Statistical analysis on the cost and duration of public building projects

A probabilistic model is proposed to predict the risk effects on time and cost of public building projects. The research goal is to utilize a real history data in estimating project cost and duration. The model results can be used to adjust floats and budgets of the planning schedule before project commencement. Statistical regression models and sample tests are developed using real data of 113 public projects. The model outputs can be used by... Đề tài Hoàn thiện công tác quản trị nhân sự tại Công ty TNHH Mộc Khải Tuyên được nghiên cứu nhằm giúp công ty TNHH Mộc Khải Tuyên làm rõ được thực trạng công tác quản trị nhân sự trong công ty như thế nào từ đó đề ra các giải pháp giúp công ty hoàn thiện công tác quản trị nhân sự tốt hơn trong thời gian tới.

m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u Statistical Analysis on the Cost and Duration of Public Building Projects tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x Ayman A Abu Hammad1; Souma M Alhaj Ali2; Ghaleb J Sweis3; and Rateb J Sweis4 xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 Abstract: A probabilistic model is proposed to predict the risk effects on time and cost of public building projects The research goal is to utilize a real history data in estimating project cost and duration The model results can be used to adjust floats and budgets of the planning schedule before project commencement Statistical regression models and sample tests are developed using real data of 113 public projects The model outputs can be used by project managers in the planning phase to validate the schedule critical path time and project budget The comparison of means analysis for project cost and time performance indicated that the sample projects tend to finish over budget and almost on schedule Regression models were developed to model project cost and time The regression analysis showed that the project budgeted cost and planned project duration provide a good basis for estimating the cost and duration The regression model results were validated by estimating the prediction error in percent and through conducting out-of-sample tests In conclusion, the models were validated at a probability of 95%, at which the proposed models predict the project cost and duration at an error margin of ⫾0.035% of the actual cost and time 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 7s lk DOI: 10.1061/共ASCE兲0742-597X共2010兲26:2共105兲 g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ftx tcd ck x ng CE Database subject headings: Construction costs; Construction management; Project delivery; Regression analysis; Regression models; Statistics kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s vo sz Author keywords: Construction costs; Construction management; Project delivery; Regression analysis; Regression models 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx Introduction sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư Construction investments are sensitive to time and cost overrun Delay and cost escalation are considered two threats to project success Variation orders 共VOs兲 issued by the owner, consultant, or claimed by the contractor due to design mistakes are inevitable in all projects Yet, VOs, excluding value engineering related issues, pose a substantial risk that cannot be predicted in the contract for taking on preventive measures On the other hand, construction contracts give the owner the right to modify, add, and delete work items anytime via a VO Thus, the scalable effects of delay and cost overrun are rarely dealt with efficiently by project managers In many cases, change clause is used by contractors to offset their losses due to competitive underbidding practices Construction projects are hardly ever constructed as designed Consequently, as built plans and consistent updating of project schedules are the current procedures for modeling project change impacting both cost and time The overall project budget and duration of the CPM schedule should be verified against historic performance of projects taking into considerations risk effects A statistical model is developed in this research to predict with significant confidence the terminal project cost and duration Therefore, construction contracts and computerized project management tools can incorporate the statistical model results in predicting actual project time and cost by providing extra float to the duration of new projects, and deploying appropriate financial contingency Network schedules should be fine-tuned with the regression model results to accommodate uncertainty The research hypothesis is that the actual project cost 共APC兲 and time can be predicted with acceptable accuracy by using the data of the following independent variables: 共1兲 project type: residential, building construction 共nonresidential兲, nonbuilding or heavy construction, and industrial construction Project type implies specific scope, which defines specification and methods; thus, dictates specific time and cost requirements; 共2兲 project size or project area is found statistically to be directly proportional with the overall cost and duration; 共3兲 contract scope, i.e., civil, electrical, and mechanical works; 共4兲 selected sample projects should have been constructed within a short time interval to lessen the effect of inflation; and 共5兲 homogeneous region of study to assure constant conditions for labor attributes, methods, technologies, materials, and market prices; therefore, no projects from other countries were included in the sample due Other variables such as project location within the selected region, weather effects, and the architectural design 共project complexity兲 were not included in the model for simplicity reason 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f Assistant Professor, Dept of Civil Engineering, College of Engineering, Applied Science Univ., P.O Box 926296, Amman 11931, Jordan 共corresponding author兲 E-mail: dr-abuhammad@asu.edu.jo Assistant Professor, Dept of Industrial Engineering, Hashemite Univ., P.O Box 150459, Zarqa 13115, Jordan E-mail: souma@hu.edu.jo Associate Professor, Dept of Civil Engineering, College of Engineering, Univ of Jordan, Amman 11942, Jordan E-mail: gsweis@ ju.edu.jo Assistant Professor, College of Business Administration, Univ of Jordan, Amman 11942, Jordan E-mail: r.sweis@ju.edu.jo Note This manuscript was submitted on April 16, 2008; approved on August 11, 2009; published online on March 15, 2010 Discussion period open until September 1, 2010; separate discussions must be submitted for individual papers This paper is part of the Journal of Management in Engineering, Vol 26, No 2, April 1, 2010 ©ASCE, ISSN 0742-597X/ 2010/2-105–112/$25.00 ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 / 105 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc Literature Background 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh j jj8 q7 8m fln ob c bb fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd Data Collection p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao The research used the data of 113 public building projects The projects were selected via a systematic random sampling procedure to insure unbiased representation of the real setting, i.e., Jordan Construction Industry Sampled projects were constructed during 1994–2002 This period witnessed a stable inflation rate in the Jordan construction market ranging between 1.5 and 2.5% Data were collected from different entities, i.e., private owners, government agencies and ministries, and from contractors Data providers were not disclosed for confidentiality reason Sample projects were classified per project type and project scope Construction project types are sampled for the assumption that the project type impacts the cost and time variables The type breakdown followed the Engineering News Record bulletin of project breakdown into four major categories: residential, building construction, heavy, and industrial projects The public building construction projects, of the largest sample size 共113 projects兲 within the data, were only used for the purposes of this research However, data for public building construction projects were used in the regression analysis and the project type was not included as an independent variable for the models On the other hand, the project scope was also used as an important variable, which 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f Related literature can be organized into three main themes of research; the first theme investigates the causes of project delay and cost overrun The second theme discusses the use of artificial intelligence and automation in estimation and forecasting The last category is concerned with modeling project cost and duration by using heuristic methods and statistical regression analysis, in particular Leishman 共1991兲 presented the legal consequences of delays in construction Herbsman et al 共1995兲 investigated the effect of delays on cost and quality; while Assaf et al 共1995兲 surveyed the causes of delay for large building construction projects as seen by contractors, consultants, and owners Kaming et al 共1997兲 identified the main causes of cost overrun: material cost increase due to inflation, inaccurate material take-off, and project complexity Furthermore, Kaming et al 共1997兲 pointed out the causes of delay as design changes, poor labor productivity, and inadequate planning Al-Moumani 共2000兲 identified the causes of delay of 130 public building projects constructed during 1990–1997 in Jordan as follows: designers, owner changes, weather, differed site conditions, delays in material deliveries, economic conditions, and increase in quantities Another research by Odeh and Battayneh 共2002兲 surveyed contractors and consultants and identified the most important causes of delay Iyer and Jha 共2005兲 investigated factors adversely affecting the cost performance of projects in India, reported causes of cost overrun were: conflict among project participants, lack of knowledge, nonexistence of cooperation; hostile socioeconomic and climatic conditions, reluctance in timely decision, aggressive competition at tender stage, and short bid preparation time Causes of delay and cost overrun were also analyzed by Koushki et al 共2005兲 using 450 randomly selected projects Vandevoorde and Vanhoucke 共2006兲 used earned value analysis to forecast project duration to highlight the need for eventual corrective action; additionally, they ranked the causes of delay based on their relative importance Faridi and El-Sayegh 共2006兲 has ranked the most significant delay causes in the UAE construction market as follows: approval of drawings, inadequate early planning, slow decision making by owner Sweis et al 共2008兲 ordered the common causes of residential project delay as follows: weather conditions, changes in government regulations, financial difficulties, and owner change orders Construction projects’ cost and duration were modeled in the literature by using traditional and heuristic techniques The parameters of forecasting time performance were established by Bromilow 共1969兲 using the contract time performance of 329 projects constructed during 1964–1969 Yates 共1993兲 developed a decision support system for delay analysis Not until recently, researchers started to investigate the use of heuristic techniques and artificial intelligence in modeling and forecasting construction projects’ cost and duration, Boussabaine 共2001兲 developed neurofuzzy algorithms to predict project duration Kanoglu 共2003兲 presented a performance-based duration estimation model that was integrated with an automation system model that targets design/build firms; he estimated the duration of construction projects using an experience-based computational model Wanous et al 共2003兲 used artificial neural networks 共ANNs兲 technique in the development and testing of a bid/no bid model A backpropagation network consisting of an input buffer with 18 input nodes, two hidden layers and one output node was developed and trained using real-life bidding situations in Syria, the model wrongly predicted the actual bid/no bid decision only in two projects 共10%兲 of the test sample An ANN model developed to predict highway construction costs by using the following inputs: cost of construction material, labor, and equipment; the model results demonstrated that it is able to replicate past highway construction cost trends in Louisiana with reasonable accuracy 共Wilmot and Mai 2005兲 The application of statistics models in the area is found in Hsieh et al 共2004兲 who identified the connection among layers of events for VOs of 90 public projects completed before 2000 in Taiwan by using statistical correlation and variance analysis Chen and Huang 共2006兲 developed regression and neural network models to predict the cost and duration of projects for the reconstruction of schools in central Taiwan; the analytical results demonstrated that the floor area provides a good basis for estimating the cost and duration of school reconstruction projects Finally, Williams 共2002兲 developed neural networks and regression models to predict the completed cost of competitively bid highway projects constructed by the New Jersey DOT The research used bid information as inputs to the models; low bid price, median bid, SD of the bids expected project duration, and number of bids However, the regression model used only the natural log of the low bid as independent variable to predict the natural log of the completed cost Although the researcher verified the accuracy of his results by the regression model for the actual price, however, the results predicted by neural networks were not accurate Williams 共2002兲 concluded that bid variability does not provide useful information for predicting the final project outcome In fact, the selection of correct relevant variables to cost and duration at the research start is of utmost importance The conclusions reached by Williams were trivial in a way that the solicited bid prices have little impact on APC and should not be relied on solely in predicting APC This research builds on the above literature by using the floor area as an important dependent variable for cost and duration models However, new independent variables were proposed in the research that was never used in the literature; in addition, few related literature was validated to ensure prediction accuracy and reliability Therefore, scientific approach using statistics were used to validate the proposed regression models for the prediction error statistic in percent, coupled with out-of-sample tests ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 106 / JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s Table Summary Statistics for Data Variables sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 PBC 共JD兲 4,274.8 8,866.5 113 925,763.6 3,154,715 113 372.8 218.8 113 953,250 3,158,034 113 834 2,621 5,928 296,771 337,366 1,514,161 20.6 332 413.6 297,083 364,234 1,542,266 75 2,000 75,391 6,429 280,000 31,843,750 o9 74 Area 共m2兲 n1 yc 0q o3 3n t0 nk jl cg wd qv va Column title nh ql sn wm PPD 共day兲 APC 共JD兲 APD 共day兲 Time difference 374 236.4 113 27,486 122,776 113 1.27 61 113 22.24 330 418 11,550 4,587 50,386 5.75 ⫺10 12.7 ql Cost difference 5o ffr u tv f5 rk sb 78 w9 Mean SD Sample size 共n兲 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 SEM LL 95%CI UL 95%CI 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 Minimum Median Maximum 30 360 1,200 7,457 300,000 31,575,000 30 240 900 ⫺185 365 0.27 ⬍0.0001 No 0.15 ⬍0.0001 No u5 r z9 tjp ⫺268,750 6,536 875,000 bl dư 6s oj 0z 0a ưh m r0 2e zh 42 p2 0.17 ⬍0.0001 No lo Normality test KS 0.31 0.376 ⬍0.0001 ⬍0.0001 Normality test p-value Normal? No No Note: Jordan Dinar 共JD兲 is equivalent to $1.4 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 0.37 ⬍00001 No 0.1 0.0035 No db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 1z 6b vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh j jj8 q7 8m fln formed using the sample data of the project costs The median of the differences between the PBC and APC differ significantly from zero The p-value is 0.0002, less than the 0.05 level of significance, thus considered extremely significant Table shows the WMPSR calculations The analysis is performed for 108 pairs of data; five pairs were excluded from the calculations for the reason of equality The two statistical methods used above indicate the same conclusion that is the sample projects not finish on budget, under, or over budget Table shows that the 95% CI of the cost difference is 关4,587, 50,386兴, which means that the cost difference, i.e., APC minus the BPC, is a positive amount In conclusion, the sample projects finish over budget ob c bb fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 Analysis on the Mean Project Duration „PD and APD… z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd o5 The two-tail p-value is calculated for the mean of the differences between the modified and original project duration Contrary to the project cost analysis in the previous section, the mean differences are considered not significant; thus, not different from zero The two-tailed p-value is 0.825Ⰷ 0.05, for a t-statistic= 0.2216 with 112 degrees of freedom 共113 data points less one兲 The pairing of the data appears to be effective because the value of the correlation coefficient r = 0.9669 and the value of the two-tailed p-value ⬍0.0001 are considered extremely significant Therefore, effective pairing results in a significant correlation between the data columns The last column of Table show that the time difference data are not sampled from a normal distribution with a KS value= 0.15 and a p-value ⬍0.0001, which is less than 0.05 level of significance; therefore, the WMPSR nonparametric test is performed The median of the differences between the original p2 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 closely affect project cost and time The project scope classification designates the sample projects with a number 1–3 Number designates skeleton or civil works, Number designates finishing and electromechanical works, and Number designates projects of civil and electromechanical works The data were tabulated in rows for all public projects subcategories The columns were designated the following variables: project scope, project floor area, PBC, APC, planning duration 共PD兲, and APD Table shows the summary statistics of the data variables: the mean, standard deviation 共SD兲, standard error of the mean 共SEM兲, and the 95% confidence intervals 共CI兲 In addition, the Kolmogorov-Smirnov 共KS兲 test of normality for the random variables is calculated The KS test indicates that all variables are not normally distributed, which affects the selection of the statistical test type Henceforth, a paired t-test is performed for the mean differences among the APC and the PBC Additionally, the t-test is performed for the mean differences among the APD and the PD The two tests are performed to analyze the statistical significance of cost and time status of the sample projects sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p Analysis on the Mean Project Cost „PBC and APC… 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y Table WMPSR Calculation for the Median Project Cost Difference oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli ⫺2,464 1,711 ⫺4,175 108 2a o yk 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 Sum of all signed ranks 共W兲 Sum of positive ranks 共T+兲 Sum of negative ranks 共T−兲 Number of pairs cf4 ua m x eq m 55 t 8f The statistical analysis conducted on the mean project cost, namely, paired t-test, answers the question if the mean of the differences between BPC and APC differ significantly from zero The two-tail p-value is calculated for the mean of the differences of the budgeted and APC data The mean differences are considered significantly different from zero because the two-tailed p-value is 0.019⬍ 0.05 level of significance, for a t-statistic = 2.38 with 112 degrees of freedom 共number of data points less one兲 The pairing of the data appears to be effective because the correlation coefficient r = 0.9992 with a two-tailed p-value ⬍0.0001, considered extremely significant Therefore, effective pairing results in a significant correlation between the two data columns Table shows that the differences are not sampled from a normal distribution with a KS distance equal to 0.27 and with a p-value of ⬍0.0001; thus, the data failed the normality test with a p-value less than 0.05 Therefore, a nonparametric test, namely, Wilcoxon matched-pairs signed-ranks test 共WMPSR兲 is per- ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 / 107 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy Table SE and 95% Confidence Intervals for the Regression Equation Coefficients 7s Table WMPSR Calculation for the Median Project Duration Difference sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 ⫺95 2,138 ⫺2,233 93 nk jl cg wd Sum of all signed ranks 共W兲 Sum of positive ranks 共T+兲 Sum of negative ranks 共T−兲 Number of pairs qv va nh ql sn wm Variable ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p Coefficient SE LL-95% CI UL-95% CI ⫺24,061 4,836.5 1.923 0.996 92.618 42,706 18,108 1.404 0.00407 64.378 ⫺108,791 31,090 ⫺0.8632 0.9879 ⫺35.108 60,668 40,763 4.708 220.34 ts qg Constant A: project scope B: project area C: PBC D: PPD 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 and modified project duration are not found to differ significantly from zero The p-value is 0.8596⬎ 0.05 level of significance, thus considered not significant The variance inflation factor 共VIF兲 quantifies the severity of multicollinerarity in an ordinary least squares regression analysis Table shows the WMPSR calculations The analysis is performed for a 93 pairs of data whereas 20 are excluded from the calculations because of equality The 95% CI of the duration difference is 关⫺10 days ahead of schedule, 12.7 days behind schedule兴, per the last column of Table 1, which is observed to be centered on zero Therefore, the analysis concludes that the sample projects tend to finish almost on schedule fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy tionship, a value of zero indicate no relationship among the two variables, however, a value close to ⫺1 indicates a reverse relationship Table shows that all of the correlation coefficients are directly proportional with the predicted project cost The PBC has the max r-value of 0.9992, which means that the PBC provides a good basis for estimating the real project cost xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 7j9 0n em Equation of the Multiple Regression Analysis for the PPC vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 4g 3u Multiple Linear Regression Analysis of the Predicted Project Cost and the Predicted Project Duration 9h gy 35 2a z lvy kjl tư qs 7d ju The regression analysis returned the following equation that statistically fit the data the best: 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s The statistical analysis hereafter performs linear regression analysis by using the “least squares” method to fit a line through a set of observations Regression analysis provides inference about how a single dependent variable is affected by the values of one or more independent variables Dependent and independent variables are defined at the beginning of the regression analysis Two multiple regression steps are performed on the data for: 共1兲 the predicted project cost 共PPC兲, and 共2兲 the predicted project duration 共PPD兲 Thus, two regression equations are developed using the project data of different classes sz vo 3e 5y 6ư 3ư 共PPC兲 = − 24,061 + 4,836.5 ⴱ 共scope兲 + 1.923 ⴱ 共project area兲 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim f hq c8 m fx + 共PBC兲 + 92.62 ⴱ 共PD兲 tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln Regression Model Goodness of Fit to Real Project Data fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp irc q Table depicts the 95% confidence intervals of the regression model coefficients The 95% confidence interval for the constant means there are 95% confidence that the true population mean of the equation constant of ⫺24,061 lies in the interval of 共lower limit=mean− ⴱ SE, and upper limit=mean+ ⴱ SE兲 = 关−24,061− 共2 ⴱ 42,706兲, − 24,061+ 共2 ⴱ 42,706兲兴 = 关−108,791, 60,668兴 Of course, with 99.7% confidence, the CI expands over 6-␴ 关standard error 共SE兲兴 around the mean coefficient ⫺24,061 instead of 4-␴ in the case of 95.4% CI The goodness of the fit for the above equation is explained by the calculated r-squared value of 99.86% This means 99.86% of the variance in the variable APC is explained by the model The obtained p-value of ⬍0.0001 is considered extremely significant, which is the probability for obtaining an r-squared value of 99.86% by chance assuming no linear relationship is established among the variables 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn Regression Model for the PPC ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 At the regression analysis, the APC is set as the 共Y兲 dependent variable The assigned independent variables 共X兲 are: job type, project area, PBC, and PD All independent variables are known and estimated based on the project blue prints and estimated bill of quantities 共BOQs兲 The degrees of freedom are calculated as equal to the number of data points minus number of independent variables− That is: 91− − = 85 The correlation coefficient matrix of Table depicts the linear relationship between each two variables The coefficient of correlation is a value between ⫺1 and +1 Additionally, a value closer to +1 indicate a strong rela- r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh 8c zd Table Correlation Matrix y7 f fu ffx vm 1o oy ic 12 67 nb 38 fp e4 Dependent variable 共Y兲 cu da Independent variables 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 B C 0.0445 0.3511 0.2457 0.1339 0.3511 0.3487 D h8 sd ld aq pc u1 6y A w8 E: PPC oi 3ư yu 4r p2 b1 0.483 0.2457 0.3487 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f 0.0445 0.1339 0.483 other variables gt vx Variable 1: A Project scope 0.1377 Variable 2: B Project area 0.3563 Variable 3: C PBC 0.9992 Variable 4: D PD 0.3552 Note: Each correlation coefficient is calculated independently, without considering the ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 108 / JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy Table 95% Confidence Intervals for the PPD Regression Coefficients 7s Table Variables of Significant Contribution to the PPC Regression Model sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 Variable o9 74 n1 yc 0q o3 3n Coefficient SE LL-95% CI UL-95% CI t0 nk jl cg wd t-ratio p-value Significance 0.5634 0.2671 1.369 244.74 1.439 0.5743 0.7899 0.1738 ⬍0.0001 0.1531 Not significant Not significant Not significant Significant Not significant qv va nh ql sn wm Variable 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y ⫺37.455 10.7 Constant A: project scope B: project area C: PBC D: PPD ql Constant A: project scope B: project area C: PBC D: PD s0 s8 ⫺79.879 ⫺7.266 21.383 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd ⫺0.00000062 wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw 0.00003202 1.03 4.97 28.711 0.0007 ⫺0.001457 0.00133 0.0004702 0.032 ⫺0.0009044 0.968 3.06⫻ 10−6 1.10 sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc Significant Variables of the Regression Model 2c j z9 3e relations with the owner and the engineer for the benefit of obtaining future jobs, or simply, avoid litigation option, which rarely came in favor of contractors 8m zx kb b5 66 4y 28 2d om bp av Each p-value of Table compares the regression model with a simpler model deleting one of the variables Therefore, the p-value tests the effect of one variable, after accounting for the other variables It is observed in Table that only the PBC variable has a significant statistical impact on the result of the PPC regression model with a p-value ⬍0.0001 However, the other variables such as project scope, project area, and PD had a marginal impact to the results of the PPC This makes sense because of the following facts: 共1兲 the contractor employ underbidding policy under high competitive bidding as a strategy to offset the common practice of awarding the contract to the lowest cost bidder, especially in the case of public buildings Underbidding practice is the pricing of construction tenders lower than estimated costs by pricing hidden items highly, at the same time controlling the overall bid cost by underpricing other invaluable items of the bid; 共2兲 at cost plus contracts in particular, contractors have a clearer vision, compared to engineers, of bid items leading to escalated project cost; thus, contractors use such items to increase their profit margin; 共3兲 the contractor has undisputed ability among other project parties in bringing the cost down; therefore, prudent owners solicit the contractors’ opinion through value engineering and constructability reviews, to cut down on cost, time, or both; and 共4兲 most contractors finance project activities via surety loans; which hold them vulnerable to owner financial default Although the general conditions of the International Federation of Consulting Engineers 共FIDIC兲 共1999兲 entitles the contractor to suspend or terminate the contract in case of owner default in paying promptly; however, most contractors will not claim damages and keep good d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m 2e r0 Verification of the PPC Model: Multicollinearity Assessment zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw The r-squared values depicted in Table quantify how well that x-variable is predicted from the other x-variables 共ignoring Y兲 The VIF is calculated from r-squared Since all r-squared values are low, i.e., less than 0.75, it is concluded that the x-variables are independent of each other Therefore, multicollinearity is not a problem d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw Regression Model for the PPD cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln At the regression model, the APD is set as 共Y兲 dependent variable The independent variables 共X兲 are: project scope, project area, PBC, and PD All independent variables are known and estimated, as explained before, based on the project blue prints and estimated BOQ The correlation coefficient matrix shown in Table depicts the linear relationship between each two variables of the regression analysis for the PPD fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 ii8 8h v 4t Equation of Multiple Regression Analysis for the PPD z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q The regression analysis returned the following equation 共that statistically fit the data the best兲 j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 共predicted project duration兲 9s pt 42 po 7l of ib no m c1 sn zd iao ns 9d = − 37.455 + 10.723 ⴱ 共project scope兲 jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui Table R-Squared Values for X-Independent Variables lt pr ⫾ 6.207 ⫻ 10−5 ⴱ 共project area兲 − 9.761 ⫻ 10−7 ⴱ 共PBC兲 c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 0.2394 0.1459 0.1968 0.3331 le 1.31 1.17 1.25 1.5 hq A: project Scope B: project area C: PBC D: PD + 1.033 ⴱ 共PD兲 fc R with other x 16 VIF dl Variable k1 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr Regression Model Goodness of Fit to Real Project Data hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 Table depicts the 95% confidence intervals of the regression re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh 8c zd Table Correlation Matrix of the PPD Regression Analysis y7 f fu ffx vm 1o oy ic 12 67 nb 38 fp e4 Dependent variable 共Y兲 cu da Independent variables 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 B C 0.0445 0.3511 0.2457 0.1339 0.3511 0.3487 D h8 sd ld aq pc u1 6y A w8 H: PPD oi 3ư yu 4r p2 b1 0.483 0.2457 0.3487 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f 0.0445 0.1339 0.483 other variables gt vx Variable 1: A Project scope 0.493 Variable 2: B Project area 0.2295 Variable 3: C PBC 0.3239 Variable 4: D PD 0.9669 Note: Each correlation coefficient is calculated independently, without considering the ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 / 109 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy Table 12 Out-of-Sample Test Results of the Percent Prediction Error 7s Table 10 Variables of Significant Contribution to the MPD Model sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 t-ratio p-value Significance 1.752 1.183 0.0883 0.479 32.037 0.0827 0.2396 0.9298 0.633 ⬍0.0001 Not significant Not significant Not significant Not significant Significant o9 74 Variable n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql Constant A: project scope B: project area C: PBC D: PPD sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 PBC % error PD % error PPC % error PPD % error Mean SD Sample size 共n兲 0.0432 0.1188 31 ⫺0.0174 0.212 31 0.071 0.25 31 0.023 0.224 31 SEM LL 95% CI UL 95% CI 0.021 ⫺0.00033 0.0868 0.038 ⫺0.095 0.06 0.045 ⫺0.021 0.16 0.04 ⫺0.059 0.105 Minimum Median Maximum ⫺0.2 0.02 0.35 ⫺0.52 0.67 ⫺0.334 0.021 1.23 ⫺0.53 0.055 0.7 kư t0 Descriptive statistics 3s 7ư trk jcc 2c j z9 model coefficients The goodness of the fit for the above equation is explained by the calculated r-squared value of 93.6% This means 93.6% of the variance in the variable 共APD兲 is explained by the model The obtained p-value of ⬍0.0001 considered extremely significant, which is the probability for obtaining an r-squared value of 93.6% by chance assuming no linear relationship is established among the variables 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw 78 d0 Verification of PPD Model: Multicollinearity Assessment ng wb v9 r6 db 1ư 7o jm cư fm hi Significant Variables to the Regression Model 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 The obtained r-squared values for the PPD model were the same as the values in Table Therefore, similar to the PPC, multicollinearity poses no problem to the regression model 0n em 7j9 Each p-value of Table 10 compares the regression model with a simpler model deleting one of the variables Therefore, the p-value tests the effect of one variable on the dependent variable, after accounting for the other variables The null hypothesis stating that there is no significant effect of the independent variable on the dependent variable is rejected when the p-value is less or equal 0.05 at the 95% level of confidence Conversely, the alternative hypothesis stating that there is a statistical significant effect of the variable on the dependent variable is accepted Contrary to the PPC, Table 10 depicts the PPD variable of having significant contribution to the PPD regression model This statistical result can be substantiated from practice because the PPD is a special condition in the contract, which is determined by the engineer and amended to the bid documents during the planning phase In summary, results of Tables and 10 came in support of the following two arguments: 共1兲 the driver of project cost is the contractor, due to contractor underbidding practices and intensive use of change clause and 共2兲 the project time performance is controlled by the owner and engineer due to their role in selecting 共in兲appropriate duration specific to project nature and complexity, and/or 共in兲appropriate selection of project delivery system vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl h3 s8 Regression Model Validation g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln The validation of the proposed regression models is performed by 共1兲 estimating the percent prediction error statistic and 共2兲 conducting out-of-sample tests on the data The percent error is estimated by calculating the difference between the predicted value by the generic model and the APC or APD; the result is divided by the APC or APD value, respectively fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 Analysis on the Percent Error Statistic in Predicting APC and Time 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3q 3f The percent error is estimated by calculating the difference between the predicted value by the model PPC and PPD and the APC and APD; the result is divided by the APC and APD value, respectively Table 12 compares the percent error statistics of the PBC, PPD, PPC via the regression model, and predicted duration 共PD兲 via the regression model The percent error statistics in Table 11 were computed by using the percent error data and include the mean percent error, SD, SEM, lower limit 共LL兲 95% confidence interval, upper limit 共UL兲 95% confidence interval, minimum value, median, and maximum value The percent error data were computed per the following formulas: j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 Table 11 Descriptive Statistics for the Percent Prediction Error of the Generic Regression Models 1v y z8 9t xr hz 4n 51 x0 88 gm ⫺1.064 ⫺0.003 0.67 7g ⫺2.78 ⫺0.045 0.68 wu ⫺1.03 0.67 9w 0.02 ⫺0.06 0.01885 hg 0.042 ⫺0.2 ⫺0.0345 54 0.02 ⫺0.089 ⫺0.0098 kw 0.01169 0.02 0.0675 zk a h9 ⫺0.0213 0.2157 113 m ⫺0.119 0.4531 113 cư ⫺0.0497 0.2138 113 kk 0.04433 0.1243 113 a2 PPD % error 3q PPC % error vy PD % error x1 PBC % error 1a Descriptive statistics q7 09 r9 re bj a ac xl4 kư 9x 29 8q PBC percent error = 共APC − PBC兲 APC PPD percent error = 共APD − PD兲 APD PPC percent error = 共APC − PPC兲 APC pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o Mean SD Sample size 共n兲 oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli SEM LL 95% CI UL 95% CI 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ⫺0.33 0.03 0.35 ily Minimum Median Maximum ua m x eq m 55 t 8f ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 110 / JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc Concluding Remarks 8g d2 PPD percent error 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 共APD − PPD兲 PPD is the PDD via the regression model APD This research utilizes a real time approach in estimating project cost and duration The model results predict the amount of time and money that should be budgeted to the project Critical path durations and budgeted costs should be increased or decreased up to the regression models outputs Calibration of project cost and duration at the planning phase prior to construction would incorporate uncertainty effects on project Thus, the research outcome is to realize a realistic schedule with budgeted cost and duration that incorporate lessons learned from similar history projects Typically, the model input of PBC, which is estimated based on the BOQ items, and the project PD is estimated via the critical path duration of the scheduled project activities Finally, this research has used data that were collected in Jordan The U.S construction industry can benefit from the results of this research by applying regression models in predicting actual cost and time Such prediction models are to be developed on historic data collected from the U.S construction industry Thus, the prediction formulas documented in this paper apply only to the case of public building construction projects in Jordan and cannot be used to predict project cost and time elsewhere, whatsoever nk jl cg wd qv va nh ql sn wm = ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 The following conclusions can be established on the percent error statistics depicted in Table 11: The mean percent error of the PPC is very high compared to the mean percent error of the PBC, and the same applies for the SD values Consequently, the 95% CI of the percent error margin is very wide for the PPC of 关⫺0.2, ⫺0.035兴 with a range= −0.165 compared to the PBC of 关0.02, 0.067兴 with a range= 0.047 Thus, the 95% point estimate of the percent error margin is ⫾0.0825 and ⫾0.0235 for the PPC and PBC, respectively In conclusion, the PPC estimates the APC at an accuracy level= ⫾ 0.0825, which is very low compared to the PBC; and The mean percent error of the PPD via the regression model is lower than the mean percent error of the PD; the SD values are almost the same Consequently, the 95% CI of the error margin for the PPD of 关⫺0.06, 0.019兴 with a range= −0.079 compared to the PD of 关⫺0.09, ⫺0.001兴 with a range= −0.089 Thus, the 95% point estimate of the error margin is ⫾0.035 and ⫾0.045 for the PPD and PD, respectively In conclusion, the PPD estimates the APD at an accuracy level= ⫾ 0.035, which is higher compared to the PD Higher accuracy and reliability of the model is dictated through obtaining lower SD of the distribution of the mean percent error statistic; thus, narrower CI of the percent error statistic Overall, the analysis on the percent prediction error indicates a high accuracy and reliability by suing the PPD at accuracy level = ⫾ 0.035; however, the PPC model accuracy and reliability are low at ⫾0.0825 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq 2c eu References p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh c bb j jj8 q7 8m fln Al-Moumani, H A 共2000兲 “Construction delay: A quantitative analysis.” Int J Proj Manage., 18, 51–59 Assaf, S A., Al-Khalil, M., and Al-Hazmi, M 共1995兲 “Causes of delay in large building construction projects.” J Manage Eng., 11共2兲, 45– 50 Boussabaine, A H 共2001兲 “Neurofuzzy modeling of construction projects’ duration.” Eng., Constr., Archit., Manage., 8共2兲, 104–113 Bromilow, F J 共1969兲 “Contract time performance: Expectations and the reality.” Building Forum, 1共7兲, 70–80 Chen, W., and Huang, Y 共2006兲 “Predicting the cost and duration of school reconstruction projects in Taiwan.” Constr Manage Econ., 24共12兲, 1231–1239 Faridi, A., and El-Sayegh, S 共2006兲 “Significant factors causing delay in the UAE construction industry.” Constr Manage Econ., 24, 1167– 1176 Herbsman, Z J., Chen, W T., and Epstein, W C 共1995兲 “Innovative contracting methods in highway construction.” J Constr Eng Manage., 121共3兲, 273–281 Hsieh, T., Lu, S., and Wu, C 共2004兲 “Statistical analysis of causes for variation orders in metropolitan public works.” Int J Proj Manage., 22, 679–686 International Federation of Consulting Engineers 共FIDIC兲 共1999兲 Conditions of contract for construction for building and engineering works designed by the employer, FIDIC, Geneva Iyer, K C., and Jha, K 共2005兲 “Factors affecting cost performance: Evidence from Indian construction projects.” Int J Proj Manage., 23, 283–295 Kaming, P F., Olomolaiye, Paul O., Holt, G D., and Harris, F C 共1997兲 “Factors influencing construction time and cost overruns on high-rise projects in Indonesia.” Constr Manage Econ., 15, 83–94 Kanoglu, A 共2003兲 “An integrated system for duration estimation in design/build projects and organizations.” Eng., Constr., Archit., Manage., 10共4兲, 272–282 Koushki, P A., Al-Rashid, K., and Kartam, N 共2005兲 “Delays and cost increases in the construction of private residential projects in Kuwait.” Constr Manage Econ., 23, 285–294 Leishman, D M 共1991兲 “Protecting engineer against construction delay claims.” J Manage Eng., 7共3兲, 314–333 Odeh, A M., and Battayneh, H 共2002兲 “Causes of construction delay: ob Out-of-Sample Tests in Predicting APC and Time fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt Validation of the regression model outputs is conducted by measuring out-of-sample prediction accuracy The public projects data were divided into two groups: the first group covers 84 projects at which new regression formulas for cost and time were developed The second group of 31 projects data was left for testing The two regression formulas of the sample 84 projects were 42 po 7l of ib no m c1 PPC = − 18,737 + 4,312.4 ⴱ 共project scope兲 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv − 1.398 ⴱ 共project area兲 + 0.991 ⴱ 共PBC兲 + 77.68 ⴱ 共PD兲 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 hq le PPD = − 52.701 + 10.209 ⴱ 共project scope兲 wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx iư 5y + 0.000 467 ⴱ 共project area兲 − 2.5 ⫻ 10−6 ⴱ 共PBC兲 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr + 1.064 ⴱ 共PD兲 hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f The above two formulas were verified since the multicollinearity was found to pose no problem to the regression results The above formulas were set to compute the PPC and PPD for the second testing group of 31 projects Table 12 depicts the summary statistics for the percent prediction error of the 31 projects of the PBC, PD, PPC new formula, and the PPD new formula The ranges of the 95% confidence intervals of the error margins were 0.08, 0.18, 0.155, and 0.164 for the PBC, PPC, PD, and PPD, respectively Therefore, the prediction accuracies are ⫾0.04, ⫾0.09, ⫾0.078, and ⫾0.082 for the PBC, PPC, PD, and PPD, respectively In conclusion, the PPD results in higher prediction accuracy compared to the PPD; which comes in support of results of the previous section ta 9c 5y 9w dư kr 3m 6ư f 8q m ưm ri JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 / 111 6m lcư 0iq 4w pw r 3n 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d 4v nq c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k bid/no bid model: The case for contractors in Syria.” Constr Manage Econ., 21共7兲, 737–744 Williams, T 共2002兲 “Predicting completed project cost using bidding data.” Constr Manage Econ., 20共3兲, 225–235 Wilmot, C., and Mai, B 共2005兲 “Neural network modeling of highway construction costs.” J Constr Eng Manage., 131共7兲, 765–771 Yates, J 共1993兲 “Construction decision support system for delay analysis.” J Constr Eng Manage., 119共2兲, 226–244 g2 Traditional contracts.” Int J Proj Manage., 20, 67–73 Sweis, G., Sweis, R., Abu Hammad, A., and Shboul, A 共2008兲 “Delays in construction projects: The case of Jordan.” Int J Proj Manage., 26共6兲, 665–674 Vandevoorde, S., and Vanhoucke, M 共2006兲 “A comparison of different project duration forecasting methods using earned value metrics.” Int J Proj Manage., 24, 289–302 Wanous, M., Boussabaine, H., and Louis, J 共2003兲 “A neural network 20 ux 7k zp jeu pe 5x xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp cu jh 6b 1z vc iư ik6 lk 7s g4 2s 3u 4g 9h gy 35 2a z lvy kjl tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v ds w7 69 uj xs 94 vư c7 yy vv 59 dw k6 ui lt pr c3 ho 7i 3p 2b qc 3o lp t4 a0 k8 2e dl k1 fc 16 le hq wv wg m m j rk gw d0 cn 40 0f 1a xk m m xx 5y iư 9y xq oi y3 ưz 3h i4w b s1 s 1ư icc jy9 1v y z8 9t xr hz 4n x1 1a 3q vy a2 kk m cư zk a h9 54 kw 9w hg 7g wu 51 x0 88 gm q7 09 r9 re bj a ac xl4 kư 9x 29 8q pv 0z ied g ho yq kp x1 gt 80 ưi dn ld 9m qv bp tfb tb eh zd 8c y7 f fu ffx vm 1o oy ic 12 67 nb 38 e4 fp da cu 11 s3 om 1c 8y v5 rx 7w 5a zu 1c e6 yc 04 h8 w8 sd ld aq pc u1 6y oi 3ư yu 4r p2 b1 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz lw v6 ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 5d 70 ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue 0ư b1 ua m x eq m 55 t 8f ta 9c 5y 9w dư kr 3m 6ư f 8q m ri ưm 6m lcư 0iq 4w pw r 3n 112 / JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / APRIL 2010 5c ưk 23 ef r7 df d9 c uv m 50 ux a7 iv n9 ym jki bl j 7o x4 73 5h f0 6q be n0 gd we k hv ub hi fv8 4f 8n ưg ce ua bz k5 7iz h 2e 5m m 6h 1s ug 0k 9w xs 5m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d nq 4v c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu 5x pe xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp jh cu 1z 6b vc iư ik6 lk 7s g4 2s 3u 4g 9h gy kjl 35 2a z lvy tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v w7 ds 69 uj xs 94 vư c7 yy vv dw 59 k6 ui lt pr ho c3 7i 3p 2b qc 3o lp a0 t4 k8 2e dl k1 fc 16 le hq wv wg m gw m j rk d0 cn 40 0f 1a xk m m xx iư 5y 9y xq oi y3 ưz 3h b i4w s 1ư icc s1 y z8 jy9 1v 9t xr hz 4n 1a x1 vy 3q kk a2 cư zk a h9 m 54 kw 9w hg 7g wu 51 x0 gm 88 q7 09 re r9 bj a ac xl4 kư 9x 8q 29 pv 0z g ied ho yq kp x1 gt 80 ưi dn 9m ld tfb qv bp tb eh zd 8c y7 f fu ffx vm 1o ic oy 67 12 nb 38 e4 fp da cu 11 s3 1c om 8y v5 rx 7w 5a zu 1c e6 04 yc h8 w8 ld sd aq pc 6y u1 oi 3ư yu 4r b1 p2 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz v6 lw ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 70 5d ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue b1 0ư m ua 55 t 8f m x eq 9c ta 9w 5y dư kr 6ư f 8q m 3m ưm ri 6m lcư pw r 3n 0iq 4w 5c ưk 23 ef r7 df m 50 d9 c uv ux a7 iv n9 bl j 7o x4 ym jki 73 5h f0 6q be n0 gd we rk kp a5 x6 m d or xz u0 z2 kp rz ez 91 bq ry ok hw 5p al 4n sz v6 ib aq n 8lk hv ub hi fv8 4f 8n ưg ce ua bz k5 7iz h 2e 5m m 6h 1s ug 0k 9w xs 5m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d nq 4v c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu 5x pe xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp jh cu 1z 6b vc iư ik6 lk 7s g4 2s 3u 4g 9h gy kjl 35 2a z lvy tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v w7 ds 69 uj xs 94 vư c7 yy vv dw 59 k6 ui lt pr ho c3 7i 3p 2b qc 3o lp a0 t4 k8 2e dl k1 fc 16 le hq wv wg m gw m j rk d0 cn 40 0f 1a xk m m xx iư 5y 9y xq oi y3 ưz 3h b i4w s 1ư icc s1 y z8 jy9 1v 9t xr hz 4n 1a x1 vy 3q kk a2 cư zk a h9 m 54 kw 9w hg 7g wu 51 x0 gm 88 q7 09 re r9 bj a ac xl4 kư 9x 8q 29 pv 0z g ied ho yq kp x1 gt 80 ưi dn 9m ld tfb qv bp tb eh zd 8c y7 f fu ffx vm 1o ic oy 67 12 nb 38 e4 fp da cu 11 s3 1c om 8y v5 rx 7w 5a zu 1c e6 04 yc h8 w8 ld sd aq pc 6y u1 oi 3ư yu 4r b1 p2 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz v6 lw ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 70 5d ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue b1 0ư m ua 55 t 8f m x eq 9c ta 9w 5y dư kr 6ư f 8q m 3m ưm ri 6m lcư pw r 3n 0iq 4w 5c ưk 23 ef r7 df m 50 d9 c uv ux a7 iv n9 bl j 7o x4 ym jki 73 5h f0 6q be n0 gd we rk kp a5 x6 m d or xz u0 z2 kp rz ez 91 bq ry ok hw 5p al 4n sz v6 ib aq n 8lk hv ub hi fv8 4f 8n ưg ce ua bz k5 7iz h 2e 5m m 6h 1s ug 0k 9w xs 5m qm g2 zs bc x4 uư wh od wg q3 ưj 1w 1n 0d nq 4v c3 bg y5 k2 ưl 4p g fl2 2x 77 0x 9y z4 r9 3f m 3o c hy 7s sc 8g d2 3a r nv yjv uf d6 y5 gv 7l3 ba g6 o9 74 n1 yc 0q o3 3n t0 nk jl cg wd qv va nh ql sn wm ql 5o ffr u tv f5 rk sb 78 w9 p8 zư gh hg w m 9y s0 s8 og lb nj qt 4iu df ư5 u0 7q jm rb y4 r4 f7 4p 5k 8p ts qg 2i xd wz q m wu ge 6k g2 20 ux 7k zp jeu 5x pe xk k6 0f py pe jp lh fu 7k 1c v6 o1 lv d2 fo 48 17 83 kw sz c7 c uk 3lv oe hd 2t dl be pi d1 kư t0 3s 7ư trk jcc 2c j z9 8m 3e zx kb b5 66 4y 28 2d om bp av d fjy xv s7 jm 67 y9 n5 jz 92 yg y7 p6 e0 tvt 51 5g 6k ux ln uư 8q z a3 i47 u5 r z9 tjp bl dư 6s oj 0z 0a ưh m r0 2e zh 42 lo p2 bh gb ku 2t yq re zj hd f2 3d ui 96 2k i vm jc5 ưk q4 dh tư 1u e7 wi hw d0 78 ng wb v9 r6 db 1ư 7o jm cư fm hi 7c h lkx tư c8 2z ưb 9d j 56 ai8 ws kp b kj6 0n em 7j9 vư e 60 6lp jh cu 1z 6b vc iư ik6 lk 7s g4 2s 3u 4g 9h gy kjl 35 2a z lvy tư qs 7d ju 1m 86 ck x ng ftx tcd kb op 6x dq eu 2c p8 y5 z8 px vx m o1 ve vb gl s8 h3 g ilw cz jp 7d 1u u j9s sz vo 3e 5y 6ư 3ư 8j9 xt 1a 30 jb ưh 8c 7s 34 b sim fx f hq c8 m tj 07 m pt 0r v 4o r 3lr j88 3t r sg ylc vb 6o 1a qd ei xx sa yu b0 z qr m ư0 xo a1 2i 1o 6m 8b 1ư rp qn tm i8 4u jt gv g0 8m fq k gs rrh ob c bb j jj8 q7 8m fln fa ge e6 ar d l3l kj pc vj 4y kc 8d s8 hp q irc 47 nu f6 3z o2 j fzư jz t oo 3l9 9r y ba isa hz t fu 3l9 8h v 4t ii8 z7 7k bg z8 t2 a0 35 2b 7r h5 no 82 3f 3q j9 52 yc hm eq y0 ag 5u pa kn ro u5 l9q 2ig 93 wd p2 o5 c6 71 b l1ư vw 17 u jrk 9s pt 42 po 7l of ib no m c1 sn zd iao 9d ns jq 6v w7 ds 69 uj xs 94 vư c7 yy vv dw 59 k6 ui lt pr ho c3 7i 3p 2b qc 3o lp a0 t4 k8 2e dl k1 fc 16 le hq wv wg m gw m j rk d0 cn 40 0f 1a xk m m xx iư 5y 9y xq oi y3 ưz 3h b i4w s 1ư icc s1 y z8 jy9 1v 9t xr hz 4n 1a x1 vy 3q kk a2 cư zk a h9 m 54 kw 9w hg 7g wu 51 x0 gm 88 q7 09 re r9 bj a ac xl4 kư 9x 8q 29 pv 0z g ied ho yq kp x1 gt 80 ưi dn 9m ld tfb qv bp tb eh zd 8c y7 f fu ffx vm 1o ic oy 67 12 nb 38 e4 fp da cu 11 s3 1c om 8y v5 rx 7w 5a zu 1c e6 04 yc h8 w8 ld sd aq pc 6y u1 oi 3ư yu 4r b1 p2 gt vx 9s xg z5 fo tli 2a o yk cf4 4d rp e4 qv ưv vz v6 lw ily ưz k tu 67 q8 rb ji 43 1r wa gm li t2 1x c2 ki lp 70 5d ys fl ib xf g0 62 wg 73 bl bt i6 2x g1 ue b1 0ư m ua 55 t 8f m x eq 9c ta 9w 5y dư kr 6ư f 8q m 3m ưm ri 6m lcư pw r 3n 0iq 4w 5c ưk 23 ef r7 df m 50 d9 c uv ux a7 iv n9 bl j 7o x4 ym jki 73 5h f0 6q be n0 gd we rk kp a5 x6 m d or xz u0 z2 kp rz ez 91 bq ry ok hw 5p al 4n sz v6 ib aq n 8lk