Bank; DB, Journal of Doing Business; KEB, Korea Exchange Bank

Table 2. Factors affecting profitability

Features Type Description of measurement Source Region Text Middle east, Asia, Europe, etc ICAK Type of project Text Infrastructure, Architecture, plant ICAK Type of contract Text Unit price, Lump sum, Cost plus fee ICAK

Type of bidding Text Open, Nominated, Negotiation, Privately financed (BOT, etc) ICAK

Type of participation Text Main contractor, Sub-contractor ICAK Type of alliance Text Single, JV or Consortium ICAK Type of owner Text Private, Public ICAK Funding source Text Owner, Domestic ODA, International ODA ICAK Size of project Numeric $ ICAK Construction capacity Numeric 100, 80, 60, 40,20 CAK Country finance reliability Numeric 100~0 KEIB, DBProject duration Numeric Day ICAK Schedule performance Numeric % (actual day/ contract day) ICAK Variation of exchange rate Numeric % (max. rate/min. rate during projects) KEB Portion of labour cost Numeric % ICAK Portion of equipment cost Numeric % ICAK Portion of management cost Numeric % ICAK Claimed cost Numeric % ( claimed cost / total contract amount) ICAK Profit rate Numeric % ICAK

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As previously mentioned, this study targets the reliable input data based on the real project performances. Based on the previous research and useful information that registered to the government-certified institutes such as the International Construction Association of Korea (ICAK) and Construction Association of Korea (CAK), 19 factors are ultimately drawn, grouped into three categories as shown in Table 2. The first group forms the feature of the owner’s factors such as region, country’s finance reliability and variation of exchange rate. The second class includes such features of the company related capabilities as construction capacity and type of alliance. The last group includes features of the project-related characters.

Of these features, construction capacity is evaluated by the annual reports performed by CAK which reflects the contractors’ annually total earned revenue, net revenue, amount of capital, ratio of liability, number of engineers employed, amount of research investment, possessions of specific license or patents such as ISO (International Standardization Organization) series. The ranking above 20 gets 100 points, while that below 450 receives only 20 points. The finance’s reliability of a host country is estimated by the Korea Export-Import Bank (KEIB); business environment of a host country can be also assessed by the information issued by the Journal of Doing Business.

2.4 Algorithms of case retrieval and revision

The algorithms for retrieval and revision of similar cases are illustrated in Figure 3. The eight features out of 19 are in the form of textual expression. At first, the retrieved cases are required to coincide with the region and the type of project of a given project to initially make a similar group. Then, other text features such as type of contract and bidding are matched with a given project. After grouping the analogical cases through an inductive classification, the top 10 similar cases are chosen among the 1,413 population cases based on the scoring of numeric type of features. In this process, the similarity score (SC) and similarity index (SI) are calculated by the follow equations:

x100V

V -V(SS) Scorey Similiarit

case problem

case problem cases previous=

x100(SI)Index y Similiarit

1

1

∑

∑

=

=

×= n

ii

n

iii

W

SSW

Where V = the value of the numeric type features, and Wi = the value of weightiness to each numeric feature (explained in the following chapter).

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Figure 3. Case retrieval and revision process

As shown in the similarity index, the top 10 similar projects are manipulated to shape the average profit and their profit distribution, which are, in turn, used to estimate the mark-up size competiveness and the probability of gaining/losing profit of a given project.

2.5 Assessing the Weightiness through Multi-regression

In order to measure how much the features affects the profitability of international construction projects, the weighted values (Wi) need to be determined. This study uses the multi-regression method based on 1,413 project cases conducted by Korean contractors all around the world from 1997 to 2006. Figure 6 shows the results of regression analysis. All numeric features portray a p-value (significance probability) under 0.05, showing 95% of reliability such that all numeric features are accepted as relevant factors affecting on the level of profitability. R-square (coefficient of correlation) also has a value of 0.442, indicating that it lies within the moderate level. Since the purpose of multi-regression is not the prediction, but the relative importance of independent variables, R-square is not considered critical in this case [13]. Table 3 indicates that the size of the project, construction capacity and country’s finance reliability show the higher values; thus these factors are reflected as the most important features in deriving the top 10 similar cases.

Features P-value Importance weight on profit Size of project 0.000 0.163 Construction capacity 0.000 0.157 Country finance reliability 0.000 0.146 Project duration 0.002 0.118 Variation of project duration 0.014 0.093 Variation of exchange rate 0.021 0.075 Portion of labour cost 0.025 0.069 Portion of equipment cost 0.029 0.064 Portion of management cost 0.038 0.058 Claim cost 0.041 0.057

Table 3. The weighted value estimation by multi-regression

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3. Verification and Applications of Mark-up Size Decision

The total of 150 project cases (among the 1,563 cases) was left out for testing a prediction accuracy. The accuracy test was performed by the use of the t-test and the mean absolute error between actual profit and predicted profit. T-test assumes the null-hypothesis, insisting no difference between actual profit and forecasted profit. The p-value of t-test has 0.160 showing that the null-hypothesis is not rejected under the 95% significant level. Also, the mean absolute error between actual profit and calculated profit is estimated at 13.25%, implying that the proposed CBR model can forecast the profit ranges up to the accuracy of 86.75%.

Mean Standard Deviation t Freedom P-Value 0.1203 0.0491 2.450 137 0.160

Table 4. t-test results between the actual profit and calculated profit

This study uses the profit and variance (standard deviation of profits) of the previous similar cases to determine a desirable mark-up size. The profit distribution of the similar cases retrieved by the CBR is not exactly the normal shape, but if many cases that are similar to a given project exist, the distribution tends to close to the normal pattern by the well-know principle of Central Limit Theorem. It is also based on our premise that the mark-up size can be assessed by profit distribution of the similar cases. This assumption enables to estimate the mark-up competitiveness as formulated by the following equation. If mark-up size of a given bidding (m) is supposed to be equal to the average profit of previous similar case (ps), mark-up competitiveness is estimated at 100, indicating that the mark-up size of a given biding is fairly determined based on the average profit of previous similar projects (ps), Also, if the firm lowers the bid mark-up size (m) to zero (no profit), the mark-up competitiveness increases to 200, implying a higher wining probability. Accordingly, the higher the value is, the more the possibility of winning a bid is.

100p

m2penesscompetitivupMarks

s ×−

=−

Where, ps = average profit of previous similar cases, m = mark-up size of a given biding The probability of a project failure (loss) also can be calculated by the following equation, under the assumption of a normal distribution. If the mark-up size of a given bidding (m) is equal to the standard deviation of a previous cases’ profit (σ), the probability of loss becomes 15.97% because it is the probability generating the random variable (x) over 1 in the case of standard normal distribution. Thus, the higher the bid mark-up (m) compared to the standard deviation of the previous cases (σ) is, the less the probability of loss is.

}x

σmp{lossofyProbabilit ≤=

Where, σ = standard deviation of the previous cases’ profit, x = random variable in standard normal distribution

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Table 5 shows the mark-up competiveness and the probability of a project loss associated with different mark-up sizes. For example, the 3% mark-up in cases of #71 and #144 generates the 13.14% and 16.11% of probability of loss, respectively. Interestingly, these values are quite similar to 15.10% of a project loss when performing real overseas projects, annually reported by Engineering News Record (ENR) [14]. Also, it is found that the less mark-up size in all cases can increase the mark-up competiveness, showing a more possibility to capture a given project by lowering the bid mark-up, but it concurrently increases the probability of loss due to the relatively low level of profit reflected in a bid proposal. Thus, a construction bidder can decide a desirable mark-up size more flexibly by weighing up both the mark-up competitiveness and probability of loss in associated with the different scenarios of mark-up sizes.

Table 5. Estimation of mark-up competiveness and probability of a project failure (bad profit)

4. Conclusions

This study developed a quantitative mark-up decision model that takes advantages over the previous approaches. First, the model is employed by the subjective and actually performed information registered on the government-certified public institutions. These input data are fundamentally different from those of expert’s opinions that are often subjective and influenced by the personal biases. Second, the amount of data set used in a CBR model is much larger than the cases of other research; hence the proposed model is more reliable and applicable to the actual projects. Third, it estimates the possible scenarios associated with different mark-up competitiveness and the probability of a project failure (i.e., loss) using the previously established profit and its distribution of the similar cases. Particularly, this estimation helps bidders to evaluate how much mark-up size can be lowered while considering the probability of a project loss. This emphasizes the benefits of a proposed model to reasonably deciding a desirable make-up size.

Case Number

Previous Similar

Profit (ps)

Profit Standard

Deviation (σ)

Mark-up Size(m)

Mark-up Competitiveness

Probability of loss

Case #1 3.50% 1.88% 3% 114 5.59% 5% 57 0.04%

Case #21 5.55% 0.47% 3% 146 0.01% 5% 110 0.01%

Case #71 7.00% 2.66% 3% 157 13.14% 5% 128 3.00%

Case #98 7.08% 1.65% 3% 158 3.00% 5% 129 0.01%

Case #144 4.50% 3.04% 3% 132 16.11% 5% 88 5.05%

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Despite its advantages, this study poses several shortcomings requiring more research. First, this paper considers relatively fewer features than those of other studies because it was shaped based strictly on the reported/registered information. Second, all data used are constituted of Korean company’s experiences and performances, which possibly constraints the applicability of other nations’ contractors. Our further study will concentrate on extending a number of features by combining the registered information as well as domain-specific expert’s knowledge. In addition, if possible, acquiring more information on the actual number of bidders and actual winning mark-up size for each case will be constructive in eliciting more reliable bid mark-up estimation.

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