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Estimating Project Times and Costs

Gray, Clifford F. and Larson, Erik W. Project Management: The Managerial Process,5th ed., 2010, McGraw Hill, New York (Chapter 5)

Jack, Meredith and Samuel Mantel, Project Management, a Managerial Approach, 4th

d., John Wiley & Sons, 2000

Sullivan et al., Engineering Economy, 11th Ed., Prentice hall, 2000.

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Estimating Projects• Estimating

– The process of forecasting or approximating the time and cost ofcompleting project deliverables.

• In order to develop a budget, we must:

WBS

ResourceRequirement

Cost Estimate

estimatingmethods

Resource rates

Project schedule

estimatingmethods

Activity Duration

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Estimating Guidelines for Times, Costs, and Resources

1. Have people familiar with the tasks make the estimate.2. Use several people to make estimates.3. Base estimates on normal conditions (one shift, 5 working

days,..), efficient methods, and a normal level of resources.4. Treat each task as independent.5. Don’t make allowances for contingencies.

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Types of Estimates

• Top-down (macro) estimates: analogy,group consensus, or mathematicalrelationships

• Bottom-up (micro) estimates: estimatesof elements of the work breakdownstructure

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Top-Down Estimates• This strategy is based on collecting the opinions and

experiences of top and middle managers, and available pastdata concerning similar activities

• The managers estimate the overall project cost and the costof major deliverables.

• These cost estimates are then given to lower level managers,who are expected to continue the breakdown into budgetestimates for the specific sub-deliverables and workpackages

• This process continues to the lowest level

• Advantages: Aggregate estimates can often be developedquite accurately for repeated projects

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Bottom-Up Estimates• The people doing the work are consulted regarding times and budgets

to ensure the best level of accuracy• Initially, estimates are made in terms of resources, such as labor hours

and materials. They are later converted to dollar equivalent.• Bottom-up budgets should be and usually are, more accurate in the

detailed tasks.• The resulting task estimates are aggregated to give the total direct cost

of the project

• Advantages:– Individuals closer to the work are apt to have a more accurate idea

of resource requirements– The direct involvement of low-level managers in estimate

preparation increases the likelihood that they will accept the resultwith a minimum of aversion

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Estimating Projects: Preferred Approach

• Develop the WBS/OBS.

• Make rough top-down estimates.

• Make bottom-up estimates.

• Reconcile differences between top-down andbottom-up estimates

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Methods for Estimating Project Times and Costs

• Macro (Top-down) Approaches

– Consensus methods

– Analogy method

– Learning curves

Project EstimateTimesCosts

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Estimation Techniques• Consensus Methods (Expert Judgment / Delphi

method)– Expert Judgment: It uses the pooled experience of

senior and/or middle managers to estimate thetotal project duration and cost. It involves severalmeeting where the experts discuss, argue, andultimately reach a decision as to their best guessestimate.

– Delphi method: Several experts familiar with theproject are consulted. They each estimate theproject cost. These estimates are compared anddiscussed. The estimation process iterates until anagreed estimate is reached.

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Estimation Techniques• Analogy Methods

– These techniques are applicable when other projects inthe same application domain have been completed.

– The cost of a new project is estimated by analogy withthese completed projects.

– The cost of a similar project is analyzed and adjusted fordifference between it and the proposed project.

– The adjustment takes into account factors such as dates,project scale, location, exchange rates,..

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An index is a dimensionless number used to indicate how acost has changed over time relative to a base year.Changes usually occur as a result of inflation, technological

advances, availability of labor and materials, changes inconsumer buying patternsMany indexes are periodically publishedEngineering News Record Construction IndexMarshall and Swift cost index (Equipment) Statistical Abstract of the United States (governmentindexes on yearly materials, labor, and construction costs)U.S Department of Labor (output per man-hour byindustry) Bureau of Labor and Statistics (Producer Price andconsumer Prices indexes).

Cost Indexes Method (ratio Method)

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Cost Indexes Method (ratio Method)

Using the indexes, if we know the cost of goods in one year, we can estimate the cost of the same goods in another year by using a simple ratio.

CN = Ck ( IN / Ik )IN = Index for current year, NIk = Index for base year, k Ck = cost of item during base yearCN = cost of the item during the current year

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Example: A certain index for the cost of purchasing and installing utilityboilers is keyed to 1974, where the baseline value was set to 100.Company XYZ installed a 50,000-lb/hr boiler in 1996 for $525,000when the index had a value of 468. This same company must installanother boiler of the same size in 1999. The index in 1999 is 542. Whatis the approximate cost of the new boiler?

C1999= $525,000 (542/468) = $608,013.

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Parametric Cost Estimating Techniques

Relates the cost of an activity to one or more costdrivers (independent variables)

Cost drivers are design variables that account for alarge portion of the total cost behavior.

Construction : floor space, roof surface area, wall surface areaTrucks / car : horsepower, gross weightTurbine engine: fuel consumptionElectrical power plant: kilowattsComputers: megabytesSoftware : # of lines of codes

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Power sizing is a cost estimating technique that uses the relationship between capacity or size and cost. It is frequently used for estimating the cost of building industrial plants and equipment.

where CNew is the cost of the new plant,C is the cost of the existing plant,SNew is the capacity of the new plant, S is the capacity of the existing plant. X is the cost-capacity factor which varies depending on the type of plant or equipment being built.X = 0.68 for nuclear generating plants and 0.79 for fossil-fuel generating plants

Power -Sizing Technique

X

NewNew S

SCC

}Both in $ as of the point in time for which the estimate is desired

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Example. Suppose that it is desired to estimate the cost ofbuilding a 600-MW fossil-fuel plant. It is known that a 200-MW plant cost $100 million 20 years ago when theapproximate cost index was 400, and the cost index is now1,200. The cost capacity factor for a fossil-fuel plant is 0.79.1. Update the known cost of the 200 MW plant 20 years ago to

a current cost. C = 100 (1200/400) = $300 million

2. Use the power-sizing model to estimate the cost of the 600 MW plant CNew= $300 million (600-MW/200-MW)0.79= $714 million

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Studies have shown that human performance usually improves when atask is repeated

The learning curve effect was first observed in the aircraft andaerospace industries with respect to labor hours per unit (T.P. Wright,“Factors affecting the cost of airplanes”, J. of Aeronautical Sciences, Vol 3., 1936.)

In general, performance improves by a fixed percent each timeproduction doubles (each time the output doubles, the worker hoursper unit decrease to a fixed percentage of their previous value)

Learning Curves

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Most learning curves are based on the assumption that the number ofinput resources needed decreases by a constant percentage each timethe number of units produced doubles.Y1 = labor hours required to produce the first output unitYn = labor hours needed to produce the nth output unit , n = 2, 4, 8, 16,…s = learning curve parameter (improvement rate, e.g., 90% )Y2 = Y1 s

Yn = Y1 sp for p = 0, 1, 2, …. and n = 2p

Y4 = Y2 s = Y1 s2

)2log()log(

)log()log(1

pn

spYY n

bsn

YYn )2log(/)log()log(/)log(

1

bn nYY 1 for n = 2, 3, 4, …. Unit Learning curve equation

b = learning curve exponent

Y8 = Y4 s = Y1 s3

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95b -0.736966 -0.621488 -0.514573 -0.415037 -0.321928 -0.234465 -0.152003 -0.074001Unit

1 1 1 1 1 1 1 1 12 0.6000 0.6500 0.7000 0.7500 0.8000 0.8500 0.9000 0.95003 0.4450 0.5052 0.5682 0.6338 0.7021 0.7729 0.8462 0.92194 0.3600 0.4225 0.4900 0.5625 0.6400 0.7225 0.8100 0.90255 0.3054 0.3678 0.4368 0.5127 0.5956 0.6857 0.7830 0.88776 0.2670 0.3284 0.3977 0.4754 0.5617 0.6570 0.7616 0.87587 0.2383 0.2984 0.3674 0.4459 0.5345 0.6337 0.7439 0.86598 0.2160 0.2746 0.3430 0.4219 0.5120 0.6141 0.7290 0.85749 0.1980 0.2552 0.3228 0.4017 0.4929 0.5974 0.7161 0.8499

10 0.1832 0.2391 0.3058 0.3846 0.4765 0.5828 0.7047 0.843311 0.1708 0.2253 0.2912 0.3696 0.4621 0.5699 0.6946 0.837412 0.1602 0.2135 0.2784 0.3565 0.4493 0.5584 0.6854 0.832013 0.1510 0.2031 0.2672 0.3449 0.4379 0.5480 0.6771 0.827114 0.1430 0.1940 0.2572 0.3344 0.4276 0.5386 0.6696 0.822615 0.1359 0.1858 0.2482 0.3250 0.4182 0.5300 0.6626 0.818416 0.1296 0.1785 0.2401 0.3164 0.4096 0.5220 0.6561 0.814517 0.1239 0.1719 0.2327 0.3085 0.4017 0.5146 0.6501 0.810918 0.1188 0.1659 0.2260 0.3013 0.3944 0.5078 0.6445 0.807419 0.1142 0.1604 0.2198 0.2946 0.3876 0.5014 0.6392 0.804220 0.1099 0.1554 0.2141 0.2884 0.3812 0.4954 0.6342 0.801221 0.1061 0.1507 0.2087 0.2826 0.3753 0.4898 0.6295 0.798322 0.1025 0.1465 0.2038 0.2772 0.3697 0.4844 0.6251 0.795523 0.0992 0.1425 0.1992 0.2722 0.3644 0.4794 0.6209 0.792924 0.0961 0.1387 0.1949 0.2674 0.3595 0.4747 0.6169 0.790425 0.0933 0.1353 0.1908 0.2629 0.3548 0.4701 0.6131 0.788026 0.0906 0.1320 0.1870 0.2587 0.3503 0.4658 0.6094 0.785827 0.0881 0.1290 0.1834 0.2546 0.3461 0.4617 0.6059 0.783628 0.0858 0.1261 0.1800 0.2508 0.3421 0.4578 0.6026 0.781529 0.0836 0.1233 0.1768 0.2472 0.3382 0.4541 0.5994 0.779430 0.0815 0.1208 0.1737 0.2437 0.3346 0.4505 0.5963 0.777531 0.0796 0.1183 0.1708 0.2405 0.3310 0.4470 0.5933 0.775632 0.0778 0.1160 0.1681 0.2373 0.3277 0.4437 0.5905 0.773833 0.0760 0.1138 0.1654 0.2343 0.3244 0.4405 0.5877 0.772034 0.0744 0.1117 0.1629 0.2314 0.3213 0.4374 0.5851 0.770335 0.0728 0.1097 0.1605 0.2286 0.3184 0.4345 0.5825 0.768736 0.0713 0.1078 0.1582 0.2260 0.3155 0.4316 0.5800 0.767137 0.0699 0.1060 0.1560 0.2234 0.3127 0.4289 0.5776 0.765538 0.0685 0.1043 0.1538 0.2210 0.3100 0.4262 0.5753 0.764039 0.0672 0.1026 0.1518 0.2186 0.3075 0.4236 0.5730 0.762540 0.0660 0.1010 0.1498 0.2163 0.3050 0.4211 0.5708 0.761141 0.0648 0.0995 0.1479 0.2141 0.3026 0.4187 0.5687 0.759742 0.0636 0.0980 0.1461 0.2120 0.3002 0.4163 0.5666 0.758443 0.0625 0.0966 0.1444 0.2099 0.2979 0.4140 0.5646 0.757044 0.0615 0.0952 0.1427 0.2079 0.2958 0.4118 0.5626 0.755845 0.0605 0.0939 0.1410 0.2060 0.2936 0.4096 0.5607 0.754546 0.0595 0.0926 0.1394 0.2041 0.2915 0.4075 0.5588 0.753347 0.0586 0.0914 0.1379 0.2023 0.2895 0.4055 0.5570 0.752148 0.0577 0.0902 0.1364 0.2005 0.2876 0.4035 0.5552 0.750949 0.0568 0.0890 0.1350 0.1988 0.2857 0.4015 0.5535 0.749850 0.0560 0.0879 0.1336 0.1972 0.2838 0.3996 0.5518 0.7486

Learning curve parameter (improvement rate)Learning Curves Unit Values

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0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95b -0.736966 -0.621488 -0.514573 -0.415037 -0.321928 -0.234465 -0.152003 -0.074001Unit

1 1 1 1 1 1 1 1 12 1.6000 1.6500 1.7000 1.7500 1.8000 1.8500 1.9000 1.95003 2.0450 2.1552 2.2682 2.3838 2.5021 2.6229 2.7462 2.87194 2.4050 2.5777 2.7582 2.9463 3.1421 3.3454 3.5562 3.77445 2.7104 2.9455 3.1950 3.4591 3.7377 4.0311 4.3392 4.66216 2.9774 3.2739 3.5928 3.9345 4.2994 4.6881 5.1008 5.53807 3.2158 3.5723 3.9601 4.3804 4.8339 5.3217 5.8447 6.40398 3.4318 3.8469 4.3031 4.8022 5.3459 5.9358 6.5737 7.26129 3.6298 4.1021 4.6260 5.2040 5.8389 6.5332 7.2898 8.1112

10 3.8131 4.3412 4.9318 5.5886 6.3154 7.1161 7.9945 8.954511 3.9839 4.5665 5.2229 5.9582 6.7775 7.6860 8.6890 9.791912 4.1441 4.7800 5.5013 6.3147 7.2268 8.2444 9.3745 10.623913 4.2951 4.9831 5.7685 6.6596 7.6647 8.7925 10.0516 11.451114 4.4381 5.1770 6.0257 6.9941 8.0923 9.3311 10.7211 12.273615 4.5740 5.3628 6.2739 7.3190 8.5105 9.8611 11.3837 13.092116 4.7036 5.5413 6.5140 7.6355 8.9201 10.3831 12.0398 13.906617 4.8276 5.7132 6.7467 7.9440 9.3218 10.8977 12.6899 14.717418 4.9464 5.8791 6.9727 8.2453 9.7162 11.4055 13.3344 15.524919 5.0606 6.0396 7.1925 8.5399 10.1037 11.9069 13.9735 16.329120 5.1705 6.1950 7.4065 8.8284 10.4849 12.4023 14.6078 17.130221 5.2766 6.3457 7.6153 9.1110 10.8602 12.8920 15.2373 17.928522 5.3791 6.4922 7.8191 9.3882 11.2299 13.3765 15.8624 18.724123 5.4783 6.6346 8.0183 9.6604 11.5943 13.8559 16.4833 19.517024 5.5744 6.7734 8.2132 9.9278 11.9538 14.3306 17.1002 20.307425 5.6677 6.9086 8.4040 10.1907 12.3086 14.8007 17.7132 21.095526 5.7583 7.0407 8.5910 10.4494 12.6589 15.2666 18.3227 21.881227 5.8464 7.1696 8.7745 10.7040 13.0050 15.7283 18.9286 22.664828 5.9322 7.2957 8.9545 10.9548 13.3471 16.1861 19.5312 23.446229 6.0158 7.4190 9.1313 11.2020 13.6853 16.6402 20.1306 24.225730 6.0974 7.5398 9.3050 11.4458 14.0199 17.0907 20.7269 25.003231 6.1770 7.6581 9.4759 11.6862 14.3509 17.5377 21.3202 25.778832 6.2547 7.7742 9.6439 11.9235 14.6786 17.9814 21.9107 26.552633 6.3308 7.8880 9.8094 12.1578 15.0031 18.4219 22.4985 27.324634 6.4051 7.9997 9.9723 12.3892 15.3244 18.8593 23.0835 28.094935 6.4779 8.1095 10.1328 12.6179 15.6428 19.2938 23.6660 28.863636 6.5492 8.2173 10.2910 12.8439 15.9583 19.7254 24.2461 29.630637 6.6191 8.3233 10.4469 13.0673 16.2710 20.1543 24.8237 30.396138 6.6876 8.4276 10.6008 13.2883 16.5810 20.5805 25.3989 31.160139 6.7548 8.5302 10.7526 13.5069 16.8885 21.0041 25.9719 31.922740 6.8208 8.6312 10.9024 13.7232 17.1935 21.4252 26.5427 32.683841 6.8855 8.7307 11.0504 13.9373 17.4960 21.8438 27.1114 33.443542 6.9492 8.8287 11.1965 14.1493 17.7962 22.2601 27.6780 34.201943 7.0117 8.9252 11.3409 14.3592 18.0942 22.6741 28.2425 34.958944 7.0732 9.0204 11.4835 14.5671 18.3899 23.0859 28.8051 35.714745 7.1337 9.1143 11.6245 14.7731 18.6835 23.4955 29.3658 36.469246 7.1932 9.2069 11.7640 14.9772 18.9751 23.9030 29.9246 37.222547 7.2518 9.2983 11.9019 15.1795 19.2646 24.3085 30.4815 37.974548 7.3095 9.3885 12.0383 15.3801 19.5522 24.7120 31.0367 38.725449 7.3663 9.4775 12.1733 15.5789 19.8379 25.1135 31.5902 39.475250 7.4222 9.5654 12.3069 15.7761 20.1217 25.5131 32.1420 40.2239

Learning curve parameter (improvement rate)

Learning curves Cumulative Values

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Example 1: A manufacturer has a new contract for 16 prototype units and a total of 800 labor hours were required for the first unit. Past experience has indicated that on similar types of units the improvement rate was 80%.

How many labor hours are required to produce the 16th unit?

How many labor hours are required to finish the whole project of 16 prototype units?Y16 = Y1 16b , where b = log(0.8)/log(2) =-0.32193

Y16 = 800 16-0.32193 = 800 (0.4096) = 327.68 labor hours

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1ttY = 800 (8.920) = 7,136 hours

The average unit labor hours = 7,136/16 = 446 labor hours per unit

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Example 2: The assembly department is to start building a newconfiguration of computer systems. The first system requires 3.5 hoursto assemble. Past experience indicates that an 85% learning curveapplies in this situation. How many units have to be assembled before aa system can be built in less than 2 hours?

Yn = Y1 nb , where Y1 = 3.5 hours and b = log(0.85)/log(2) =-0.2345

n =? such that Yn < 2 hours,

3.5 n-0.2345 < 2 => n0.2345 > 1.75 => n > 10.87 or n = 11

The 11th unit will be assembled in less than 2 hours.

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Linear regression is a statistical technique used to estimate therelationship between two variables.

Linear Regression

Value of Independent Variable

Valu

es o

f Dep

ende

nt V

aria

ble

Deviation1

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation

Trend line, y = a + bx^

For small data sets, this technique can be used by hand. For large datasets, spreadsheet and statistic packages can be used to estimate therelationship.

Least squares method minimizes the sum of the

squared errors (deviations)

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The graph shows a data set involving a cost driver, X, and a dependentcost, Y.

The dataset suggest a linear relationship.

Least Squares Method

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Equations to calculate the regression variables a and b

The variables a and b are the ones that minimize the sum of squarederrors

n

iii

n

iii YbXaYYMinimize

1

2

1

2 )()(

n

ii

n

iii

XnX

YXnYXb

1

22

1

XbYa

bXaY

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Example 1. Find a linear equation to predict the packaging and processing cost for an order (y) given its weight x = 250 lb.

∑x2∑xy

xya

b

279.0813.31813.31)253)(279.0(4.102

279.0)253)(10(658900

)4.102)(253)(10(2643202

Y =31.813 +0.279 (250) = $101.563.

n

ii

n

iii

XnX

YXnYXb

1

22

1

XbYa

xi weight Line Fit Plot

020406080

100120140

180 230 280 330

xi weight

yi (

Pack

agin

g co

st)

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Example 2. For a certain drilling operation within a flexible machiningcell, data regarding the time (in hours) to drill 1, 2, 3, and 4 holes in a ¼inch sheet of carbon steel have been obtained.

xya

b

0241.001295.001295.0)5.2)(0241.0(0732.0

0241.0)5.2)(12(90

)0732.0)(5.2)(12(5568.22

xi (No. of holes) Line Fit Plot

0.0000

0.0200

0.0400

0.0600

0.0800

0.1000

0.1200

0.1400

0 1 2 3 4 5

xi (No. of holes)yi

hou

rs∑x2∑xy

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Model validationDetermine how well the model can estimate the cost/time.

Validation can be accomplished using statistical “goodness of fit”measures such as standard error and the correlation coefficient

The standard error (SE) measures the average variation between theactual and estimated cost/time values

The correlation coefficient (R) measures the closeness of the actualdata points to the regression line.

n

yySE

n

iii

1

2)(

n

ii

n

ii

n

iii

xxyy

xxyyR

1

2

1

2

1

)()(

))((

29

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Excel Tutorial: Regression analysis1.Make sure that the Analysis ToolPak Add-In is loaded into Excel.

Otherwise click on “Office Button”. Then click on “Excel Option”1

2

3

4

5

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Excel TutorialTo perform simple linear regression:While on the page where you entered your data, from the menu bar,select DATA and Data Analysis. Scroll down and highlight"Regression" and click OK.

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Excel TutorialA data-entry window will pop up.1. Under "Input Y Range," type:$C$1:$C$7.2. For "Input X Range," type:$B$1:$B$7.3. Click to add a checkmark inthe box for "Labels.“4. For "Output Options," select“Output Range“ and type $E$15. Click to add a checkmark inthe box for "Line Fit Plots.“6. Click OK.7. Excel will perform theregression and place the outputon the same worksheet.

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Excel TutorialReformatting the outputBefore interpreting the output, you'll need to do some reformatting. Thecolumns do not automatically adjust to their optimal widths. To do this, withinthe worksheet that you just created, double-click on the boundary to the right ofany column heading. Your table should look similar to the one in the next slide.

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a

b

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Parametric Estimate of Material CostsJ. Nicholas, Project Management for Business and Engineers, 2nd Ed., Elsevier Inc., 2004.

A warehousing contractor wants a quick way to estimate the material cost of afacility. The company’s engineers investigate the relationship between severalbuilding parameters and the material costs for eight recent projects comparablein terms of general architecture, layout and construction material. Using themethod of Least Square Method, they develop the following regression modelthat relates material cost (y) to floor space (x1) in terms of 10,000 sq. ft. and thenumber of shipping/receiving docks (x2) in a building.

y = 201,978 + 41,490 x1 + 17230 x2

Suppose a proposal is being prepared to construct a new 300,000 sq. ft. facility with two docks. The estimated material cost is

y = 201,978 + (41,490) (30) + (17230) (2) = $1,481,138