Resource-constrained project management using enhancedtheory of constraint

Chiu-Chi Weia,*, Ping-Hung Liub, Ying-Chin Tsaic

aDepartment of Industrial Engineering and Management, Chung-Hua University, Hsin-Chu, TaiwanbDepartment of Industrial Engineering and Management, Yung-Ta Institute of Technology and Commerce, Ping-Tung, Taiwan

cTaiwan Semiconductor Manufacturing Company, Hsin-Chu, Taiwan

Received 11 May 2000; received in revised form 8 December 2000; accepted 5 September 2001

Abstract

One of the vital problems in the project management is the determination of the project schedule, especially, when the resourcesrequired are limited and conflicted. Traditionally, the resources constrained project schedule is determined using heuristic algo-rithms, in which there are no other measures to shorten the project completion time delayed due to the resource constraint. Dr.

Goldratt proposed the theory of constraint (TOC) in 1986, which provides the concept of activity duration cut. However, since theintroduction of TOC, only the Harries semiconductor construction project was reported, and a complete and realistic applicablemodel for resource constrained project management is yet to be developed. The purpose of this study is to compare and contrast the

advantages and disadvantages of traditional project management and TOC project management. An enhanced TOC method forscheduling the project under resource constraint is also proposed in this manuscript. # 2002 Published by Elsevier Science Ltd andIPMA.

Keywords: Theory of constraint; CPM; PERT

1. Introduction

The theory of constraint (TOC) proposed by Dr.Goldratt emphasizes on the systematic management ofproject by discovering the uncertain factors hinderingthe project implementation, and suggests the globaldeployment of resources [1–3]. The concept of thinkingglobally and acting locally recommends the use of theglobal safety time and the reduction of the activityduration. However, a practical method to reduce theactivity time and exert the management control remainsnonexistent. The critical chain [4] coupled with the pro-ject buffer and the activity buffer incurs several pro-blems that need to be clarified.By combining the traditional project management

tools and the existing TOC concepts, this article intendsto propose a resource constraint-based project manage-ment model for project planing, project implementation,

and project control. Issues discussed in this study aregiven below:

1. The disadvantages of the traditional approaches ofhandling the resource constrained project man-agement.

2. An enhanced resource-constrained project sche-duling method by using the theory of constraint topromote the applicability of TOC is proposed.

3. To review both the strategic and the practical per-spectives of the enhanced approach, and point outapplicable conditions to emphasize the effective-ness of the proposed method.

Three popular project scheduling techniques areGanntt chart, Critical Path Method (CPM) and ProjectEvaluation and Review Technique (PERT). Gannttcharts or bar charts are most commonly used for exhi-biting project progress, and it often includes items aslistings of activities, activity duration, schedule datesand progress-to-date. It is advantageous because theyare simple to understand and easy to change. They arethe simplest and least complex means of portrayingprogress and can easily be expanded to identify specific

0263-7863/02/$22.00 # 2002 Published by Elsevier Science Ltd and IPMA.

PII : S0263-7863(01 )00063-1

International Journal of Project Management 20 (2002) 561–567

www.elsevier.com/locate/ijproman

* Corresponding author. Tel.: +886-3-5374281; fax: +886-3-

5373771.

E-mail address: ccwei@chu.edu.tw (C.-C. Wei).

activity that may be either behind or ahead of the sche-dule. However, there are major drawbacks in the use ofa bar chart. Firstly, Ganntt charts do not show theinterdependencies of the activities. The relationshipbetween activities is crucial for controlling project costs,without this relationship, Ganntt charts have little pre-dictive value. Secondly, Ganntt chart can not show theresult of either an early or a late start in activity.Finally, Ganntt charts do not show the uncertaintyinvolved in performing the activity and, therefore, donot admit itself to sensitivity analysis.The primary goal of a CPM analysis of a project is the

determination of the critical path, which determines theminimum completion time of a project. The computa-tion analysis includes forward pass and backward passprocedures. The forward pass determines the earlieststart time and the earliest completion time for eachactivity in the network, while the backward pass deter-mines the latest start time and the latest completion timefor each activity. During the forward pass computation,it is assumed that each activity begins at its earliest starttime. In other words, an activity can begin as soon as itspredecessor is finished. The completion of the forwardpass determines the earliest completion time of the pro-ject. The backward pass analysis is the reverse of theforward pass analysis. The project begins at its latestcompletion time and ends at the latest start time of thefirst activity in the project network. The activities on thecritical path have no float time, therefore, limitedresources must be first assigned to those activities toavoid project delay [5,6].The project evaluation and review technique can be

considered as an extension of CPM by incorporatingvariability in activity duration into project network.Thus, the potential uncertainty in activity duration isconsidered by using three time estimates for each activ-ity. The PERT formulas are based on a simplification ofthe expressions for the mean and variance of a betadistribution. The approximation formula for the meanis a simple weighted average of the three time estimates,with the end points assumed to be equally likely and themode four times as likely [5,7].

2. Heuristics for scheduling project

Traditionally, the resource-constrained project-sche-duling problem is tackled using the following methods:

1. Visual inspection: arrange resource utilizationsequence by visually inspecting the project net-work to provide limited resources to the activitiesin the critical path. The main objective is to com-plete the project as early as possible. This methodis only suitable for small and non-complicatedprojects requiring few resources [5,8,9].

2. Graphical method: this method provides limitedresources to the activities in the critical path. Here,two rules must be followed: (1) limited sourcesshould be first assigned to the activity with lesstotal float when several activities are under takenat the same time, and (2) resources should be firstassigned to the activity with less duration if totalfloats of activities are identical [5].

3. Heuristic method: this method is suitable for largeand complex projects. It seeks the near-optimalproject schedule using criteria such as: (1) theactivity with the longest duration first (LAF); (2)the activity with the shortest duration first (SJF);(3) first come first serve (FCFS); (4) the activitywith the latest finish time first (LFT); (5) theactivity with the smallest earliest completion timefirst (MEF); (6) the activity with the smallest slacktime first (MSF); (7) the activity with the largestslack time first (MSF); (8) the activity with thelargest ratio of the resource over activity time first(ROT) [5,9–13].

The existing project scheduling software commercia-lized include Super Project Expert, Timeline, Primavera,Microsoft Project for Windows, Harvard Total ProjectManagement, Permaster Advanced and Hornet. Mostof them use PERT and CPM to compute the earliestand latest completion time. Some of them provideresource-leveling capability to resolve resource conflict.However, most software does not allow segmentation ofthe activity and extension of the task duration. There-fore, when applied for resource leveling, all softwaresgive similar results [14,15]. It means that the computer-aided-resource-leveling remains unclear and needs fur-ther investigation.

3. Existing TOC for scheduling project

TOC uses the global safety time to schedule the pro-ject, and stresses that a system must have a constraint.Otherwise, its output would increase without the upperbound. Thus, TOC project management focuses on theconstraint that blocks the achievement of goal of theproject. Five steps used to apply the TOC skill to theproject scheduling are given below [16–20].

1. Identify the project constraint.2. Exploit the project constraint.3. Subordinate everything else to the project constraint.4. Elevate the project constraint, and5. If, in the previous step, a new constraint has been

uncovered, repeat the process. Do not let inertiabecome the project constraint.

Fig. 1 is an example of project network adopted todemonstrate the project-scheduling problem when the

562 C.-C. Wei et al. / International Journal of Project Management 20 (2002) 561–567

resource is limited and conflicted. The critical path isdenoted using the bold line (activities B and G), and theproject length is found to be 19. The problem indicatesthat there are four units of resource to be used in activ-ities A, B, D, E, F, G and H. The parentheses (4, 2) of Adenote that the duration of the activity A is 4 and theresources needed are 2 units.Using the existing TOC approach, the critical chain

due to the resource constraint is obtained as shown inbold line later (Fig. 2). The project length is now exten-ded up to 29.25.

4. Enhanced TOC for scheduling project

The existing TOC project-scheduling technique suffersfrom several drawbacks that are summarized below:

1. The right time to apply the project buffer andfeeding buffer is not clear in TOC.

If they are established at the project planning phase,by applying 50–50% cut [1] to the activity duration,the original schedule finalized by the project leaderwill be overruled and this could damage the reputa-tion of the project leader. On the other hand, if theyare established at the stage of proposing the activityduration to the project leader, who then, can apply50% duration cut to the activity. Consequently, theactivity duration will be overestimated by the per-sonnel responsible for the task thereafter to compen-sate the duration cut.

1. The duration cut is not applicable to all activities.

The difficulty and duration of activities are not iden-tical, applying 50% cut to all tasks could unreason-ably shorten certain tasks. For example, construction

of one floor requires 10 days to continue to the nextoperation, a 50% cut can deteriorate the quality ofthe building. Therefore, different cutting ratios mustbe used for different tasks.

1. There is no rule to establish the resource buffer.

After establishing the project buffer and feeding buf-fer, a forewarned resource buffer must be deployed infront of the critical chain activities sharing the sameresources. However, a clear guideline remains non-existent.

The enhanced TOC scheduling approach proposes aclear guideline for conducting the activity duration cutand establishing the various buffers on the critical chain.It emphasizes both the strategic and practical perspec-tives to adapt the dynamic change of the project envir-onment. The implementation procedures are brieflydescribed later.

4.1. Implementation procedures

Step 1. Determine the critical path and project length(T1) without considering the resource constraint, andobtain the critical chain and project length (T2) usingheuristics when the resources are limited.

Step 2. Compute the duration cut ratio (C.R.= T1/T2), where T1/T241, and modify the critical chainwhen no other resource utilization alternatives arefeasible.

Step 3. Use the strategic project flexible coefficient(kP) and the practical activity flexible coefficient (kA

m)to modify the revised critical chain (R.C.C.). Theproject flexible coefficient allows the management torectify the project length by considering the strategicfactors, such as market pressure, delay penalty, etc.,while the activity flexible coefficient enables the pro-ject leader to control the activity based on its uniquefeature by using strict, moderate and loss means.

(a) If resource constraint is resulted form strategicfactors, for example, equipment is too expensive to bepurchased, the management may decide not to procurethis machinery etc. The project flexibility coefficient cannow be applied to revise the critical chain.

R:C:C Pð Þ ¼ TFIN þ kP ð1Þ

where TFIN is the original project length, and kP is theadjusted time, kP > 0 denotes that the managementdecides to lengthen the project after considering allstrategic factors. However, the following inequalitymust be maintained.

If kP > 0; T1 < TFIN þ kP 4T2 ð2Þ

Fig. 1. Critical path of example network.

Fig. 2. Resources constrained critical chain using existing theory of

constraint (TOC) approach (Critical chain: A–D–E–G–H–P.B; Project

length=29.25; F.B, feeding buffer; P.B, Project buffer).

C.-C. Wei et al. / International Journal of Project Management 20 (2002) 561–567 563

If kP <0, meaning that the management decides toshorten the project length using means, such as thepurchasing of additional equipment and recruitment ofworkers. In this case, the following inequality shall behold,

If kP < 0; 0 < TFIN þ kP 4T1 ð3Þ

(b) The activity duration can also be adjusted by theproject leader based on project features, however, theproject length of the modified critical chain should notbe exceeded. The activity flexibility coefficient can onlybe applied to the activities associated with resourceconstraint on the critical chain. Considering the activityflexibility coefficient, the project length (R.C.C(A)) canbe expressed as given below in Eq. (4).

R:C:C Að Þ ¼ TFIN

þX

m2U

tm2 � tm1� �

� kmA

� �4TFIN þ kP

¼ R:C:C Pð Þ ð4Þ

where U is the set of resource-constrained activities; tm1is the activity duration not considering resource con-straint; tm2 is the activity duration considering resourceconstraint; 04 km

A , m indicates the resource-constrainedactivities on the critical chain.

Step 4. Establish the resource buffer (flag time) infront of the resource-conflicted activity on the criticalchain to enhance the effectiveness of resource con-straint project management. Two conditions shouldbe satisfied:

(a) The flag time (F.T m) of each activity must followthe inequality (5).

04 F:Tmð Þ4 tm2 � tm1� �

ð5Þ

(b) The total flag time of all activities should agreewith inequality (6).

04X

m2U

F:Tmð Þ4X

m2U

tm2 � tm1� �

ð6Þ

Step 5. Periodical monitor the important point suchas milestone in order to review the conditions ofproject performance both in strategic and practicalaspects to avoid any substantial change of the projectschedule.

The earlier implementation procedures are applied tothe example project shown in Fig. 1, and the detailedsteps are described later:

Step 1. Determination of T1 and T2, T1=19 (Fig. 1),T2 can be obtained using the existing heuristics.

(a) The project length is obtained as T2=39(TFIN=39) using ACTIM method (Activity Time) asshown in Table 1. Where ACTIM value of activity A,i.e. arrow (1–2; Fig. 1), is computed as ACTIM(A)=Max{4+11+2, 4+6+8}=18, i.e. summation of timefor route A–E–H and route A–D–F.(b) The project length is obtained as T2=39

(TFIN=39) using LFT method.(c) The project length is obtained as T2=39

(TFIN=39) using ACTRES (Activity Resource)method. Where ACTRES value of activity A, i.e. arrow(1–2; Fig. 1), is computed as ACTRES(A)=Max{4�2+11�2+2�1, 4�2+6�4+8�1}=40, i.e. sum-mation of duration times resources needed for routesA–E–H and route A–D–F.

Therefore, when considering the resource constraint,the project length is extended to T2=39 (the bestheuristic solution) from the original project scheduleT1=19 (critical path). The resource constrained pro-ject network is depicted in Fig. 3.

Step 2. Computation of the duration cut ratioC.R.=T1/T2.C:R: ¼ 19=39 ¼ 48:8%The duration of each activity on the critical chain isnow reduced by 48.8%, for ease of computation,50% is used to revise the schedule (Fig. 4).

The total project length is now changed to 20 from 39after duration cut, this is the first article that providesrational means to decide the duration cut.

Table 1

Resources constrained project length using ACTIM methoda

Activity

1–3 1–2 3–6 2–4 2–5 3–4 4–6 5–6

ACTIM value 19 18 16 14 13 10 8 2

Activity time 3 4 16 6 11 2 8 2

Resource needed 1 2 3 4 2 0 1 1

Earliest start time 0 0 3 4 4 3 10 14

Actual start time 0 0 4 20 26 3 26 37

Actual finish time 3 4 20 26 37 5 34 39

a ACTIM, activity time.

Table 2

The levels of kmA

Importance kmA Easiness kmA

Very high 0 Very high 0

High 1/4 High 1/4

Moderate 1/2 Moderate 1/2

Low 3/4 Low 3/4

Very low 1.0 Very low 1.0

564 C.-C. Wei et al. / International Journal of Project Management 20 (2002) 561–567

Step 3. Use of strategic (project) and practical (activ-ity) flexible coefficients kP and km

A to modify therevised critical chain (R.C.C.).The activity flexibility coefficient km

A can be adjusteddepending on the importance and the easiness of theactivity. Table 2 suggests the levels for the km

A values.

(a) Assign kmA to each resource constrained activity on

the critical chain. It is assumed that the importance andeasiness of the resource constrained activities A, D, E,G, H are listed later:

Activity A D E G H

Importance 1/2 0 3/4 1 1/4Easiness 1/2 3/4 1/2 1/4 0

(b) Use matrix analysis to combine the importanceand easiness into single index. Three kinds of combina-tions can be used: Strict control: choose the minimalvalue of km

A to complete the project as early as possible.

kmA ¼ Min importance km

A ; easiness kmA

� �ð7Þ

Normal control: use the average of the two kmA values

and 04kmA41.

kmA ¼ Avg importance km

A ; easiness kmA

� �ð8Þ

Loss control: give more slack time to the worker.

kmA ¼ Max importance km

A ; easiness kmA

� �ð9Þ

If the project leader wants to control the activitystrictly, the matrix analysis can be obtained asTable 3.If kP=0 and the resource constrained activities arestrictly controlled, the R.C.C(A) can be obtained asbelow:

R:C:CðAÞ ¼ 20þ ½ð4� 2Þ � 0:5þ 0þ ð11� 6Þ

� 0:5þÞ16� 8Þ � 0:25þ 0

¼ 26

The network is now changed to Fig. 5, where durationA, E and G is lengthen. Take activity A as an example,(4–2)�0.5=1 is added to duration of A, which is 2 inFig. 4, as a result, the duration of A in Fig. 5 becomes 3.

Step 4. Establishment of resource buffer (Flag time)in front of the resource-conflicted activity on the cri-tical chain to trigger the management intervention.

FTA=2 (Fig. 5) denotes that 2 days before A starts,the resources must be checked.In this case, total flag time 42(A)+3(D)+5(E)

+8(G)+1(H)=19

Step 5. Periodically monitor the progress of activitieson the critical chain coupled with the performanceevaluation mechanism to prevent the project frombeing delayed due to unexpected changes.

To reveal the applicability of the proposed approach,the presented enhanced TOC scheduling technique iscompared with the previous heuristics and the existingTOC method, and the result is summarized in Table 4.

Table 3

The matrix analysis of strict controlled kmA

Easiness

Level

Importance

A D E G H

1/2 0 3/4 1 1/4

A 1/2 1/2

D 3/4 0

E 1/2 1/2

G 1/4 1/4

H 0 0

Fig. 4. Resources constrained critical chain after duration cut.

Fig. 5. Critical chain for kP=0 and strict control.

Fig. 3. The resources constrained critical chain using heuristics.

C.-C. Wei et al. / International Journal of Project Management 20 (2002) 561–567 565

However, several issues should also be carefully man-aged to efficiently apply the enhanced TOC technique tothe project scheduling problem, they are,

1. All project members should be made aware of theproject objective and their own role in order toprevent project from being delayed due to uncer-tain factors.

2. Use of the specialized subcontractors to avoid theinexperienced technical problems and to focus onthe project control issues.

3. Apply the effect of learning curve to reduce theactivity duration and project length [21].

4. Analyze the utilization efficiency of each resourceand performance of activity to ease the projectcontrol decision [21,22], however, the inequalitiesconcerning the project and activity flexible coeffi-cients should be complied.

5. Proper trade-off between time and cost [23,24].6. Conduct risk analysis of kP and km

A to prepare thecontingency plan.

5. Conclusions

The enhanced TOC project scheduling techniquedetermines the lower bound of the project length byusing the combination of the existing heuristic algo-rithms. The lower bound is then used to conduct theactivity duration cut and establish project buffer, feed-ing buffer and resource buffer. The enhanced TOC isbetter than the existing TOC in the following two ways:

1. It provides rational guideline for controlling theproject length practically.

2. The project schedule can be globally and strategi-cally adjusted using kP, and locally and practicallycontrolled using km

A and, therefore, it can be com-pleted in a rational and quick fashion.

Future researches can be directed in the areas listedlater:

1. The trade-off between project length, project costand project quality.

2. The practical approach for scheduling multi-pro-ject sharing multi-resource.

3. The concrete guideline for obtaining the projectflexible coefficient kP.

4. The relation among the activity flexible coefficientkmA , the resource buffer and the flag time.

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Table 4

Comparison of enhanced TOCa with other methods

Methods Advantages Disadvantages

Heuristics 1. Apply algorithm to find the optimal

or near-optimal project schedule

1. Optimal solution is not guaranteed

2. One algorithm may not be suitable for all projects

3. Computation is tedious for large and complex projects

4. The strategic and environmental aspects are not considered

Existing TOC 1. Use systematic approach to find critical

chain and establish related buffers

1. Lack of guideline to establish project, feeding and resource buffers

2. Stress global management of conflicted

resources and strategic issues

2. Use passive approach to establish buffers without active measures

to shorten the project length

3. Unclear definition of estimation and reduction of activity duration

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practical (local kmA ) aspects to control the

project schedule

1. All dynamic factors affecting the activity duration and project

length should be included to manage the project schedule correctly

2. Propose guidelines to establish various

buffers and activity duration cut to shorten

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