A theoretical framework for determining the minimum number of bidders in construction bidding compet

A theoretical framework for determining the minimum number of bidders in construction bidding compet

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Unformatted text preview: Construction Management and Economics (2002) 20, 473—482 A theoretical framework for determining the minimum number of bidders in construction bidding competitions STEPHEN C. NGAI', DEREK S. DREW”, H. P. L02 and MARTIN SKITMORE3 'Depamnent of Building and Real Estate, Hang Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong ‘Depamnent of Management Science, City University of Hong Kong, Tat Ghee Avenue, Kowloon, Hong Kong ’Schaol of Commotion Management and HM, Queensland University of Technology, Gardens Point, Brisbane Q4001, Australia Received 28 February 2001 ; accepted 19 April 2002 A theoretical framework is proposed for determining the minimum number of bidders in competition for projects in the construction industry. This is based on the neo-classical micro-economic theory for price determination in construction and the assumption of random contractor-selection. Empirical analysis of the Hong Kong data set not only illustrates the applicability of the framework, but also supports the relevance of the microeconomic model for construction price determination. The main implication for clients is that, in order to obtain the most competitive bids for projects in the most cost-eficit way, they should vary the minimum number of bidders in competition according to market conditions. ngords: Construction price determination, tendering theory, commotion economics, number of bidders Introduction This paper proposes a theoretical framework for deter- mining the minimum number of contractors in com- petition for projects in the public contracting sector of the Hong Kong commotion industry. The framework aims to provide a more cost efl'ective approach for the Hong Kong Special Administrative Region (HKSAR) Government to obtain competitive bids while contin- uing to maintain its public accountability. In order to provide a theoretical foundation for the fi'amework, the linkage betwe market conditions and the degree of competition is explored. Based on the neo-classical micro-economic theory for construction price deter- mination, it is uggested that the number of potential competitors in competition will depend on the market conditions. A set of regression models is formulated to *Author for correspondence. e-mail: derekdrew@unsw.edu.au estimate the number of potential competitors in the market. Following from this, the minimum number of contractors to be included in competition is deter- mined. This is based on the asumption that the con- tractor-selection process is random. However, the framework does not quantify the cost efi'ects of an addi- tional number of contractors in bidding competition for projects. An empirical analysis ofa data set from the HKSAR Governmt further confirms the applic- ability of the framework. Since there is a large amount of literature on tender- ing theory, it is not realistic to expect a paper of this format to provide a comprehensive literature review, particularly, on the debate on the relevance of tender- ing theory and micro-economic theory for construction price determination. See Runeson and Raftery (1998) for a thorough literature review. Reference to the lit- erature is made whenever appropriate. The primary purpose of this paper is to construct a framework for Construction Management and Economics ISSN 0144—6193 print/ISSN 1466-433X online 0 2002 Taylor & Francis Ltd http://www.tand£co.ukliournala DOI: 10.1080/01446190210151041 474 determining the minimum number of bidders in com- petition and to conduct an empirical analysis for testing the applicability of the framework. Construction price determination The construction economics literature contains two fundamentally different approaches to construction price determination. The first is the probabilistic approach that originated from Friedman in 1956 and has gained wide publicity. There is a large amount of literature, that has become known as tendering theory, on the analysis of how construction prices are deter- mined, e.g. Gates (1967, 1970, 1976), Rosenshine (1972), Dixie (1974), Fuerst (1976), Weverbergh (1978), Benjamin and Meador (1979) and Carr (1982, 1987). The second approach, by Hillebrandt (1974), follows the neo-classical micro-economic theory of price determination in construction. A more compre— hensive literature review and evaluation on the rele- vance of neo-classical micro-economic theory for construction price determination in the building indus- try was conducted by Runeson and Raftery (1998). They concluded that the neo-classical micro-economic theory is a more suitable analytical framework than tendering theory, both in terms of its predictions and in the conformity with empirical studies of the con- struction industry. It is outside the scope of this paper to further evaluate further the appropriatenes of the neo-classical micro-economic theory for construction price determination. Instead, this line of thinking forms the basis for the proposed empirical study. The basic assumption for the application of neo- classical micro-economic theory in construction is that the building industry is very competitive and conforms to the model of perfect competition. A perfectly com- petitive market is characterized by the stence of a ‘going market price' (i.e. perceived equilibrium price) that all buyers pay and all sellers receive, and no one player in the market can individually afi'ect that price. In other words, each buyer and each seller is much toosmallapartoftheoverallmarketfortheiractions to afiect the market price. Other standard descriptions of such a market include homogeneity of the product, perfect information and easy entry to and exit from the market. Here the market can be considered as a process of interaction between buyers and sellers of a commodity for a mutually agreed price (Perman and Scouller, 1999). A direct analogy in construction is that the buyers areconstruction clients, either from the public or private sectors, who are procurers of facili- ties. The sellers are construction companies (or con— tractors) who construct facilities to customized designs specified by the clients. Most contracts are awarded Ngai et a]. through competitive tendering processes where clients and contractors reach a mutually satisfactory price. Normally the contractors who submit lowest tender prices obtain the contracts. In this competitive market, price determination is based on the interaction of demand and supply. The market price for a commodity is the equilibrium price where the downward-sloping demand curve and the upward-sloping supply curve intersect. The construc- tion industry responds to changes in demand in the short run by changing the price of its product and in the long run by a change in the capacity of the indus- try. On an a priori basis, it is assumed that firms in the industry would tender only when they had, or anti- cipated they would have, excess capacity and, would not tender when all capacity is being utilized. Consider a reduction in demand in the construction industry; lower prices will result initially because of the lower capacity utilization in the industry. The non- utilized capacity in the industry will lead to lower mar— ginal costs. The lower the marginal costs, the higher the opportunity costs of losing projects for individual firms, and hence the lower the tender prices. As a result, competitiveness increases. In the long run, the industry will reduce the excess supply capacity because of insuflicient profit, and prices will be restored to their level. On the other hand, an increase in demand in the construction market will result in higher capa- city utilization in the industry. The higher capacity uti- lization results in higher marginal costs and hence lower opportunity costs of not winning projects, and hence the higher the tender prices. In the long run, the indusz supply capacity will be adjusted and prices and profits will return to their initial levels. Numberofpotendalcompefltorsasa measureofdegreeofcompetition Based on the above price determination model for the construction industry, changes in dand and/or supply will change the degree of competitiveness in the industry initially, and result in movements in tender price level. In the long run, however, the supply capac- ity will be adjusted and prices will be restored. In this way, the degree of competition must be measured in terms of capacity utilization rather than in terms of the total level of output (Runeson and Bennett, 1983). In addition, it is a reasonable assumption that the number of potential competitors in the market is a reflection of supply capacity utilization in the industry. In line with this basic assumption, Runeson (1988) estimated empirically that prices systematically changed by more than :I: 20% over the economic cycle and that 85% of these price changes could be explained by variables Minimum number of bidders for construction projects describing market conditions, such as changes in demand and capacity utilization in industry. Therefore, the degree of competition in the industry can be mea- sured in terms of the likely number of potential com- petitors for projects in the market, and the degree of competition will depend on the market conditions. There is much empirical evidence showing that market conditions afi'ect tendering behaviour (e.g. De Neufville et al., 1977; Flanagan and Norman, 1985; Runeson, 1990; Rawlinson and Raftery, 1997). The market conditions afi'ect at least the contractors’ bid prices and number of competitors for a project. These would seem obvious given the price determination model just described. De Neufville et a1. (1977) showed that in a boom period (which they referred to a ‘good’ years) wh there are more projects available in the construction market, contractors generally bid for pro- jects at higher profit margins, and competition for pro- jects is relatively less intense. In a slump period (i.e. referred to as ‘bad’ years) with fewer projects avail- able, contractors bid lower than in the boom period, and competition becomes more intense. They showed also that market conditions afi'ect the number of competitors for a project. Interestingly enough, they showed further that the market conditions afi'ect con- tractors' bid prices independently of the competition intensity (or the number of bidders) for a project. Measuring market conditions It seems that no definitive measure for market condi- tions in construction exists in the literature. It is sug- gested that, in these circumstances, the standard approach is to identify a measurable quantity that can be taken as an indicator, or proxy, for the variable we are actually trying to measure (Flanagan and Norman, 1983). These proxy variables’ values, and changes in values, constitute an indirect measure of the variable we are trying to measure. In this sense, many possible proxy variables for market conditions can be envisaged. McCafi'er ct a1. (1983) ued the ratio tender price index to construction cost index to represent changes in prices due to market conditions. Flanagan and Norman (1983) used number of bidders received for particular projects as a manifestation of market conditions. They further suggested that the rate of change of a price index (such as tder price index) would be a more appropriate proxy variable for market conditions. Runeson (1990) derived an economic con- ditions index based on the average of all tenders’ markup, in an attempt to incorporate market conditions into tendering models. Because of data limitations, as in our case, there is no formal compilation of either a market condition 475 ind or building cost index in Hong Kong. For the purpose of dis pirical study, we shall take the rate of change of tender price index TPI (hereafter doted as TPI,) as an indirect measure of market conditions. In Hong Kong, generally the TPI is compiled by com- paring the prices of a proportion of the items within a number of successful tenders during a given period against the prices of similar items in a base schedule of rates (Chau, 1998). It represents the cost a client must pay for a building. It includes all input prices and takes into account the prevailing market condi- tions. The movements of tender prices and input prices are monitored by tender price and building cost indices, respectively, and one of the major uses of the TPI is for forecasting tender price level (I‘ysoe, 1981). Empirical analysis (I): minimum number of bidders As stated above, we shall use TPIr (i.e. rate of change of TPI) as an indirect measure of market conditions. Additionally, we shall use l/N as a measure of the degree of competition (since the number of potential competitors also depends on type of project and geo- graphical location, the average number N of bidders per project is used) and examine the relationship between market conditions and the degree of compet- itivess for each project in a Hong Kong data set. In order to develop a regression model for UN using the TPIr as predictor, there are basically three steps involved. The first step is to use a polynomial to model the time series of the TPI over a period of time. By using time t as predictor in a polynomial regression analysis of the TPI, we shall construct a best model of a poly- nomial of degree n that provides a very good fit to the TPI: TPI = a0 + alt + trth + a3? + + alt" (1) Once the model of the time series of the TPI is con- structed, the second step is to difi'erentiate the poly- nomial with respective to time t (see Eq. 2 below). By substituting difi'erent values of t into Eq. 2, TPIr values can be obtained for difl'erent values of t. TPIr = cu:l + 2a2t + 3113:2 + + notut'"l (2) When TPIr values are found, the third step is to work out the ordered pairs of (UN, TPI,) for the time period. Then a regression model for UN using TPIr as pre- dictor can be constructed, as shown in Eq. 3 below. Thus, based on this approach, we can estimate the average number of potential bidders N in the market for further analysis. Since the TPI is a time series, inferential time-series regression or autoregressive 476 models can be constructed to forecast the TPI level in the industry. While there is a key advantage in regres- sion analysis over other smoothing forecasting tech- niques (i.e. it provides a measure of reliability of each forecast through prediction intervals), it is generally risky for prediction outside the range of the observed data that may make the model (i.e. Eq. 1) inappro- priate for predicting a future TPI level. Therefore, it is suggested that the forecasting of a TPI level in the industry generally be confined to the short run. —1=b,,+b,x'n=1,+b,x N )1+... (3) One major problem facing construction clients, par- ticularly the HKSAR Government, is how to obtain competitive bids for their projects in a cost efi'ective way and at the me time maintain its public account- ability. Traditionally, construction clits, at least for the I-lKSAR Government, encourage large numbers of contractors to submit bids for each project. Drew and Skitmore (1990, 1992) showed fi'om their sample data set taken from Hong Kong’s private and public sectors that tendering competitions average 10 and 17 con- tractors, respectively. Empirical studies have shown that a greater number of bidders in competition for each project reduces the value of the lowest bid (McCafier, 1979; Skitmore, 2002). However, there has been quite a body of literature concerning the issues of limiting number of potential bidders and bid prepar- ation costs in competitive tendering (e.g. Engelbrecht— Wiggans, 1980; Skinnore, 1981; Schweizer and Ungern-Sternberg, 1983; Flanagan and Norman, 1985; Samuelson, 1985; Wilson at al., 1987; Wilson and Sharpe, 1988; De Neufville and King, 1991; Holt er al., 1994; Remer and Buchanan, 2000). The key idea is that a large number of contractors in tender— ing competition will increase procurement costs. It is a waste of limited resources when there are many com- petitors in tendering competition for projects in the market, for instance, during a period of lower demand level in the industry, when only the lowest bidder will win the project. The high proportion of wasted resources as a result of abortive tendering may ofl'set any potential savings obtained from the lowest bid—win tender. Therefore, policies of limiting the number of bidders in competition would be beneficial to the industry as a whole. Some research findings recommend restricting com- petition to between four and eight contractors for each project (Schweizer and Ungern-Sternberg, 1983; Flanagan and Norman, 1985; Wilson and Sharpe, 1988; De Neufville and King, 1991). The main argu- ment for this approach is that a higher number of con- tractors in competition has only marginal impact on the value of the lowet bid received. Another approach Ngai et .11. suggests that there ts an optimum number of com- petitors for each construction project. This approach is based on the assumptions that: (1) there is a quan- tifiable cost of tendering from the competitors associ- ated with every bid; (2) the total cost of tendering increaes in proportion to the number of competitors; and (3) potential savings diminish with increasing numbers of competitors. The argument for this approach is that ultimately this cost of tendering must be recovered from clients in the long run. Which approach to adopt poses one fundamental question: why do tenders vary? Only by answering this question can a well-founded theoretical basis for further progressive thinking be formulated. For this, Runeson and Raftery (1998) have given a comprehensive account of assessing the variations between tenders. They suggested that nee-classical micro-economic theory provides an explanation of the variations in ten— ders that is consistent with the available empirical evi- dence. If their argument is right, then the above approaches fail to explain the fundamental question properly, because they are based on the basic assump— tions either implicitly or explicitly: (1) that tendering is a random process; and (2) that there is a direct cost of tendering. There are serious conceptual problems con- cerning thee approaches. First, based on neo-classical micro-economic theory, more tenders would not neces- sarily guarantee a lower price, because price determin- ation is actually based on interaction of demand and supply. Firms that are most desperate for jobs would also be the firms most likely to tender, and thus prob- ably the number of bidders is unlikely have much effect on the price. Second, even if it is assumed that more tenders result in a lower price and there is a direct cost of tender- ing, the reduction in cost is for the individual project, but the increase in cost of tendering is an industry wide increase. A little reflection shows that two such differ- ent concepts cannot simply be combined and added together. Moreover, if it is asumed that the cost of tendering is a fixed cost, then the arguments for these approaches fail to stand as well. For instance, if it is assumed that there are 10 firms each with an estimat- ing department set up to produce 20 estimates per year, then there are 200 estimates per year for the market. Ifit is assumed further that one year there are 100 new projects coming on the market, while the next year there are only 20 new projects, the cost of ten— dering has not changed for the industry or the firm but the average number of estimates per project has increased from two to 10. Instead of the above approaches as evaluated, another approach will be suggested based on micro- economic theory for construction price determination in rendering. This leads to variations in the tenders Minimum number of bidders for commotion projects received. The selection of contractors to submit tenders can be assumed to be random for the purpose of public accountability. If the random contractor-selection assumption is adopted, then the probl of predicting the lowest tender is non-deterministic. Skiunore (1981) assumed a random contractor-selection process in tendering to predict tender prices. He used an example in which amples of six bidders to submit tenders were selected from a population of 20 potential bidders. He then worked out the fi'equency distribution of the bidders’ success from all possible combinations of six bidders. From this example he showed that random selection of bidders reduces the predictability of the lowest tender by reducing the chances of including potentially low tenders, whereas increasing the number of bidders in competition will increase predictability. In other words, it is impossible to predict the lowest tender with certainty. The best that can be achieved is to predict a range of value where the lowest tender is expected to land. Following Skitmore’s (1981) example, instead of grouping a population of 20 potential bidders into ascending order of potential values, N potential bids will be arranged in ascending order of tender prices and numbered X accordingly. After determining the average number of potential bidders N in the market from the set of equations 1—3, suppose that these N potential bidders in the market are on the approved list and they would have estimated their potential tender prices if they were asked to submit tenders for this project. X= {1, 2, 3, . . ., N, where potential bid is ranked Xth lowest in the group of N tenders. From these N potential contractors, k contractors will be selected at random to submit their tenders. Then the total number of possible competitions for this project can be calculated from Total number of possible competitions for (4) this project = 1 The probability that the Xth lowest bid in N bids is the lowest bid in competition is given by the proba- bility density function famed wh randomly select- ing k contractors from the group of N potential contractors: [”_' fav. M") = k The simplest way to identify the lowest bid (i.e. X = 1) from the group of N potential contractors is to where x=l, 2, ...N—k+l (5) 477 ask all of them to submit their tenders. However, as mentioned before, this would not be cost efi'ective. Therefore, the most important question now becomes: how can the chance of including the most competitive bids be maximized, by randomly selecting k contrac- tors in competition for this project, once the average number of potential contractors N competing for this project in the market is estimated? Although there is no theoretical definition for the meanings of maximiz- ing the chance and the most competitive bids, for sim- plicity and practicality, the chance will be taken at the 95% confidence level and the most com- petitive bids refer to one of the first four lowest bids among the N potential competitors. In other words, there exists an ‘optimum’ value of k for each N such that a 95% confidence level of including one of the first four lowest bids in competition for this project can be obtained. Based on this criterion, the minimum number of contractors to submit tders for projects will depend on the potential number of bidders N in the market that in turn will depend on the market conditions. Suppose it is estimated that the average number of competitors N in the market for a particular project is 20, based on market conditions fi'om the set of equa- tions 1—3. A probability density function for randomly selecting the 1: bidders per project to submit bids can be established. The probability and cumulative prob- ability distribution values of winning tenders for select— ing k contractors fi'om N = 20 potential competitors in the market is shown in Table l. The cumulative probability distributions as shown in Figure 1 indicate that the k values afi'ect the range of lowest bids received. As It increases from 3 to 10, the range of potential lowest bids in competitions reduces from the lowest possible eighteenth bid in N bids received to the lowest possible tenth bid in N bids received. Therefore, it is desirable, at least from the client’s view- point, that those lowest potential bids in N bids will have higher chances of being included in tendering competitions, whereas those higher potential bids in N bids will be excluded from the tendering process. The winningtenderwillfallwithinarangeofvalues depending on the choice of k. However, in order to include one of the first four lowest bidders in compe- tition for projects at the 95% confidence level, the minimum number of contractors to submit tenders is when Ie = 10, giving the cumulative probability of 0.9567. The foregoing empirical analysis led to, the proposed theoretical framework for determining the minimum number of competitors to be included in construction bidding competitions for projects. The following empirical analysis on a HKSAR Government data set sets out to test the applicability of the fi'amework. 478 Ngar' et at. Table 1 Probability and cumulative probability distribution values of tenders for N = 20 X fan, 3! (3‘) Va 3! (x) fao, 5) (x) 21129, 5) (1‘) fan, ma) Ef .20. m; (x) 1 0.1500 0.1500 0.2500 0.2500 0.5000 0.5000 2 0.1342 0.2842 0.1974 0.4474 0.2632 0.76.32 3 0.1193 0.4035 0.1535 0.6009 0.1316 0.8947 4 0.1053 0.5088 0.1174 0.7183 0.0619 0.9567 5 0.0921 0.6009 0.0880 0.8063 0.0271 0.9837 6 0.0798 0.6807 0.0646 0.8709 0.0108 0.9946 7 0.0684 0.7491 0.0461 0.9170 0.0039 0.9985 8 0.0579 0.8070 0.0319 0.9489 0.0012 0.9996 9 0.0482 0.8553 0.0213 0.9702 0.0003 0.9999 10 0.0395 0.8947 0.0135 0.9837 0.0001 1.0000 11 0.0316 0.9263 0.0081 0.9919 0.0000 1.0000 12 0.0246 0.9509 0.0045 0.9964 0.0000 1 .0000 13 0.0184 0.9693 0.0023 0.9986 0.0000 1.0000 14 0.0132 0.9825 0.0010 0.9996 0.0000 1.0000 15 0.0088 0.9912 0.0003 0.9999 0.0000 1.0000 16 0.0053 0.9965 0.0001 1.0000 0.0000 1 .0000 17 0.0026 0.9991 0.0000 1.0000 0.0000 1.0000 18 0.0009 1.0000 0.0000 1.0000 0.0000 1 .0000 19 0.0000 1 .0000 0.0000 1 .0000 0.0000 1 .0000 20 0.0000 1 .0000 0.0000 1 .0000 0.0000 1 .0000 12 3 4 5 G 7 I 91011121314151811181020 XMNI.) Figure 1 Cumulative probability distribution values of winning tenders for N = 20 Enpiricalanalysisfl):fiongKongdntaset The following pirical analysis is based on a sample of 229 projects with 3285 bids received over the period from the fourth quarter of 1990 to the third quarter of 1996. The sample was derived fi'om HKSAR Governmt Architectural Services Departmt (ASD) data. Projects awarded through selective tendering (where the number of competitors is an administrative decision rather than a consequence of market condi- tions) have been excluded for homogeneity purposes. Figure 2 shows the positively skewed frequency distri- bution of number of bidders per project for the data set. On average, there are 14 contractors (betwe 3 and 33, with standard deviation about 7), competing for each contract. Table 2 shows the variations in the TF1 level and the average number N of contractors per project for the data set. The TPI used is a quarterly index com- piled by ASD primarily as an aid to adjust building cost data for estimating purposes. It is prepared also to provide an indication of the price level of tender prices for new building works undertaken by ASD. The best model (i.e. using time t as a predictor in a polynomial regression analysis of the TPI) is found to be a polynomial of degree 3, as shown below. This polynomial, as shown in Figure 3 (time series of the TPI is shown as a solid line and predicted TPI as a dotted line), provides a very good fit to the TPI since the corresponding R2 is 0.9773 and the residual plot exhibits no special pattern for the violation of regres- sion assumptions. Manama-rm Figure 2 Distribution of number of bidders per project for ASD projects from 4th quarter of 1990 to the 3rd quarter of 1996: (Std. Dev. = 7.14; Mean = 14 and number of pro- jects in sample = 229) Minimum number of bidders for construction projects 479 Table 2 Variations in the TPI and average number of bidders N (1990-1996) Year (muanur 'Tunet 111 1990 4 1 596 1991 l 2 608 2 3 592 3 4 573 4 5 515 1992 1 6 531 2 7 548 3 8 519 4 9 518 1993 1 10 527 2 11 527 3 12 541 4 13 563 1994 1 14 586 2 15 594 3 16 615 4 17 666 1995 1 18 708 2 19 712 3 20 733 4 21 747 1996 1 22 772 2 23 813 3 24 848 Ibud No. of Total number Av. no. of projects of bidders bidders/project (N) 8 112 14 6 116 19 5 119 24 9 204 23 8 189 24 10 189 19 6 129 22 6 99 17 8 148 19 10 158 16 4 61 15 7 98 14 5 100 20 14 239 17 7 81 12 14 210 15 9 98 11 14 171 12 11 110 10 17 142 8 13 123 9 14 157 11 10 121 12 14 111 8 229 3285 Tmmlm §§§§§§§§§§§ 412341234123412341234123 1H1 1 ms 1" 1“ 190s “II-(mlflllll’lhm1m Figure 3 Time series ofthe TPI and polynomial regres- sion analysis of the TPI using time t as a predictor TPI = 695.6” — 37.62: + 2.893:2 — 0.04l9t3 (R2 = 0.9773) Hence, the rate of change TPIr at time t is given by TPIT = —37.624 + 5.7862 — 0.1257:2 By substituting difl'erent values of t into the above equation, 24 ordered pairs of (UN, TPI.) can be found as shown in Table 3, and the scatter plot of these 24 ordered pairs is produced as shown in Figure 4. The plot shows a non-linear relationship between UN and TPI,. A regression model can be esmblished to best fit the set of data with the following result (R2 = 0.7550; F = 32.36; p < 0.0001): 1/N = 0.04843 + 0.0007134 x TPI, + 0.00003809 x TPII.2 Suppose the forecast of TPIr (i.e. the rate of change of TPI) is 23, then from the above regression model, the estimated potential number of competitors for a project is N = 12. The probability density fimction values for randomly selecting the I: bidders per project to submit bids are as shown in Table 4. At the 95% confidoe level, to include at least one of the first four lowest bid- ders among 12 potential competitors in competition, the minimum number of contractors to submit tenders is when k = 6, giving the cumulative probability 0.9697. Therefore, by randomly selecting six contractors from the approved list of qualified contractors to sub- mit tenders to compete for a project in this period, the HKSAR Government can have a 95% confidence that at least one of the first four lowest bids in the market will be included in competition for projects. In this way, not only will this approach be more cost efi'ective in terms of procurement costs, but also the Government can still maintain its public accountability in the ten- dering competitions. 480 Ngat' at al. Table 3 Variation of TPI, and UN (1990-1996) Year Quarter Time I TPI TPIr Av. No. of bidders! LIN Project (N) __ 1990 4 1 596 —3l.9637 14 0.0714 1991 1 2 608 —26.5548 19 0.0517 2 3 592 —21.3973 24 0.0420 3 4 573 —l6.4912 23 0.0441 4 5 515 —11.8365 24 0.0423 1992 I 6 531 -- 7.4332 19 0.0529 2 7 548 --3.2813 22 0.0465 3 8 519 0.6192 17 0.0606 4 9 518 4.2683 19 0.0541 1993 1 10 527 7.6660 16 0.0633 2 11 527 10.8123 15 0.0656 3 12 541 13.7072 14 0.0714 4 13 563 16.3507 20 0.0500 1994 1 14 586 18.7428 17 0.0586 2 15 594 20.8835 12 0.0864 3 16 615 22.7728 15 0.0664 4 17 666 24.4107 11 0.0918 1995 1 18 708 25.7972 12 0.0819 2 19 712 26.9323 10 0.1000 3 20 733 27.8160 8 0.1197 4 21 747 28.4483 9 0.1057 1996 1 22 772 28.8292 1 1 0.0892 2 23 813 28.9587 12 0.0826 3 24 848 28.8368 8 0.1261 0.14 9 .a 1m .0 .o .o 8 8 8 an -10 o 10 mundane-urn) M4 Scatterplotoft:hangeofmarketconditionTPIr with degree of competition llN b 8 Conclusions 'I'hispapersetsouttoexploreanddemomrrateame- oretical linhge between market conditions and the number of potenn'al contractors in competition. Based on neo-classical micro-economic theory for construc- tion price determination and the assumption of random contractor-selection in the bidding competitions, a the- oretical framework for determining the minimum number of competitors in the tendering process has been proposed. The framework comprises two basic parts. The first part applies micro-economic theory in linkingchangesindemandtochangesinpricesand subseth changes in supply capacity to explain con- struction price determination and tender variations. The rate of change of the TPI is used to measure market conditions in the building industry, and the degree of competition can be measured in terms of number of potential competitors in the market. From these, a set of regression models is formulated to esti- mate the number of potential contractors competing inthemarketbytheforecastTTIlevel.1hesecond part determines the minimum number of contractors to submit tenders for the particular projects concerned such that a 95% confidence can be achieved that one ofthefirstfourlowestbidsinfltemarketwillbe included in the bidding The implication is that the HKSAR Governmt can deriveamore costefi'ectiveapproachinitsopentmder— ingsystembyselectingtheminimumnumberkofcon— tractors in bidding competitions based on the market conditions (or the TPI, value) while its public accountability for contractor-selection in tender- ing. The limitations for this framework are: (l) gener- allythepredictionoftheTPIisconfinedtotheshort termbecause ofreducedaccuracyoffmecastsfxther intothefiiture,andhencemaymaketheTPIforecast- ing model inappropriate; and (2) the framework is Minimum number of bidders for construction projects 481 Table 4 Probability and cumulative probability distribution values of winning tenders for N = 12 __—____——_______———————— X faz, (3‘) Elm, (I) f 12, 5) (x) 1 0.3333 0.3333 0.4167 2 0.2424 0.5758 0.2652 3 0.1697 0.7455 0.1591 4 0.1 131 0.8586 0.0884 5 0.0707 0.9293 0.0442 6 0.0404 0.9697 0.0189 7 0.0202 0.9899 0.0063 8 0.0081 0.9980 0.0013 9 0.0020 1.0000 0.0000 10 0.0000 1.0000 0.0000 1 1 0.0000 1.0000 0.0000 12 0.0000 1.0000 0.0000 Zfaz, 5) (x) f 12, 9(3) 2’ (12, (x) 0.4167 0.5000 0.5000 0.6818 0.2727 0.7727 0.8409 0.1364 0.9091 0.9293 0.0606 0.9697 0.9735 0.0227 0.9924 0.9924 0.0065 0.9989 0.9987 0.001 1 1.0000 1.0000 0.0000 1.0000 1 .0000 0.0000 1 .0000 1 .0000 0.0000 1 .0000 1 .0000 0.0000 1.0000 1 .0000 0.0000 1 .0000 _____—__—_—_—————— based on the assumption that the contractor-selection process is random. 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A theoretical framework for determining the minimum number of bidders in construction bidding compet

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