Quality, Time, And Cost Tradeoffs in Project Management Decision Making

Quality, Time, and Cost Tradeoffs in Project Management Decision Making

Matthew J. Liberatore1, Bruce Pollack-Johnson2 1Villanova University, Department of Management and Operations, Villanova, PA - USA

2Villanova University, Department of Mathematical Sciences, Villanova, PA - USA

Abstract--This paper presents a mathematical programming model that allows quality to be explicitly considered in project planning and scheduling, while addressing the tradeoffs between quality, time, and cost. A quality function is used to represent the relationships between time, cost, and quality for individual tasks. The initial problem formulation maximizes the minimum quality (weakest link) over all project tasks, subject to bounds on cost and completion time. Using a construction example we show how this model can be adapted to generate quality level curves to illustrate the trade-offs among time, cost, and quality. These level curves can then be used by project managers to make project scheduling decisions that explicitly model and consider quality as well as time and cost, so that better and more appropriate decisions can be made for a particular situation. We also offer some managerial insights for project planning and scheduling that are derived from the analysis through improved understanding of these choices and tradeoffs.

I. INTRODUCTION

Project planning and scheduling research has focused on managing the relationship between time and cost, with little if any attention directed to quality. However, in most situations there are alternative approaches for completing each task, each having its own values of time, cost, and quality. Quality differences can arise due to bids offered by competing subcontractors to complete specific tasks. Even different bids by the same subcontractor could imply different quality levels. Also, subcontracts might have some flexibility with time and cost to allow for different quality levels of the same task. This can also be true for alternative work plans offered in-house.

In this paper we introduce the notion of a quality function for individual tasks in terms of time and cost, and incorporate quality at the task level into an analytic model for project planning and scheduling. We show how the problem of maximizing the quality of the weakest link subject to time and cost limits can be formulated and solved. An alternative formulation leads to the creation of iso-quality curves that will allow managers to evaluate the tradeoffs between time, cost, and quality across the project. Using either formulation, the results lead to specific decisions about the planned values for each task along these three dimensions. We also offer some managerial insights for project planning and scheduling that are derived from the analysis through improved understanding of these choices and tradeoffs.

II. LITERATURE REVIEW A. Project Quality

“Quality management has equal priority with cost and schedule management” [7]. The International Organization for Standards (ISO) has set forth ISO 9000 as a set of international standards for both quality management and quality assurance that has been adopted by over 90 countries worldwide. ISO 9000, clause 3.1.1 defines quality as “the degree to which a set of inherent characteristics fulfills requirements” [5].

The ISO 9000 definition of quality has been adopted by the Project Management Body of Knowledge [15]. The PMBOK considers quality planning, quality assurance, and quality control. According to the PMBOK, quality must address both the management of the project and the product of the project. However, the manner in which quality considerations influences the design, planning, and scheduling of individual project tasks is unclear.

Overall project quality could be assessed using a measure of customer-perceived service quality such as SERVQUAL [13], or by developing a related measure that is targeted to a specific situation, e.g., [19]. A study conducted by the Quality Performance Measurements Task Force of the Construction Industry Institute produced the quality measurement matrix [17] and led to the development of a methodology to measure quality performance of engineer-procure-construct (EPC) projects [18]. The focus of this Total Quality Management (TQM) approach is on identifying and then tracking critical quality measures for each project phase.

Karnes et al. [6] identified nine dimensions of product quality and then applied the Analytic Hierarchy Process (AHP) to measure overall quality. Along the same lines but from the project perspective Paquin et al. [12] contend that a method for assessing quality must enable project managers to elucidate and structure the client’s needs and expectations. Client satisfaction can be decomposed into a hierarchical structure of quality criteria or dimensions. This is performed through a top-down process whereby the more general objectives are decomposed into lower-level objectives in greater detail. The project manager and the client must jointly determine the rules by which objective as well as subjective quality criteria are to be measured and aggregated. A multicriterion approach such as the Analytic Hierarchy Process or AHP [16] can be used for this purpose. Paquin et al. [12] apply the multicriterion approach to measure planned quality of work scheduled and work performed, and earned

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quality of work performed by task during the course of the project.

In the present research we are interested in measuring planned quality of work for different designs of specific project tasks so that the project manager can evaluate the tradeoffs between quality, time, and cost. Following the general approach of [12], Pollack-Johnson and Liberatore [14] illustrate how the quality of a task option can be determined using the AHP. This example shows how quality of different approaches for laying a foundation in construction could be related to two quality attributes: compressive strength of the concrete used, and the depth of the excavation. An alternative approach for measuring quality at the task level is to make a direct subjective assessment of quality [1], [8]. Our method for modeling quality at the task level can incorporate either the multicriterion or subjective assessment approaches.

B. Relationships between Quality, Time, and Cost

The relationships between quality, time, and cost have been studied and modeled in the new product development literature. Morgan et al. [11] model the time to market versus quality tradeoff when there are multiple product generations. Decisions relate to the number and length of development cycles and intensity of development in each period. They assume that quality and cost increase with time spent in development, that firms can spend more (less) money per period to increase (decrease) the rate of quality improvement, and that firms engage in efficient new product development so they cannot simultaneously reduce development time (to achieve a given level of quality) and development cost.

In the project management literature the relationship between time and cost has been studied with and without consideration of their relationship with quality. The literature contains linear, nonlinear, and discrete formulations of the time-cost problem. The linear formulation assumes that each activity’s time can range over a closed interval, and that the cost of completing the activity is linear and decreasing over the interval [2]. The nonlinear problem in its simplest form has been modeled using a piecewise linear representation of the time/cost tradeoff for each activity [10], to represent the common situation in which it becomes proportionately more expensive to reduce duration by each successive time. The discrete version requires specifying a set of discrete processing times and associated costs for each project activity, which is a different way to model nonlinearity. Convex [4] and quadratic [3] crashing functions have been studied and modeled. A review of the time-cost literature can be found in [2].

Babu and Suresh [1] present a linear programming model that addresses time, cost, and quality in project management. Their approach is to associate both a normal cost and a normal quality with a normal activity time, and a crash cost and crash quality with a crash activity time. They assume a linear crashing relationship for both cost and quality as functions of time, and optimize one objective with bounds on

the others. That is, quality is assumed to depend only on time and is independent of cost for a given time, a major limitation of their approach. Project quality is measured as the arithmetic or geometric mean of the quality of the activities or as the minimum quality of the activities. Iso-curves are used to show the relationships between two of the three factors, with the other held at constant levels.

Khang and Myint [8] applied the method found in [1] to an actual cement factory construction project. In both papers the quality levels associated with all normal times was set at 1.0, while the lower quality level at the crash time for each activity was measured relative to this level. The linearity assumption between quality and time was found to be problematic. The authors found that the most difficult and controversial task was to assess the quality reduction associated with crashing. The authors suggested the need for a more holistic measurement of performance quality and a more realistic model to describe the relationships between the quality of individual activities (and therefore of the whole project) and the budget and time allowed. In response to the suggestion in [8] and the limitations of [1], in this research we model quality at the task level as a nonlinear function of both cost and time.

III. THE MODEL

A. Developing the Quality Function

Our approach begins by formulating a model of the quality of each task as a function of the time (t) and cost (c) allocated to it. We assume that there could be different entities who could perform the task (individuals or groups, subcontractors, etc.), and that each entity could do the job with different allocations of time and budget. Each entity would have its own quality function in terms of time and cost. If those quality functions are graphed on the same time/cost/quality axes, then the overall quality function for the task that we are interested in is the maximum, or the upper envelope, of the individual entity quality graphs. This approach is consistent with the assumption of efficiency in new product development found in [11]. Figure 1 shows an example for three different entities that could perform a particular task. Graph (a) shows three individual quality surfaces for a given task, and graph (b) shows the upper envelope of these three surfaces, which we consider the overall quality surface for this task.

We assume that this overall quality function for a task has two basic properties: � Holding time constant, quality is increasing in cost. Thus

if time is fixed, we assume that spending more money on the task will increase quality.

� Holding cost constant, quality is increasing in time. Thus if cost is fixed, we assume that spending more time on the task will increase quality.

If we normalize quality to be on a 0-100 scale, and limit

time and cost to reasonable values for the task at hand, based

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on the two nondecreasing assumptions above, we would expect the graph to show quality being lowest at the corner of the domain with the smallest values of time and cost and highest in the opposite corner (the highest values of time and cost). For a fixed quality, we would expect a time/cost tradeoff curve that is decreasing and convex. Thus, to

maintain the same level of quality, to reduce the time, one has to pay increasingly more money per unit, such as in standard project activity crashing [2]. This suggests a basic hill shape rising out of a plain, although we would only be interested in a one-quarter wedge of the hill (such as the individual quality curves in Figure 1a).

(a) 3 individual quality graphs (b) the upper envelope overall quality graph

Figure 1: Quality graphs

A familiar mathematical functional form that has this

shape is the bivariate normal distribution in probability. We propose using this functional form for the overall quality function for each task. Our quality function is normalized so that the maximum time ( μt ) and cost ( μc ) values considered reasonable correspond to a quality of 100. The “standard deviation” parameters ( �t and �c ) give a measure of how slowly the quality drops from the top of the hill compared to the maximum values for time and cost, respectively. Thus, our resulting quality function is given by

� � � �2 2

( , ) 100t ct c

t cQ t c e� �

� ��

� � � �� (1)

The quality curves in Figure 1 are of this form. We have

eliminated the ½ in the exponent, which means that each � in the quality function definition would be multiplied by �2 to be interpreted as the usual � in the bivariate normal distribution. Notice that if we hold either variable constant, the marginal graph for the other will be a bell curve (actually, a subset of a graph that is a constant multiple of a normal distribution curve). Notice also that the upper envelope graph may not be smooth, but we are assuming that we can fit a smooth function that is a reasonable estimate of the upper envelope. For a given value of quality using this bivariate normal functional form, there is a nonlinear relationship between time and cost, generalizing the standard linear approach. This quality function is increasing with respect to both time and cost (holding the other constant), consistent with the assumption of efficiency in new product development [11]. This version of the bivariate normal

distribution upon which this functional form is based assumes independence of the two random variables. We have chosen this version for a simpler model, but the dependent version could also be used, with one more parameter, corresponding to the correlation/interaction between the variables. B. Quality Function Estimation

In situations where n bids, alternative work plans, or scenarios specifying levels of quality, time, and cost ( , , )j j jq t c have been received for a given activity, the four parameters of the bivariate normal function can be determined using nonlinear least squares estimation:

Minimize 2

1{ ( , | , , , ) )

j j j j

n

j j t c t c jj

Q t c q� � � ��

�� (2)

It is necessary to add the constraints: , 1, 2,...,

, 1, 2,...,j

j

j t

j c

t j n

c j n

�

�

� �

� � (3)

because the μ parameters are upper bounds on the values of the t and c variables. C. Model Formulation

To model the quality-time-cost tradeoff problem, we start with standard assumptions for modeling projects: that the project network has no cycles, that the start activity (activity 0, a dummy activity) is the only activity that is not an immediate successor of any activity, and that the finish activity (activity �+1 , also a dummy activity) is the only activity that has no successors. It is common to use

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predecessors rather than successors for project scheduling formulations of this type, but for this example, the formulation turns out to be much more concise and elegant using successors. Define the following parameters and variables:

ti = the duration of activity i , for i = 1,…,� ci = the cost of activity i , for i = 1,…,� qi = the quality of activity i , for i = 1,…,� Si = the set of activities that are immediate successors of

activity i , for i = 0,…,� TUB = upper bound on the total project time CUB = upper bound on the total project cost si = the scheduled start time for activity i , for i =

0,…,�+1

minit = lower bound on the duration of activity i , for i =

1,…,�

minic = lower bound on the cost of activity i , for i =

1,…,�

Relevant quality measures from a project perspective could involve maximizing average quality, or maximizing minimum quality, of the tasks. We select the latter, Qmin , as our quality metric, since from a systems perspective if the project is viewed as an integrated set of activities, the quality of a project is only as high as its weakest link. Qmin is defined as:

Qmin = min1

iqi ��

(4)

The quality-time-cost problem can be thought of as having three objectives, and can be modeled as a goal programming problem. In our formulation, we first maximize Qmin while setting an upper bound on total project cost and total project time. The nonlinear program is given as equations (5) – (17) below:

minMaximize Q (5) subject to:

min , 1, 2, ,...iQ q i �� (6)

� �2 2( , ) 100 * exp [( ) / )] [( ) / )]i i i i i ii i i t t i c cq Q t c t c� � � �� ,

1,2,,...i �� (7)

1

�

i UBi

c C�

�� (8)

0 0s � (9) 0,..., ,k i i is s t i � k S� � � � � (10)

1� UBs T � (11) 0 1,..., 1is i �� (12)

min , 1, 2,...,iit t i �� (13)

min , 1, 2,...,iic c i �� (14)

, 1,2,...,ii tt i �� (15)

, 1, 2,...,ii cc i �� (16)

, , 0, 1, 2,...,i i iq t c i �� (17) Equation (6) is a modeling device to obtain the minimum

of the iq . The mathematical program is nonlinear due to Equation (7), the bivariate normal quality function. Equations (8) and (11) set bounds on project cost and completion time, respectively. Equation (10) is needed to enforce the successor relationships among the tasks in the network. Lower bounds on the time and cost variable values are set by equations (13) and (14), respectively. These bounds are normally based on the smallest completion time and cost possible for each activity. Equations (15) and (16) reflect the upper bounds on the cost and time for each activity imposed by the definition of the quality function, although other values for the upper bounds could be considered. The independent decision variables are the time and cost for each project activity (which determine the quality for each activity). This problem can be solved using Lingo’s global solver [9] and generalizes the standard time/cost tradeoff problem [2]. D. Construction Example

A general contractor planning to start construction of a new house has organized the project into activities, with corresponding immediate successor activities, as given in Table 1. The precedence relationships are shown in Figure 2. She has put the various activities individually up for bids, and has received bids for both duration and cost from different subcontractors. These bids were used to estimate the bivariate normal quality functions for each activity, with parameters given in Table 1.

To illustrate the process of quality function estimation, activity 3, Erect Rough Wall and Roof, had three quality, time, and cost (q, t, c) bids: (80, 4, 28.8), (70, 3, 39.6), and (90, 4, 35.0). The quality of these bids may differ in terms of the quality of the materials used and the skill of the workmen employed. This means that task 3 can be completed in 4 days for $28,800, at a quality level of 80 (option 1). It could also be completed in 3 days for $39,600, but the quality would go down to 70 (option 2; for example, workers are added to reduce the completion time, but are less skilled). Finally, to complete the task in 4 days but at a higher quality of 90, the cost would need to go up to $35,000 (option 3, up from the $28,800 of option 1 with the same 4 day completion time). Using nonlinear least squares estimation as described above (using (2) and (3), n = 3 bids) yields ( 4, 1.79, 48.6, 42)t t c c� � � �� as the bivariate quality function parameters for activity 3 shown in Table 1.

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TABLE 1: TASK, IMMEDIATE SUCCESSOR, AND QUALITY FUNCTION INFORMATION FOR CONSTRUCTION PROJECT IMMEDIATE QUALITY PARAMETERS TASK DESCRIPTION SUCCESSORS ( , , , )t t c c� � � � 0 START 1 dummy activity 1 Excavate and Pour Footers 2 (4.01, 11.3, 52.4, 52.4) 2 Pour Concrete Foundation 3 (2, 2.33, 11.2, 8.52) 3 Erect Rough Wall & Roof 4,5,6 (4, 1.79, 48.6, 42) 4 Install Siding 11 (13, 19, 79.2, 99.4) 5 Install Plumbing 7 (3, 1.62, 26.6, 20.4) 6 Install Electrical 7 (10.9, 12.8, 29.7, 77.9) 7 Install Wallboard 8,9 (5, 2.73, 16.8, 8.05) 8 Lay Flooring 10 (8.09, 7.18, 64, 67.5) 9 Do Interior Painting 10 (4.57, 4.3, 16.8,12.7) 10 Install Interior Fixtures 13 (8.40,11.9, 9.94,7.03) 11 Install Gutters & Downspouts 12 (2, 12, 17.7, 18.9) 12 Do Grading & Landscaping 13 (3.36, 2.4, 21.5, 12.3) 13 FINISH -- dummy activity

The solution to this problem, with T = 26 and C= 185.3

(and with the lower bounds on time and cost for each activity again assumed to be 30% of their upper bound � values), is given in Figure 2, using the Global Solver in LINGO [9]. The critical path is indicated in bold. The optimal value of Qmin is 73.4, and the time and cost limits are binding. The quality values are all equal to the optimal value of Qmin .

Note that for non-critical-path activities, LINGO may find optimal solutions that do not necessarily start at the earliest start times (e.g., activities 4 and 5 in Figure 2). However, since using slack does not affect quality, time, or cost of an activity, there are a range of alternative optimal solutions having different start times.

KEY: s i

7.288 20.483 22.562

0.0 0.0 1.833 3.283 7.291 16.107 26.000

11.872 23.479

7.210 18.893

0.0 0.0 00.0 N/A

1.8 0.0 125.1 73.4

1.4 0.0 26.9 73.4

3.9 0.0 325.3 73.4

3.0 1.7 515.3 73.4

4.7 0.0 68.9 73.4

4.2 0.0 712.9 73.4

7.4 0.0 8

27.1 73.4

4.6 2.8 99.7 73.4

2.5 0.0 108.1 73.4

13.0 0.4 424.0 73.4

2.0 0.4 117.2 73.4

3.4 0.4 1214.7 73.4

0.0 0.0 130.0 N/A

t i slacki

task i

c i q i

Figure 2: LINGO solution to construction Max Qmin example with T = 26 & C = 185.3 E. The Minimum Cost Formulation

An alternative formulation of the problem considers minimizing total project costs with bounds on project completion time and quality. In the problem formulation (5) – (17), the objective in (5) becomes minimizing total cost or

1

�

ii

c�� , thus eliminating equation (8), and then specifying a

lower bound for project quality in equation (6), which becomes

, 1, 2, ,...LB iQ q i �� (20) Figure 3 shows an optimal solution for a single run of this

model using QLB = 65 and TUB = 26 . An inspection of Figure 3 shows that activity 6 does not have a quality at the lower bound of 65. This is because its quality at its minimum time and cost values is 65.3, above the quality lower bound.

The minimum cost formulation presented above relates to the standard time/cost tradeoff problem. The latter implicitly assumes a fixed level of quality, while the former allows quality possibly to be higher for some tasks.

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KEY: s i

8.126 14.552 16.167

0.0 0.0 2.550 4.172 8.396 15.855 26.000

11.396 23.479

8.126 18.909

0.0 0.0 00.0 N/A

2.6 0.0 118.7 65.0

1.6 0.0 25.8 65.0

4.0 0.0 321.1 65.0

3.0 0.3 513.2 65.0

3.3 0.0 68.9 65.3

4.5 0.0 711.8 65.0

7.6 0.0 8

19.9 65.0

4.6 3.1 98.5 65.0

2.5 0.0 106.9 65.0

6.4 6.5 423.8 65.0

1.6 6.5 115.3 65.0

3.4 6.5 1213.4 65.0

0.0 0.0 130.0 N/A

t i slacki

task i

c i q i

Figure 3: LINGO solution to construction min cost example with T = 26 & QLB = 65 F. Quality Level Curve Graphs

Analyzing the minimum cost model for different total project times UBT , we can find the minimum cost possible that finishes the project within a given time and maintains a minimum quality of at least the lower bound. A set of iso-quality (level) curves for the construction example is shown in Figure 4. Computational times for all runs were less than 0.5 seconds. These iso-quality curves assist managers in evaluating the tradeoffs between time, cost, and quality across the project.

150

175

200

225

250

275

18 19 20 21 22 23 24 25 26 27

critical path length

tota

l cos

t

6566676869707172737475

Figure 4: Iso-quality curves for construction example

Notice that the graph for a higher quality level lies above and to the right of that for a lower quality level. As shown in

Figure 4, in some cases it is not possible to obtain a higher level of quality at a low critical path length (a critical path length of 18 is not feasible for quality values of 71 or greater, and a length of 19 is not feasible for a quality value of 75). Each iso-curve in Figure 4 provides the concave time-cost tradeoffs traditionally discussed in the project management literature. The graph in Figure 4 provides a concise summary of the relationship among quality, time, and cost, and can be used by the project manager to make well-informed decisions about how to execute the project in terms of specific decisions about the work plans for all project tasks.

The iso-curves also show an overall nonlinear relationship between time and cost based on nonlinear time/cost tradeoffs for each activity that are embedded in the individual quality functions, generalizing the standard linear approach in a straightforward manner. For some quality levels, there seem to be budget threshold values of project times that are probably not worth the crashing effort (a similar point is made in [8]). For example, for the quality level of 75 in Figure 4, it will probably not make sense to try for a project time of 19 days or less, since the cost increase of reducing from 20 days to 19 days is so much more than the cost of reducing from 21 to 20 days.

IV. CONCLUSIONS Quality is acknowledged to be an important component of

project management, but previously has received limited consideration in planning and scheduling. The standard implicit assumption is that time/cost trade-offs are evaluated given that some unspecified and unknown level of quality exists for each task. However, in many situations project managers must evaluate alternative options for accomplishing project activities, and these involve differing levels of time, cost, and quality. In such situations it makes sense to analyze the relationship between cost, time, and quality, and decide on their levels for each project task that best achieves the

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project’s objectives. We have introduced the concept of a quality function that represents the relationships between quality, time, and cost for each task. Using this quality function we have presented a nonlinear programming model for the quality/time/cost problem. The basic problem formulation seeks to maximize minimum project quality over all project tasks, subject to bounds on cost and completion time. We then modified the problem formulation to minimize cost with bounds on project quality and completion time and showed how quality level curves can be a very useful managerial tool in making final project planning and scheduling decisions that explicitly model and incorporate quality. These iso-curves depict a nonlinear relationship between time and cost, generalizing the time-cost tradeoff problem.

Without explicitly considering quality, inferior decisions may be made concerning the planned levels of efforts for the various tasks. A key notion is that the quality of each project task is important and cannot be compromised without compromising the quality of the project itself. A conscious part of the project planning process should include identification of alternative work plans that consider the tradeoffs between quality, time, and cost. If time and cost considerations are inflexible, the quality maximization model presented here can help project managers to select work plans for individual tasks that will increase overall project quality. If there is some flexibility in time and cost considerations, the iso-curve analysis may lead to important realizations such as that a significant increase in quality can occur with minimal impact on time and cost, or that time and/or cost could be appreciably improved with minimal effect on quality. The modeling framework proposed can provide managerial insight on these issues and help to improve decision making in the project management planning and scheduling process.

Objective functions other than maximizing the minimum quality over all tasks are possible, such as maximizing average project quality or a weighted average of minimum and average project quality, or goal programming models using the three objectives. A consideration of these varying model objectives and their impact on optimal solutions can form the basis of future research.

REFERENCES

[1] Babu, A. J. G., and N. Suresh, “Project Management with Time, Cost, and Quality Considerations,” European Journal of Operational Research, vol. 88, pp. 320-327, 1996.

[2] Brucker, P., A. Drexl, R. Mohring, K. Neumann, and E. Pesch, “Resource-Constrained Project Scheduling: Notation, Classification, Models, and Methods,” European Journal of Operational Research, vol. 112, pp. 3-41, 1999.

[3] Deckro, R. F., J. E., Hebert, W. A. Verdini, P. H. Grimsval, and S. Venkateshwar, “Nonlinear Time/Cost Tradeoff Models in Project Management,” Computers & Industrial Engineering, vol. 28, pp. 219-230, 1995.

[4] Foldes, S., and F. Soumis, “PERT and Crashing Revisited: Mathematical Generalizations,” European Journal of Operational Research, vol. 64, pp. 286-294, 1993.

[5] International Organization for Standards, ISO 9000:2000, 2000. [6] Karnes, C. L., S. V. Sridharan, and J. J. Kanet, “Measuring Quality

from The Consumer’s Perspective: A Methodology and Its Application,” International Journal of Production Economics, vol. 39, pp. 215-225, 1995.

[7] Kerzner, H., Project Management: A Systems Approach to Planning, Scheduling, and Controlling (8th ed.). New York: Wiley, 2003.

[8] Khang, D. B., and Y. M. Myint, “Time, Cost and Quality Trade-Off in Project Management: A Case Study,” International Journal of Project Management, vol. 17, pp. 249-256, 1999.

[9] Lindo Systems (2008). Lingo Version 11.0. Chicago, 2008. [10] Moder J.J., C. R. Philips, and E. W. Davis, Project Management with

CPM, PERT, and Precedence Diagramming (3 ed.). New York: Van Nostrand Reinhold Company, 1983.

[11] Morgan, L. O., R. M. Morgan, and W. Moore, “Quality and Time-To-Market Tradeoffs When There Are Multiple Product Generations,” Manufacturing & Services Operations Management, vol. 3, pp. 89-104, 2001.

[12] Paquin, J. P., J. Couillard, and D. J. Ferrand, “Assessing and Controlling the Quality of a Project End Product: The Earned Quality Method,” IEEE Transactions on Engineering Management, vol. 47, pp. 88-97, 2000.

[13] Parasuraman, A., V. A. Zeithaml, and L. L. Berry, “SERVQUAL: A Multiple-Item Scale for Measuring Consumer Perception of Service Quality,” Journal of Retailing, vol. 64, pp. 12-40, 1988.

[14] Pollack-Johnson, B., and M. Liberatore, “Incorporating Quality Considerations Into Project Time/Cost Trade-Off Analysis and Decision Making,” IEEE Transactions on Engineering Management, 53(4), 534-542, 2006.

[15] Project Management Institute, A Guide To the Project Management Body of Knowledge (3rd ed), Newtown Square, PA, 2004.

[16] Saaty, T. L., The Analytic Hierarchy Process, Pittsburgh: RWS Publications, 1996.

[17] Stevens, J. D., C. Glagota, and W. B. Ledbetter, “Quality-Measurement Matrix,” Journal of Management in Engineering, vol. 10, pp. 30-35, 1994.

[18] Stevens, J. D., “Blueprint for Measuring Project Quality,” Journal of Management in Engineering, vol. 12, pp. 34-39, 1996.

[19] Yang, Z., M. Jun, and R. T. Peterson, R. T., “Measuring Customer Perceived Online Service Quality,” International Journal of Operations and Production Management, 24, pp. 1149-1174, 2004.

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Quality, Time, And Cost Tradeoffs in Project Management Decision Making

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