Stochastic Budget Simulation

Martin Elkjaer

Grundfos A/S, Thorsgade 19C, Itv., 5000 Odense C, Denmark

Abstract

The purpose of this article is to present a new method for cost estimation. The innovative idea is to combine the conventionalcalculation method stochastic simulation with basic facets of the successive principle. The purpose of this is to avoid theassessment of dependencies between cost items in the budget. The method is named Stochastic Budget Simulation (SBS), and it

is made operational with a software application. The method can be applied to most projects with a simple cost structure at theearly stages where uncertainty plays a signi®cant role in estimating the overall cost. The most likely users are planners, projectmanagers or consultants. It is not necessary to understand the calculations, the statistical theory or the simulation technique in

order to use the method. However, users should be able to arrange items and overall in¯uences in accordance with the urgentrequirement of statistical independence. SBS is a new and radically di�erent way to analyse and evaluate the economicconsequences of large-scale projects by quantifying intervals for cost items and using simulation as a tool to representdistributions of the possible costs. # 2000 Elsevier Science Ltd and IPMA. All rights reserved.

Keywords: Cost estimation; Stochastic simulation; Uncertainty analysis

The aim of the method is to establish a reliable andinformative economic result based on careful uncer-tainty analysis and the use of stochastic simulation(synonymous with Monte Carlo simulation). Themethod combines the conventional Monte Carlo simu-lation technique with basic facets of the successiveprinciple. [3] The purpose is to avoid statistical corre-lation between the budget items. This can be done byisolating and separating the overall issues and commondependencies. The successive principle is brie¯ydescribed in the Appendix.

The purpose of using stochastic simulation is todescribe the potential uncertainty of an economicresult. The simulation technique makes use of prob-ability distributions to generate a number of thedesired overall cost estimate.

SBS may present useful results under certain con-ditions, which can assist decision-makers in identifyinga reliable total cost. However, correct results will alsorequire the use of various other techniques or con-ditions to ensure that all important matters areincluded. In addition, the systematic use of evaluation

techniques is required to ensure against evaluation pit-falls. The use is restricted to cost estimates of a verysimple structure, while for instance Net Present Valuecalculations and project durations cannot be dealtwith.

1. Context

Many projects are undertaken in a complex environ-ment. Earlier de®nitions are annulled or at least chan-ged and new situations continually arise. Often thereare no reliable data when estimating cost items. At theproposal stage where a feasibility study is usually in-itiated, the design and demands are still relativelyunclear. At this stage it is sensible to consider uncer-tainties and to use probabilistic range estimation ratherthan single point estimation, because a probabilisticrange re¯ects the fact that outcomes vary. Stochasticsimulation in the form of Monte Carlo simulation isperhaps the most easily usable form of probabilityanalysis.

International Journal of Project Management 18 (2000) 139±147

0263-7863/00/$20.00 # 2000 Elsevier Science Ltd and IPMA. All rights reserved.

PII: S0263-7863(98 )00078 -7

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Current practice, which uses a contingency allow-ance to cover subsequent design or project changes, isbased on deterministic methods or single point esti-mates. Such methods may serve well under stable con-ditions, but as the scale and range of variationsincreases, the utility of this approach is reduced. Manyvariations require an explicit assessment of uncertainty,and deterministic methods are simply unable to pro-vide this. The situation demands non-deterministic,stochastic methods.

The method can be applied to di�erent types oflarge-scale projects at the conception stages.Throughout developing projects, software or buildingprojects uncertainty has a crucial impact on the costcomponents and therefore the total cost. As anexample, Stochastic Budget Simulation can be used atthe proposal stages of a construction project or infeasibility studies with great e�ort to evaluate the poss-ible result or total cost.

2. Risk and uncertainty

Before describing the approach of Stochastic BudgetSimulation it is necessary to explain the di�erencebetween risk and uncertainty. There seems to be somedisagreement in the literature regarding the distinctionbetween risk and uncertainty. [4] However, the author®nds it suitable to distinguish between the two words,and be careful not to use the words as synonyms.Confusion arises when one regards a subjective riskassessment as an uncertainty analysis.

A risk is a normally unwanted event. It can beidenti®ed and quanti®ed through the impact and prob-ability of occurrence. A risk can also be positive,meaning that a risk can be an opportunity to reducethe project cost. Risk can be assessed either objectivelyor subjectively. Often when no reliable data are avail-able, one has to use subjective judgement to evaluatethe consequences of certain risks, which inevitablyinvolves uncertainty. Risks are inevitable in every pro-ject and because of risks, uncertainty in¯uences projectcost calculations

Risks are therefore integrated into the budget inorder to establish a more reliable result. Risks are theoverall in¯uences or issues that are common for all theactivities or items in the budget. Risks that in¯uencethe whole project are named generic risks. These thensubstitute the traditional contingency allowance in abudget. As the software program cannot handle risksthat partly a�ect some of the items, those risks areneglected. Generic risks are estimated in percentageand multiplied to the sum of the cost items accordingto normal practice. Generic risks could be price rises,project management, common workforce, commonequipment, weather conditions, environmental factors

or team spirit. A risk management procedure can assistin identifying and assessing the potential risks. Howthis is done lies outside the purpose of this article.

Uncertainty on the other hand is rather more dif-fuse. In relation to cost estimation, it means that thecost of an item cannot be exactly de®ned. Uncertaintyis an intangible value and is used in case of insu�cientknowledge of estimation. Assessment of cost items andgeneric risks in the budget encompasses uncertainty.Thus the items are regarded as stochastic variables.

Uncertainty analysis should be performed as an inte-gral part of assessing each cost item. Uncertaintyanalysis is based on the triple estimate using intuitiveand subjective judgement. A triple estimate is a way inwhich to quantify an uncertain value. Uncertaintyanalysis allows one to obtain quantitative results in theform of con®dence intervals. To perform this analysisone must frequently rely on subjective judgement inthe absence of information in order to estimate therange of each item in the budget. Using a triple esti-mate for uncertainty analysis provides planners withan opportunity to quantify the uncertainties involvedfor the di�erent project items.

3. The approach

This section outlines the approach of SBS. Theapproach is illustrated below in Fig. 1. It is urgent atthis point to emphasise the conditions required for arealistic and reliable economic result. Prior to conduct-ing SBS, the following ®ve steps are recommended.

1. An identi®cation and grouping of all relevant mat-ters with an overall in¯uence upon the project. Thisrequires use of the Work Breakdown Structure(WBS) as well as a consideration of stochasticdependencies. In other words, all cost items need tobe identi®ed and included in the budget.

2. A non-biased quanti®cation of conditional coste�ects from the above mentioned groups of overallissues. To avoid stochastic dependencies betweencost components, a group of generic risks or overallin¯uences is made. The generic risks are assumed toa�ect all the cost items.

3. The quanti®cation of cost items and generic risksrelevant to the inherent uncertainty. A triple esti-mate is used to quantify the budget items. Carefulassessment and systematic judgement are necessaryto ensure an accurate total result.

4. The use of algorithms to calculate the total projectcost, as well as the local uncertainty for each item.The prime problem here is to avoid stochasticdependencies. If ignored, the results generated willbe meaningless.

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147140

5. Results must be presented in such a way that pro-ject managers can use them to inform stakeholdersabout the possible economic outcome.

This article focuses on steps 4 and 5 in order toimprove the procedures for generating correct andinformative results. However, steps 1 to 3 must becarefully handled. Otherwise the mathematical algor-ithm (the simulation technique) and the idea of group-ing common issues seems worthless. Below, theapproach for SBS is described and illustrated in Fig. 1.

Initially the project must be structured into a limitednumber of cost items. These main items are later suc-cessively listed according to their priority or e�ectupon the uncertainty of the total result. The customaryspeci®cation of costs into hundreds of items allowsserious biases to go undetected, such as systematicunderestimation. The normal approach generallyneglects the importance of focusing on a few vitalitems and overall in¯uences.

By brainstorming and general experience the planneridenti®es generic risks and groups these into indepen-dent groups. Standard checklists can be valuable toensure that no matters of major potential e�ect areomitted. The generic risks must be well-de®ned in

order to avoid double counting and hidden dependen-

cies in the estimates. The description can include a

®rm reference de®nition, which can be used as a com-

mon precondition when costs and especially risks are

quanti®ed. This works as a baseline for the assess-

ment.

Subsequently each cost item and generic risk is

assessed by a triple estimate. At this point generic risks

are estimated in percentage. If the estimate for a cost

item is cost per unit, for instance £ per m2, then the

estimate must be multiplied with the value for the unit

since the input to the simulation technique has to be

monetary values. Generic risks also have to be esti-

mated in cost. As generic risks are regarded as a con-

tingency allowance to the sum of the mean of the cost

items, the values are converted into monetary units. As

an example, if the sum of the means is 1200, the triple

estimate (ÿ10%. 5%. 15%) is transformed to (ÿ120.60. 180). The range estimation therefore contains three

estimates:

A minimum or optimistic value: the lowest poss-

ible estimate.

A most likely value: the conventional estimate.

Fig. 1. The approach of Stochastic Budget Simulation.

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147 141

A maximum or pessimistic value: the highestpossible estimate.

The actual values for minimum, most likely andmaximum can be determined in several ways. Themost straightforward method is simply to select thevalues subjectively, relying upon the expertise of theestimator to determine reasonable values. However,many pitfalls typically violate the result seriously.Sometimes the estimator underestimates the minimumand maximum value. Therefore an approach for care-ful and systematic assessment is required. This is a sig-ni®cant precondition of a reliable result. A simple andsystematic way to estimate the values could be the fol-lowing:

1. Imagine the lowest possible value.2. Imagine the highest possible value.3. Estimate a most likely value between the maximum

and minimum value based on experience or reliableinformation.

After assessing the triple estimate a distributionmust be selected. It is possible to choose between anasymmetric triangular function, the Erlang family ofdistributions or a combination of the possible distri-butions (see Fig. 2). As described above, the precondi-tions of structuring the items, identifying the overallin¯uences or generic risks, and systematically quantify-ing uncertainty are more signi®cant than choosing acorrect distribution. However, in order to reduce thedi�culty involved in choosing a fair distribution, thesoftware program allows the user to combine all theincorporated distributions.

All cost items are assigned the same distribution dueto the functionality of the software program. Thisreduces the di�culty in choosing a fair distribution foreach item. Choosing a correct distribution can be dis-cussed exhaustively, yet it is not the intention here toinvestigate the choice of a fair distribution.

This topic has been the challenging subject of otherpapers. [5, 6] The author has included the above men-

tioned distributions, because they are recommended byscienti®c engineers, [2, 4] and are fairly widespread andfamiliar.

Simulation can begin once each interval is assigneda probability distribution. The simulation techniqueconsists of the following:

1. A random number between zero and one is gener-ated.

2. By the inverse cumulative distribution a `random'cost for each item is selected on the basis of therandom number between zero and one. It is import-ant to understand that the random number is usedto select a value, but the selection process ensuresthat the frequency with which values are selectedconforms to the appropriate distribution.

3. The random cost for each item is summarised topresent an overall cost of the project.

4. 1, 2 and 3 are repeated several times to construct adistribution of the total cost.

The simulation process steps through each distri-bution including the generic risks, determining a singlevalue from the distribution at random. A cost com-ponent is then generated within the boundaries of theintervals. The cost components are then added in aconventional way to calculate a total cost for that par-ticular iteration. At the end of each iteration the totalcost estimate is recorded prior to repeating the entireprocess over multiple iterations. Typically 500 iter-ations are more than enough to produce a result forthe total cost. A larger number of iterations gives onlya marginal increase in accuracy, and it is of relativelylittle importance compared with the assessment of thetriple estimate. However, the larger the number of iter-ations, the smoother the graph. This increases visibilityduring the presentation of the results.

Finally the frequency and cumulative distributionare calculated. These are produced on the basis of anumber of iterations for the overall cost. See Fig. 3.

The mean value (m) and standard deviation (s) arecalculated on the basis of the frequency distribution of

Fig. 2. The ®gure shows a triangular distribution and an Erlang-5 distribution, which are among the possible underlying distributions for the

cost items in the budget. The values a, b and c represent respectively the minimum, most likely and maximum estimate which de®ne the interval.

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147142

the total cost. The formulas for mean and standard de-viation are listed below:

m � 1

n

Xni�1

Yi

s2 � 1

n

�Xni�1

Y 2i ÿ n�m�2

�

The mean m is calculated by adding all the valuesfor the total cost (Yi) and dividing the sum by thenumber of iterations for the total cost (n). The stan-dard deviation s is a measure of the spread of the dis-tribution. Due to the application of the simulationtechnique, the results di�er from using the calculationmethods in the successive principle. In short, the simu-lation technique produces a mathematically correctresult for the total cost whereas the successive principleproduces approximate results.

The SBS is quite di�erent from earlier suggestionsfor cost simulation. [1, 2, 4] The idea is to combine fea-tures from the successive principle with the calculationmethod stochastic simulation. Conclusively, statisticaldependency between cost elements is now treated bythe systematic separation of overall in¯uences or gen-eric risks, and the correlation e�ects are included in anappropriate manner. Range methods and most othersimilar methods generally neglect important stochasticdependencies, and thus violate statistical laws. The cor-relation e�ects are seriously treated as an importantcontribution to the ®nal result. Common issues andgeneric risks are therefore identi®ed and estimated aswell as the regular items in the budget. The simulationtechnique ensures that the inherent uncertainty in allitems is treated explicitly and in a mathematically cor-

rect manner and transferred to the ®nal distributionthrough a large number of iterations.

4. Features of the software application

The method Stochastic Budget Simulation is madeoperational by a software program application basedon Excel spreadsheets and Visual Basic. The main fea-ture of the software program is to handle the stochas-tic simulation. The software program makes it possibleto perform a sensitivity analysis, as it is possible tochange the parameters (the minimum estimate, themost likely estimate and the maximum estimate) forspeci®c cost items. This might be done if the calculatorassesses that for instance the pessimistic parameter istoo low. With a sensibility analysis, it is possible toanalyse the outcome of the simulation or the conse-quences for the overall cost by changing the value ofcost components.

The software program also allows the user to ident-ify the cost items, which carry most uncertainty. It isoptional for the user to specify cost items in order toreceive a more reliable result. The simulation processcan be performed any time the user ®nds it appropri-ate. The user does not have to understand the math-ematical theory to use the software program.

5. An example

Although the primary objective of this paper is topresent a new approach to calculating the overall costof any project in the conception phases, the followingexample will be used to illustrate the operational useand features of SBS. The example is based on a ®ctivedeveloping software project. The budget is thereforenot complete and the estimates do not re¯ect realisticvalues. Due to a better comprehension of the appli-cation of SBS the spreadsheets are visualised.

After having identi®ed the cost items and genericrisks, a triple estimate for each item is calculated. Theitems and their estimates are entered in the main sheetbelow (see Fig. 4). When the user types the estimatesfor the items, it is possible to protect the main items.This feature secures that headings for groups are notestimated, if they are wanted in the budget.

The sum of the means for the cost items is$1451000. The generic risks are ®rstly estimated in per-centage, and subsequently added to $1451000. Forinstance the triple estimate for project management is(ÿ15%. 0%. 30%) which equals (ÿ217,6. 0. 435,3).

The mean and standard deviation are calculated foreach item by using the approximate formulas from thesuccessive principle. The purpose of these calculationsis to rank the ten items that contribute most to the

Fig. 3. The ®gure shows the cumulative distribution for the overall

cost, where F(t) represents the probability between [0,1]. m2s indi-

cate the 70% con®dence interval. For instance, the cumulative fre-

quency curve can be used to indicate the probability that the total

cost will not exceed a particular value. The probability distribution

will approximately be a normal distribution according to the central

limit theorem.

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147 143

Fig.4.Main

sheet.

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147144

total uncertainty. These are therefore automaticallyplaced in the priority list, which can be updated atanytime (see Fig. 5).

The priority list calculates a comparable e�ect ofeach uncertain cost item or generic risk upon theuncertainty of the total result measured by the stan-dard deviation. The list indicates how important thelocal item is compared to others. The user can thenspecify an item into sub-items. The value for the rela-tive deviation in the priority list is the indicator forfurther speci®cation into independent groups. The rela-tive deviation is calculated by dividing the local stan-dard deviation for each item with the total standarddeviation. In the example co-operation with suppliersis the most uncertain factor, and in order to reduce thetotal uncertainty of the project, it must be further

speci®ed. This can be done by marking the item withthe cursor, and then pushing the `Speci®cation' button.A new sheet is then ready for detailed analysis intosub-items.

A speci®cation usually results in di�erent values forthe mean and deviation, hence the values are updatedand replaced in the main sheet (see Fig. 4). After eachspeci®cation the priority list is normally updated.

The main sheet for the triple estimates also containsother facilities. The user has to determine the numberof iterations or how many times the total cost must becalculated. In this example 1000 iterations are chosen,which is more than su�cient for an acceptable result.The monetary unit for the items must also be deter-mined, and here $1000 is selected.

Due to the visualisation of the frequency graph anumber of ranges must also be speci®ed. This makes itpossible to count the number of iterations in speci®cintervals. The number of ranges a�ects the visualisa-tion of the frequency distribution. The more rangesare chosen the smoother the illustration of the graph.

Finally, the distribution can be selected. The user isfree to choose any of the possible distributions inwhich the user has most con®dence. Even though thechoice of distribution type has an in¯uence on the®nal results, the preconditions outlined in steps 1 to 3are more signi®cant. In Fig. 4 an Erlang±10 distri-bution for each item is preferred.

Fig. 5. Prio.

Fig. 6. Graph.

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147 145

Then the budget is ready for stochastic simulation.By activating the button `Run simulation', the totalexpected mean and standard deviation are calculatedrespectively to $1 588 000 and $208 000. A probabilityand cumulative distribution is also generated as illus-trated in Fig. 6. Using the cumulative distribution, de-cision-makers can make decisions based on reliablemathematical documentation for the ®nal cost.

The graph illustrates the calculated mean and stan-dard deviation for the total cost. It is particularly im-portant to notice that these are calculated on the basisof the outcome of the simulation. The cumulative dis-tribution can be used to indicate the chances that thetotal costs do not exceed a particular value. As anexample, Fig. 6 shows that there is a 70% probabilitythat the total cost will be less than about $1 750 000. Ifthe investor has a speci®c amount of money, he canevaluate the success for implementing the projectwithin the budget limits. For example, a speci®edinvestment of $1 500 000 has a 30% chance of stayingwithin the budget cost (see Fig. 6). These conclusionsare dependent upon a su�cient analysis and successfulcompletion of the mentioned ®ve steps.

Although the selection of a correct distribution isnot very signi®cant compared to the preconditions, theresults for the total cost will di�er depending on theselected distributions. Table 1 illustrates the values forthe total cost for selected distributions on the basis ofthe ®ctive example. The values are in $1000.

There is a di�erence of approximate 8% and 11%respectively between the highest and lowest value forthe excepted mean and standard deviation. Eventhough research indicates that the Erlang family of dis-tributions expresses relatively reliable uncertainty esti-mations, the author recommends choosing acombination of all the included distributions.

6. The results

By using Stochastic Budget Simulation planners, de-cision-makers are able to make decisions based on amathematically exact distribution instead of approxi-mate algorithms. If the preconditions are well per-formed the total distribution might show the actualcosts. The distribution of the total costs presents theexpected mean and standard deviation and sub-sequently establishes a con®dence interval. The distri-

bution further indicates the probability that costs willnot exceed a particular value. The priority list enablesproject managers to focus on the most important itemsthat need further speci®cation in order to reduce theoverall uncertainty.

After quanti®cation by use of the triple estimate, thedistribution of the total cost is dependent on the typeof underlying distributions and the amount of iter-ations. As seen above, a triangular distribution and anErlang distribution give di�erent results for the ap-proximate normal distribution of the total cost. It can-not be concluded which distribution is the mostappropriate, because the ®nal cost of a project is natu-rally not known. As seen, it is relatively important foranalysing the expected total cost which underlying dis-tribution is used, if the preconditions are well executed.However, it should be noted that the k value for theErlang±k distribution for the mean value of the totalcost is not of importance, but the standard deviationdecreases as the k value increases in accordance withthe theory.

Instead of using direct approximate algorithms tocalculate the overall cost, this method performs anexact calculation using the stochastic simulation tech-nique.

7. Conclusions

Most projects are conducted in a changing environ-ment, which makes the analysis of the project economyin the early stages quite di�cult. It is necessary tostudy the uncertainties involved in the project and tolet the economic result re¯ect the possible total costs.By using a probabilistic approach by including distri-butions for each item in the budget, decision-makerswill have an analytical tool with which to evaluate themost likely total cost. This is done with the use of sto-chastic simulation technique. By using facets of thesuccessive principle, the users do not have to worryabout correlation between the cost items as commondependencies are isolated and separately estimated.

SBS is an operational tool for planners, which iseasy to use and quickly presents an overview of thetotal cost. Furthermore, the estimator can conduct asensibility study and focus on the items with mostlocal uncertainty compared to the overall uncertainty.A speci®cation of the items can be performed toensure a more accurate result. SBS may improve pro-ject results subject to the condition that cost items andgeneric risks are properly identi®ed and evaluated.

The author does not claim that the method is the ul-timate tool to present a reliable economic result at theearly project stages, but the author has introduced analternative method, which is a good example of afuture application.

Table 1

Triangular Erlang-10 Combination

Expected mean 1731 1588 1639

Expected standard deviation 234 208 229

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147146

Appendix A. The successive principle and its scope

The successive principle is a tool for project man-agers and decisions-makers who require the inclusionnot only of regular cost items, but also of all the rel-evant fuzzy factors a�ecting their work.The principleis used in most private ®rms and public companies tosupport and facilitate estimations, allowance andguarantee decisions, scheduling, commercial riskanalysis as well during start-up and teambuildingphases of new ventures. The applications and bene®tsare primarily the following three: Firstly, it is possibleto make very realistic budget estimates, project dur-ations etc., and thus largely eliminate overruns andother unpleasant surprises. This can even be done at avery early phase of the plans. Secondly, as part of abuilt-in ranking process, the responsible managers aregiven a prioritised list of critical items or activitiesthat contribute strongly to uncertainty in the project.Thirdly, the mutual understanding of the aims andcharacteristics of a given project or program are radi-cally improved among the involved key persons, thusalso improving the important teambuilding process inthe project group.The method basically involves listingall factors of importance, not only the physical andformal items, but also the fuzzy and sensible matters,and openly and correctly to control and handle uncer-tainty and even to consider uncertainty as an existingaspect in planning and managing. For reasons ofoverview and rapid performance the successive prin-ciple uses a top down approach starting with themain items and successively developing a work breakdown structure for those items where uncertainty ishighly critical. Due to the complexity of projects, it isconsidered essential to perform the analysis jointly viaa group of key persons. This also has positive sidee�ects such as increased consensus and strengthenedteam building. The general procedure outlined:

1. A group of key persons gather. The ®rst task ofthe group is to thoroughly discuss the tasks, pre-conditions and objectives.

2. All general sources of potential uncertainty areidenti®ed, organised in groups and de®nedaccording to relevant sub routines.

3. A set of main items or activities is chosen, and atriple estimate for each item is made. One ormore generic risks or overall in¯uences areadded, based upon potential deviations from thereference de®ned in step 2.

4. Direct approximate procedures are performedusing statistical rules. The mean and standard de-

viation of the total is calculated, and the prioritylist is created. The formulas for the local meanand local standard deviation are respectively(min.+3*most likely+max.)/5 and (max.ÿmin.)/5. (By comparison in using stochastic simu-lation, these values are added respectively to thetotal mean and standard deviation for the overallcost.)

5. The most critical items are successively detailed.The guidance in this detailing process is the pri-ority list, which indicates the relative importanceof the individual item to the total uncertainty.This continues until a reasonable minimum ofuncertainty is reached.

6. The results of this procedure are a highly meanvalue and a `top ten list' with the remainingmajor items or risks that consist of most uncer-tainty. This list is typically followed up by anaction plan suggested by the analysis group.

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Martin Elkjaer graduated in April1998 from the Technical University ofDenmark. He works as a manage-ment consultant for PricewaterhouseCoopers in Copenhagen, Denmark.This article is based on Mr. Elkjaer'sreport ``Project management of costand risk'' [7] which concluded hisMaster of Science in Engineering(Planning and Technology Man-agement). Requests or questionscan be forwarded to martin_elkjaer@hotmail.com

M. Elkjaer / International Journal of Project Management 18 (2000) 139±147 147