DETERMINING THE OPTIMAL FEE-TECHNICAL PROPOSAL COMBINATION IN TWO ENVELOPE FEE BIDDING THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 1 DETERMINING THE OPTIMAL FEE-TECHNICAL PROPOSAL COMBINATION IN TWO ENVELOPE FEE BIDDING Professor Derek S. Drew, Connie W.K. Kwong and Patrick X.W. Zou University of New South Wales L.Y. Shen, The Hong Kong Polytechnic University INTRODUCTION Bid strategy modelling has traditionally been concerned with setting the mark up level to a value that is likely to provide the best pay off. Famous construction bid strat- egy models include those proposed by Friedman (1956), Gates (1961) and Carr (1982). More recently bid strategy modelling has expanded to encompass contracts awarded on a multi-criteria basis. For ex- ample, construction clients are increasingly calling for bids that require competing con- tractors to submit both bid price and con- tract time (Shen et al., 1999). In such cases contractors’ bid prices and proposed con- tract times are commonly assessed in ac- cordance with the following equation (Herbsman et al., 1995): TCB = p + (UTV x t) (1) where TCB = Total combined bid p = price UTV = unit time value specified by the client (such as liquidated damages rate) t = time The contractor with the lowest TCB is awarded the contract. Shen et al. (1999) have considered this from a contractor’s bid strategy viewpoint by relating the contrac- tor’s price-time curve to the client’s price- time curve and from this they have devel- oped a mathematical bid optimisation model. The rationale behind the model is illustrated in Figure 1. It is widely accepted (e.g. Callahan et al., 1991) that every com- peting contractor has an optimum price- time point for each construction contract. The price-time curve of a contractor is shown in Figure 1 as being S1 with the opti- mum point as B1 and the corresponding bid price-time combination as p1, t1. The liqui- dated damages rate, commonly used to represent UTV, is shown as a straight line (S2) since it is a constant rate. The total combined bid curve S (i.e. assessed cost to the client) becomes S1 + S2. The optimum point at which the contractor is most com- petitive from the client’s viewpoint is B0. The contractor should, therefore, submit the bid price-time combination p0, t0 to the client. Consultants are faced with a similar prob- lem in two envelope fee bidding given that the commission is awarded on the combined basis of price (i.e. fee) and quality (i.e. tech- nical proposal). Consultants are required to submit to the client one envelope containing the technical proposal and a second enve- lope containing the fee. Each competing consultant’s technical proposal and fee is then converted by the client to a score and aggregated. The consultant with the highest overall score is then awarded the commis- sion (see, for example, Construction Indus- try Board (1996) for a detailed explanation of two envelope fee bidding procedures). Bid strategy decision making is more com- plicated in price-time contracts and two en- velope fee bidding. In addition to setting the mark up level to provide the best pay off, bidders need to make an additional decision with regard to the second criterion. For ex- ample, they must decide whether to submit a higher (or lower) tender price with a shorter (or longer) contract period, or in the case of two envelope fee bidding, on whether to aim for a higher technical score (which is likely to require a higher fee) or submit a lower fee (which is likely to result in a lower technical score). The objective of an optimum bid strategy model is to provide the bidder with an optimal solution, whether it be optimum mark-up (as with traditional price only models) or optimum price-time or fee-technical score combination (with bi- parameter models). DEREK S. DREW, CONNIE W.K. KWONG, PATRICK X.W. ZOU AND L.Y. SHEN 2 THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 Figure 1: The price-time relationship between the contractor’s price-time curve (S1) and the client’s price-time curve (S) (Source: Shen et al. 1999) Based on the same logic proposed by Shen et al. (1999), Drew et al. (2002b) offered con- sultants an optimum bid strategy model for two envelope fee bidding. They show that consultants have a choice of aiming for a low scored technical proposal-low fee com- bination or a high scored technical pro- posal-high fee combination or a combination in between, and that only one of these combinations will result in the highest possible aggregated score. They claim that if consultants follow the modelling approach set out in their paper, they should be in a position to better identify their optimum fee- technical score combination, thereby in- creasing their chances of winning the com- mission. Drew et al. (2002b) introduced the modelling approach using hypothetical ex- amples. This paper sets out to test the mod- elling approach using data supplied by a Hong Kong quantity surveying consultant. Aggregating fees and technical score Construction clients set out the two enve- lope bidding procedures that consultants are required to follow. This includes using a particular formulation with which to aggre- gate the fees and technical scores. Drew et al. (2001) identified seven different fee- technical score formulations from the lit- erature and also suggested two more new formulations. A commonly used formulation (Connaughton, 1994), also used by the Hong Kong Housing Authority (one of Hong Kong’s largest public sector clients), is: CA = Wqq/qmax + Wf fmin/f (2) where qmax = highest technical score q = consultant’s technical score f = consultant’s fee fmin = lowest fee Wq = predetermined weighting for technical score Wf = predetermined weighting for fees CA = total score The consultant with the highest CA value wins the contract. For example, suppose there were four competing consultants la- belled A, B, C and D who submitted respec- tive fees of $5.43, $5.14, $4.42 and $4.62 million and whose technical proposals were given scores of 82, 76, 69 and 73. Suppose also that the technical score/fee predeter- mined weightings were 70/30 respectively. Table 1 shows Consultant A winning the competition. Construction time t T e n d e r p ri c e P Time value curve (LDR x t) Price-time curve Total combined bid curve (S1 + S2) S2 S1 S b0 B0 b1 B1 TCB1 TCB0 P0 P1 t0 t1 DETERMINING THE OPTIMAL FEE-TECHNICAL PROPOSAL COMBINATION IN TWO ENVELOPE FEE BIDDING THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 3 Table 1: Aggregating fee and technical score using Equation 2 Consultant Identities TM F$M TSc FSc TotSc Rank A 82 5.43 70.0 24.3 94.30 1 B 76 5.14 65.1 25.8 90.90 3 C 69 4.42 58.8 30.0 88.80 4 D 73 4.62 62.3 28.7 91.00 2 The example also shows that fees and tech- nical scores are, to some extent, positively correlated (i.e. Consultant A submitted the highest fee and obtained the highest techni- cal score, Consultant C submitted the low- est fee and obtained the lowest technical score and Consultants B and D somewhere in between). It can be seen that this be- comes a negative correlation when con- verted to a ratio since the fee ratio is an inverse ratio. An important reason for such a correlation is that architectural, engineer- ing and surveying commissions are re- garded as a ‘complex intellectual process’ (Construction Industry Board, 1996) and as such, in order to deliver a good quality ser- vice, two important variables are total time spent on the commission, and experience of the consultant. With a lower fee the consult- ant will not be able to spend so much time on the commission and/or use less experi- enced staff. Spending less time and/or using less experienced staff should result in the consultant receiving a lower raw technical score. On the other hand, greater experi- ence and more involvement are likely to re- sult in a consultant receiving a higher technical score. Since experienced staff are normally paid higher salaries this is likely to require a larger fee. A higher technical score therefore requires a larger fee, and fees are likely to go up at an increasing rate according to the technical score (because of the increased rate of salary differences be- tween lower and higher paid staff). This suggests that there is a positive convex cor- relation between fee and raw technical score. The fee-raw technical score correlation that is often produced when consultants are in competition with one another will also occur with a particular consultant deciding on whether to aim for a low scored technical proposal-low fee combination or a high scored technical proposal-high fee combination or something in between. For example, suppose Consultant A had devel- oped three technical proposals for the commission just described. The three tech- nical proposals may attract full fees of say $4.43, $5.43 and $6.43 million respectively. If all three technical proposals were scored it is quite likely that the raw technical scores and corresponding fees would, to some ex- tent, be positively correlated. Determining the optimum fee and technical score The consultant’s objective in two envelope fee bidding is to get the highest possible total score since this maximizes the chance of winning the commission. In the previous example the consultant would submit the fee-technical proposal combination that it thought would result in the highest score. Drew et al. (2002b) claim that consultants can actually determine the highest scoring fee-technical proposal combination for a particular commission by following the fol- lowing seven steps: 1. Assemble the technical proposal and calculate the corresponding fee in the nor- mal way, then estimate the corresponding technical score. 2. Determine the absolute lowest full fee for the commission and estimate the corre- sponding technical score 3. Estimate the absolute highest technical score for the commission and determine the corresponding full fee. 4. Use the client’s formulation (e.g. Equa- tion 2) and calculate the three respective total scores using (1) the original fee and corresponding technical score, (2) absolute lowest fee and corresponding technical score and (3) absolute highest technical score and corresponding fee. DEREK S. DREW, CONNIE W.K. KWONG, PATRICK X.W. ZOU AND L.Y. SHEN 4 THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 Figure 2: Possible optimum fee outcomes (Source: Drew et al. 2002b) 5. Regress the three total scores against the fee to produce a total score con- tinuum. Since the continuum, represented by a line, is regressed on three points it will almost certainly be curvilinear in shape, being either concave or convex. Figure 2 shows that there are three possible out- comes. If concave, the optimum fee will fall at the highest point along the continuum (i.e. Outcome 1). If, however, the continuum is convex, the optimum fee will fall at either the low end (i.e. Outcome 2) or high end (i.e. Outcome 3) of the continuum. 6. Determine the optimum fee for Outcome 1 using differentiation since the total score continuum, represented by a curvilinear re- gression line, is based on the equation: Y = a + bx +cx2 (3) where Y = total score x = fee For Outcome 2 and 3 the optimum fee is simply that shown at either the low end (i.e. Outcome 2) or high end (i.e. Outcome 3) of the continuum. 7. Determine the optimum technical score for Outcome 1 by inserting the optimum fee and total score into the client’s formulation to find the corresponding technical score. For Outcome 2 and 3 the optimum technical score is the one already estimated. The original technical proposal should then be adjusted to reflect the optimum technical score. This may involve including more/less staff with greater/less experience and/or spending more or less time on the commis- sion. The optimum fee and the adjusted technical proposal should then be submitted to the procurer. In addition to illustrating the foregoing ap- proach using hypothetical examples, Drew et al. (2002b) were able to show the effect of using the optimum bid strategy on bidding performance. They identified that this could be done by measuring the optimum total score percentage increase on the original total score. This seven step approach will be replicated and developed in this paper using data collected from a leading Hong Kong quantity surveying consultant. DATA COLLECTION The consultant, who regularly tenders for Hong Kong Housing Authority commissions, provided the following data for 51 bidding attempts: 1. Original fee 2. Estimated raw score 3. Absolute low fee 4. Corresponding estimated technical score 5. Absolute high estimated technical score 6. Corresponding fee Case 36 Case 37 Fee ($) T o ta l s c o re Optimum Fee Outcome 2 Optimum Fee Outcome 1 Optimum Fee Outcome 3 DETERMINING THE OPTIMAL FEE-TECHNICAL PROPOSAL COMBINATION IN TWO ENVELOPE FEE BIDDING THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 5 7. Fee/technical score predetermined weighting 8. Tender date The commissions were tendered for be- tween September 1997 and April 2001. The Hong Kong Housing Authority used fee- technical score predetermined weightings of 30/70 for 14 cases and 50/50 for the remain- ing 37 cases. The fees submitted ranged from just under HK$1 million to just under HK$17 million. The Hong Kong Housing Au- thority uses Equation 2 to aggregate fees and technical scores. ANALYSIS The analysis is in three parts. Three repre- sentative cases are used in the first part of the analysis to illustrate each of the three possible outcomes (i.e. Outcome 1 = in be- tween absolute low fee/absolute high tech- nical score, Outcome 2 = absolute low fee/low technical score, Outcome 3 = abso- lute high technical score/high fee). The fre- quency of the three possible outcomes and the effect of the predetermined weightings are considered in the second part of the analysis. The last part considers the effect that the optimum bidding strategy has on the consultant’s original bidding performance. REPRESENTATIVE CASES ILLUSTRATING THE THREE DIFFERENT OUTCOMES The three possible outcomes are illustrated with cases 36, 37 and 38. Table 2 shows the (1) original fee/estimated raw score, (2) ab- solute low fee/corresponding estimated technical score and (3) absolute high esti- mated technical score/corresponding fee combinations for these three representative cases. The fees and technical marks are converted into fee, technical and total scores using Equation 2. For Case 36 it can be seen the consultant’s original fee and estimated raw score produced the highest score, while for Case 37 the absolute high estimated technical score and correspond- ing fee resulted in the highest total score and for Case 38 the absolute lowest fee/corresponding technical score combina- tion yielded the highest total score. Regression analysis is used to produce the total score continuums. Figure 3 shows a concave curve for Case 36 (i.e. Outcome 1), a positive convex curve for Case 37 (i.e. Out- come 3) and a negative convex curve for Case 38 (i.e. Outcome 2). For Case 36 the regression equation coefficients generated by the Excel software package are: Y = -1397.81 + 890.84x – 132.60x2 (4) Table 2: Technical Scores, Fee Scores and Total Scores for Competition Nos. 36, 37 and 38 using Equation 2 with a 50/50 predetermined weighting Case No. TM F$M TSc FSc TotSc Rank 45.00 3.20 45.00 50.00 95.00 3 46.95 3.24 46.95 49.43 96.38 1 36 50.00 3.50 50.00 45.71 95.71 2 Mean 47.32 48.38 SD 2.52 2.33 SD Ratio 1.08 40.00 5.40 40.00 50.00 90.00 2 42.53 6.06 42.53 44.59 87.12 3 37 50.00 6.50 50.00 41.54 91.54 1 Mean 44.18 45.38 SD 5.20 4.29 SD Ratio 1.21 35.00 4.00 38.89 50.00 88.89 1 38.86 6.23 43.18 32.09 75.27 3 38 45.00 7.00 50.00 28.57 78.57 2 Mean 44.02 36.89 SD 5.60 11.49 SD Ratio 0.49 DEREK S. DREW, CONNIE W.K. KWONG, PATRICK X.W. ZOU AND L.Y. SHEN 6 THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 70.00 75.00 80.00 85.00 90.00 95.00 100.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 Fee $ M T o ta l S c o re Figure 3: Total score continuums for Cases 36, 37 and 38 Using differentiation the optimum fee be- comes: Y1 = 890.84 – 265.20x (5) x = 890.84/265.20 (6) x = 3.359 (7) With an optimum fee of $3.359 million, the optimum total score becomes: Y = -1397.81 + (890.84 x 3.359) – (132.60 x 3.3592) (8) Y = -1397.81 + 2992.33 – 1496.11 (9) Y = 98.41 (10) Given an optimum fee of $3.359 million and an optimum total score of 98.41, the corre- sponding technical score can be found by using Equation 2 i.e. 98.41 = 50 (q / 50) + 50 (3.00 / 3.359) (11) 98.41 = q + 44.66 (12) q = 98.41 – 44.66 (13) q = 53.75 (14) The original technical proposal should be amended to achieve a raw score of 53.75. The amended technical proposal and a fee of $3.359 million should be submitted to the client. For Cases 37 and 38 the solution is much simpler since the highest score occurs at the either end of the continuum. For Case 37 the consultant should submit a fee of $6.5 million and adjust the technical proposal to obtain a raw score of 50.00. For Case 38 the consultant should put in a fee of $4.00 mil- lion and adjust the technical proposal to obtain a raw score of 35.00. FREQUENCY OF THE THREE DIFFERENT OUTCOMES AND EFFECT OF THE PREDETERMINED WEIGHTINGS The three cases illustrate each of the possi- ble outcomes. The same approach was used to analyse all 51 cases. Interestingly Table 3 shows that in only 10 cases did the optimum total score fall in between absolute low fee and absolute high technical score (i.e. Outcome 1), while in 20 cases it aligned with absolute low fee (i.e. Outcome 2) and in 21 cases with absolute high technical score (i.e. Outcome 3). The results show that the optimum fee – technical proposal combina- tion will most likely occur at one end of the consultant’s continuum and there is an al- most even chance of it occurring either at the low fee or high technical score end of the continuum. DETERMINING THE OPTIMAL FEE-TECHNICAL PROPOSAL COMBINATION IN TWO ENVELOPE FEE BIDDING THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 7 The reason why there are only 10 cases that produce a result in between absolute low fee and absolute high technical score (i.e. Outcome 1) is because of the variability dif- ferences between fees and technical score. This can be explained by referring back to the three representative cases. Table 2 shows the respective fee and technical score standard deviations of 2.52 and 2.33 for Case 36. This produces a standard devia- tion ratio of 1.08 meaning that fee and tech- nical scores are almost equal in terms of variability (see Drew et al. 2002a for ade- tailed treatment of this aspect). For Case 37 it can be seen that technical scores vary more than fee score meaning that technical score is more dominant in the aggregation and for Case 38 fee score varies more than technical score meaning that fees are more dominant in the aggregation. In other words, Outcome 1 (i.e. in between) will be most likely to occur where the fee/technical score variability is more or less equal. However, where fee score varies more than technical score, Outcome 2 (i.e. absolute low fee) is likely to occur and where technical score varies more than fee score, Outcome 3 (i.e. absolute high technical score) is likely to occur. The even split of 15 low fee competitions to 15 high technical score competitions for 50/50 and corresponding 5 to 6 for 70/30 indicates that the change in weightings from 70/30 to 50/50 has very little effect on the proportion of competitions that require a low fee or high technical score. The effect of optimum bidding strategy on original bidding performance Tables 4 and 5 show the actual and percent- age differences between optimal total scores and original total scores obtained by the consultant for the 70/30 and 50/50 pre- determined weightings. For 70/30 prede- termined weightings Table 5 shows that the consultant’s overall total score increased from 88.08 to 92.19 giving an average im- provement of 4.84%. For 50/50 Table 6 shows that the consultant’s overall score increased from 82.61 to 88.74 making an average improvement of 7.90%. Tables 5 and 6 also show that the overall improve- ment range is from 30.80% to just 0.41%. Interestingly there were eleven competitions whereby the original total score could be improved on by more than 10%. The average improvement of optimal total score on origi- nal total score over the 51 cases was 7.07%. Table 3: Effect of predetermined weightings on optimum bid strategy outcome Weightings Absolute Low Fee Absolute High Technical Score In-between Total 50 / 50 15 15 7 37 70 / 30 5 6 3 14 Total 20 21 10 51 Table 4: Original total score/ optimum total score comparisons using 70/30 predetermined weightings Competition No Optimal Score Original Score Actual Difference Percentage change 1 88.00 86.77 1.23 1.41 2 88.20 80.27 7.93 9.88 3 88.36 87.09 1.27 1.46 4 85.83 78.56 7.27 9.25 5 88.24 81.92 6.32 7.71 43 95.00 85.07 9.93 11.67 44 94.00 87.33 6.67 7.64 45 95.00 93.65 1.35 1.45 46 93.64 88.67 4.96 5.60 47 95.45 94.47 0.98 1.04 48 95.92 95.53 0.39 0.41 49 95.00 92.01 2.99 3.25 50 93.99 92.75 1.24 1.34 51 94.00 88.98 5.03 5.65 Average 92.19 88.08 4.11 4.84 DEREK S. DREW, CONNIE W.K. KWONG, PATRICK X.W. ZOU AND L.Y. SHEN 8 THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 Table 5: Original total score/ optimum total score comparisons using 50/50 predetermined weightings Competition No Optimal Score Original Score Actual Difference Percentage change 6 85.63 80.03 5.60 7.00 7 78.69 73.39 5.30 7.22 8 80.25 71.49 8.76 12.26 9 80.00 68.54 11.46 16.72 10 80.19 76.44 3.75 4.90 11 84.68 77.56 7.11 9.17 12 84.87 81.63 3.24 3.97 13 90.83 86.76 4.07 4.70 14 91.55 84.74 6.81 8.04 15 86.84 66.39 20.45 30.80 16 99.74 90.58 9.16 10.12 17 87.50 83.50 4.00 4.80 18 95.65 92.14 3.51 3.81 19 86.96 83.50 3.46 4.15 20 86.96 85.26 1.70 1.99 21 88.64 87.82 0.82 0.94 22 87.56 86.30 1.27 1.47 23 86.96 81.66 5.29 6.48 24 86.96 83.51 3.44 4.12 25 86.96 85.11 1.85 2.17 26 89.47 86.04 3.43 3.99 27 86.96 81.87 5.09 6.21 28 90.80 89.28 1.52 1.71 29 86.96 67.30 19.66 29.21 30 88.46 86.66 1.81 2.08 31 88.89 82.23 6.66 8.10 32 92.94 81.97 10.97 13.38 33 86.96 73.24 13.71 18.72 34 87.50 85.57 1.93 2.25 35 91.82 88.92 2.89 3.25 36 98.41 96.44 1.97 2.05 37 91.54 87.12 4.42 5.07 38 88.89 75.27 13.62 18.09 39 88.89 78.18 10.71 13.70 40 96.43 94.98 1.45 1.53 41 96.43 85.97 10.46 12.17 42 95.00 89.20 5.80 6.50 Average 88.74 82.61 6.13 7.90 CONCLUSIONS Drew et al. (2002b) proposed an optimal two envelope fee bid strategy model using hypo- thetical examples. 51 bidding attempts, supplied by a Hong Kong quantity surveying consultant, were used in this paper to test the model. It was found that consultants could improve there total score by an aver- age of 7.07%. The difference in total score improvement varies from just 0.41% to 30.80%. There are eleven competitions where the consultant’s original total score could be improved by more than 10%. It was found that when fee scores vary more than technical scores, fees become the dominant variable. In such cases the opti- mum strategy is to aim for an absolute low fee—low scored technical proposal combi- nation. Where technical scores vary more than fees, the optimum strategy is to aim for an absolute high technical score—high fee combination. Where the variability of fee DETERMINING THE OPTIMAL FEE-TECHNICAL PROPOSAL COMBINATION IN TWO ENVELOPE FEE BIDDING THE AUSTRALIAN JOURNAL OF CONSTRUCTION ECONOMICS AND BUILDING VOL.2 NO.2 9 scores and technical scores are more or less equal, the optimum strategy is to aim somewhere in between these two extremes. The optimum strategy was to aim for an ab- solute low fee—low scored technical pro- posal on 21 occasions, absolute high scored technical proposal—high fee on 20 occa- sions and somewhere between these two extremes on the remaining ten occasions. A key reason for the optimum bidding strategy being at the end of the consultant’s total score continuum for the vast majority of competitions is the differences in fee and technical score variability. A limitation of this model is that the con- sultant’s total score continuum is repre- sented by three points, the minimum number required to produce a quadratic equation. In addition this model is based on the consultant’s best estimates of the cli- ent’s technical score. Suggestions for fur- ther research are to improve the model’s reliability by (1) including additional combi- nations of fees and technical scores and measure the effect on the optimum total score and (2) measure the consultant’s ac- curacy of the consultant’s estimate of the client’s technical score, determine the rea- sons for the inaccuracy and then attempt to improve the accuracy. The analysis could also be extended by comparing the compet- ing consultant’s optimal fee/technical score with those of the successful consultants. REFERENCES Callahan, M.T., Quackenbush, D.G. and Rowings, J.E. (1992) Construction Project Scheduling. McGraw-Hill, New York. Carr, R. I. (1982) General bidding model, Journal of the Construction Division. Ameri- can Society of Civil Engineers, 108, 639–650. Connaughton, J. (1994) Value by Competi- tion. Construction Industry Research and Information Association, London. Construction Industry Board (1996) Select- ing Consultants for the Team: Balancing Quality and Price. Construction Industry Board, Thomas Telford Publishing, London. Drew, D.S., Li, H. and Shen, L.Y. (2000) Feedback in competitive fee tendering. Journal of Construction Procurement, 6 (2), 220–230. Drew, D.S., Ho, L.C.Y. and Skitmore, R.M. (2001) Analysing a consultant’s competitive- ness in two envelope fee tendering. Con- struction Management and Economics, 19, 503–510. Drew, D.S., Tang, S.L.Y. and Lo, H.P. (2002a) Developing a tendering strategy in two enve- lope fee tendering based on technical score fee variability. Construction Management and Economics, 20, 67–81. Drew, D.S., Shen L.Y. and Zou, P.X.W. (2002b) Developing an optimal bidding strategy in two envelope fee bidding. Construction Management and Economics (accepted for publication). Friedman, L. (1956) A competitive bidding strategy. Operations Research, 1 (4), 104– 112. Gates, M. (1967) Bidding strategies and probabilities. Journal of the Construction Division, American Society of Civil Engi- neers, 93, 75–107. Herbsman, Z.J., Chen, W.T. and Epstien, W.C. (1995) Time is money: innovative contracting methods in highway construction. ASCE Journal of Construction Engineering and Management, 121 (3), pp.273–281. Hong Kong Government (1993) Handbook on Selection, Appointment and Administration of Architectural and Associated Consultants. Architectural Services Department, Hong Kong Government. Hoxley, M. (1998) Value for Money? The Impact of Competitive Fee Tendering on Construction Professional Service Quality. The Royal Institution of Chartered Survey- ors, London. Shen, L.Y., Drew D.S. and Zhang Z.H. (1999) An optimal bid model for price-time bi- parameter construction contracts. ASCE Journal of Construction Engineering and Management, 125 (3), pp.204–209. AJCEB_Vol2_No2_28-11-02_Part7 AJCEB_Vol2_No2_28-11-02_Part8 AJCEB_Vol2_No2_28-11-02_Part9 AJCEB_Vol2_No2_28-11-02_Part10 AJCEB_Vol2_No2_28-11-02_Part11 AJCEB_Vol2_No2_28-11-02_Part12 AJCEB_Vol2_No2_28-11-02_Part13 AJCEB_Vol2_No2_28-11-02_Part14 AJCEB_Vol2_No2_28-11-02_Part15