A practical approach to project scheduling

A practical approach to project scheduling: considering the potential qualitya Department of Industrial Engineering, Graduate School, Hanyang University, Seoul 133-791, Republic of Korea

A practical approach to project scheduling: considering the potential quality

a Department of Industrial Engineering, Graduate School, Hanyang University, Seoul 133-791, Republic of Korea

b Department of Industrial and Management Engineering, Hanyang University, Gyeonggi-do 426-791, Republic of Korea

c Department of Industrial and Systems Engineering, Kongju National University, Chungcheongnam-do 330-717, Republic of Korea

Received 16 April 2010; received in revised form 12 May 2011; accepted 31 May 2011

Abstract

Crashing project activities is a typical way to shorten their completion times to meet project due dates, and previous research on quality in

takes into account the potential quality loss cost (PQLC) in time–cost tradeoff problems is a practical approach, since individual activity quality is defined by conformance to project contractor requirements We propose a mixed integer linear programming model that considers the PQLC for excessive crashing activities This model will help project planners develop practical project schedules

Crown Copyright © 2011 Published by Elsevier Ltd APM and IPMA All rights reserved

Keywords: Project scheduling; Quality; Potential quality loss cost; Time –cost tradeoff; Critical path method

1 Introduction

Successful projects should be completed before project due

dates and within budget; however, these limits are sometimes

surpassed There may therefore be significant variance between

the assumptions made regarding a project and actual outcomes

Sudden unexpected changes in construction technology,

tech-niques, materials, or human resources can create budgetary and

scheduling pressures that in turn may increase the possibility of

failure (Zeng et al., 2007) A survey exploring the completion of

construction projects in Saudi Arabia showed that 76% of project

contractors experienced delays of 10–30% of the projected

duration (Assaf and Al-Hejji, 2006)

A typical technique used to mitigate scheduling pressure is to

crash project activities Crashing activities involves allocating

more resources (such as materials, labor, and equipment) than

planned in order to complete a project more quickly (Kessler and

In time–cost tradeoff problems, projects are not always completed as scheduled without reworking or modification A project is a one-time task constrained by time, cost, and quality, and its success depends on how well these constraints are balanced

burdens may fall on the other two Hence, crashing project activities should be considered a significant factor in the time–cost tradeoff problem

Some previous studies have treated quality as an important factor in tradeoff problems, claiming that overall project quality attained by project activities should be maximized within a given deadline and budget These studies have also promoted using a continuous scale from zero to one to specify the quality of each activity (Babu and Suresh, 1996; Tareghian and Taheri, 2006,

However, a study evaluating the application of the time–cost– quality tradeoff model to linear programming for a cement factory construction project in Thailand revealed two facts: overall project quality cannot be sacrificed by crashing, and individual activity quality is primarily determined by subjective judgements,

⁎ Corresponding author Tel.: +82 31 400 5264; fax: +82 31 409 2423.

E-mail addresses: jykimle@gmail.com (J Kim), cwkang57@hanyang.ac.kr

(C Kang), ikhwang@kongju.ac.kr (I Hwang).

0263-7863/$ - see front matter Crown Copyright © 2011 Published by Elsevier Ltd APM and IPMA All rights reserved.

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with the exception of a few measurable activities (Khang and

meets project quality targets, if any single project activities do not

meet the project contractor's requirements, rework or

modifica-tion may be necessary and are associated with time delay and cost

overrun The possibility of rework or modifications must be

considered when crashing project activities to develop practical

and cost effective project schedules

This paper proposes a mixed integer linear programming

model and procedure that accounts for potential quality loss cost

(PQLC) associated with rework or modifications that may occur

due to excessive crashing activities The rest of the paper is

organized as follows.Section 2 summarizes previous research

related to time–cost tradeoff problems considering project

quality.Section 3describes the mixed integer linear programming

model used to compute direct project costs, which was previously

considered to be equal to the nonconformance activity rate of the

project activities.Section 4validates this model with an example

and discusses the PQLC estimation method of the example

project.Section 5provides the conclusions of the study

2 Literature review

The critical path method (CPM) that is used for all types of

projects, such as construction, engineering, facility maintenance,

software development, and research and development is a

mathematical algorithm used to schedule a set of activities in a

project This method is fundamentally related to the tradeoff

between completion time and the costs of the project (Kelley and

conditions rather than probabilistic conditions The CPM can be

used to determine the time–cost tradeoff for activities that meet

given completion times at minimum cost, and is useful when there

are similar experiences from previous projects (Hillier and

Time–cost tradeoff problems from the late 1950s mostly

concentrated on shortening overall project duration by crashing

the time required to complete individual activities Researches

in this area include linear programming models (Elmaghraby

and Salem, 1982; Goyal, 1975; Kelley and Walker, 1959; Kelly,

1961; Perera, 1980; Phillips and Dessouky, 1977; Siemens,

1971) and nonlinear programming models (Deckro et al., 1987,

1995; Fulkerson, 1961; Meyer and Shaffer, 1963; Patterson and

for individual activities are linear, the relationship can be

represented as a straight line on a graph depicting the relationship

between activity time and cost (Wiest and Levy, 1997) The cost

of completing the activity varies linearly between the normal time

and the crash time (Fulkerson, 1961)

If there is concern over quality degradation then crashing

project activities is not desirable, and more time should be

allowed to finish the project (Deckro et al., 1995; Vrat and

taken to avoid rework or modifications that might occur during

project execution

Time, cost, and contractor requirements for project

manage-ment are significant elemanage-ments for judging the successes of

information systems and technology projects (Wateridge, 1998) Once a project has been completed, the time and cost tradeoff problem is no longer an issue for the project manager, and quality

or performance becomes key issues (Avots, 1984) The earned quality method assists project managers in detecting the quality variance of project activities, and allows them to take early corrective actions by comparing actual quality with planned quality (Paquin et al., 2000) Project quality is a consequence of the accumulated contributions of all individual activities executed during a project's life cycle

If the outcome of a project meets or exceeds the project contractor's expectations, the project is deemed successful (Martin

availability of the outcome in the longer-term perspective, because the project must be profitable Simply completing the project by the given due date and within budget is not sufficient, because the work must also be of acceptable quality

Previous research indicates that the quality of project scheduling is not only more important than other factors such

as time and cost, but also that it is significant for defining project success Contractor satisfaction is necessary for success, since the project outcome is transferred to the contractor (Icmeli-Tukel and

Linear programming models that simultaneously consider time, cost, and quality were proposed in a previous study (Babu

constraints for project quality In an binary integer programming model and the meta-heuristic solution procedure that solves discrete time, cost, and quality tradeoff problems (Tareghian and

quality of each project activity These quality level classifications are theoretically significant, but are inapplicable to real problems, since project contractors do not accept quality degradation Hence, project planners require mathematical models that are applicable to real problems related to project duration crashing

3 Proposed mathematical model Project completion time and cost are affected by the crashing of individual activities If individual activities are excessively crashed, rework, modifications, or even project failure may occur Quality checks must be performed immediately after the completion of each individual activity, and corrective actions such

as rework or modification can be taken if the quality is not acceptable The PQLC is needed to execute such corrective actions

3.1 Problem description Project costs are generally classified into two categories: the direct costs related to individual activities and the indirect costs related to overhead items The problem we explore in this paper focuses on individual activities under the assumption that the time–cost tradeoffs for project activities are linear (Swink et al.,

2006) The direct costs, considering the PQLC, are minimized under the following assumptions:

– Nonconformance activity requires rework or modification,

and the contractor requirements or specifications are

identified immediately after the activity is completed

– The activity can start immediately after all of the preceding

activities have been completed

– The rework or modification time of the activity is bounded

by crash duration

– The rework or modification cost of the activity is bounded by

the direct costs of crashing

3.2 Mathematical model formation

The time–cost tradeoff problem in project management

originates when activity time can be reduced with some extra

direct cost (Schwindt, 2005) Previous approaches to solving

the project duration problem include mixed integer linear

programming formulations (Wiest, 1963) and linear

program-ming with integer variables (Brucker and Knust, 2006) Below,

we describe a mixed integer linear programming model that

incorporates the PQLC This PQLC is the estimated direct cost

of rework or modifications related to nonconformance activity

that may occur if excessive crashing of project duration is

required Each project consists of individual activities, and the

completion time for each individual activity must be crashed in

order to meet project deadlines When activities with additional

direct costs are crashed, the PQLC for these activities are

considered at the same time The notations used for this model

are indicated below

Variables

Yj Crash time for the completion of activity j

Zj 1 if activity j is selected as a nonconformance risk

activity, otherwise 0

Parameters

mj Direct cost per unit time for activity j

tj Normal time required when activity j is performed

under normal conditions

cj Normal direct cost when activity j is performed in the

normal time tj

t′j Crash time required to complete activity j by assigning

resources beyond those originally allocated

c′j Crash direct cost when activity j is completed in the

crash time t′j

E Additional direct cost when activity j is completed in

the crash time t′j

Rj Reduced time for activity j

Xj Start time for activity j

Xi Start time for predecessor activity i

K Normal completion time for predecessor activity i

Yi Crash time for predecessor activity i

Xn Start time for activity n

tn Normal completion time for activity n

Yn Crash time for activity n

D Due date of the project

N Number of activities in the project

qj Potential quality loss cost for activity j

α Nonconformance risk activity rate predetermined by

the project manager

k An arbitrarily large number The model is formulated as:

Min∑n

j = 1

mjYj+ ∑n

j = 1

qjZj

Subject to

Zj∈ 1; 0f g

Yj≥0

mj= c′j−cj

tj−t′j : The above formulation includes five constraints The first constraint (1) states that the time for each activity cannot be reduced by more than its maximum time reduction The start time of each activity in the second constraint (2) must be at least

as great as the finish time of all of the immediate predecessors, because the activity finish time is reduced by the amount of time that each activity is crashed The third constraint (3) indicates that the project must be completed by its due date The fourth constraint (4) states that the project manager limits the number

of nonconformance risk activities in the project The arbitrarily large number k is given in the fifth constraint (5) to prevent the equation from becoming binding

Time–cost tradeoff problems in project scheduling have been researched extensively since the introduction of CPM in the late 1950s A number of models and/or procedures for solving the time–cost tradeoff problems have been proposed by linear programming (LP), nonlinear programming (NP), integer

programming (IP), dynamic programming (DP), mixed integer

linear programming (MILP) and heuristic algorithms (HA), but

most of the models and/or procedures did not consider activity

quality in the problems Hence, existing models and/or

pro-cedures without consideration of the activity quality are too

optimistic Although some researchers have attempted to take into

account the activity quality in the time–cost tradeoff problems

since the late 1990s, unfortunately their models and/or procedures

are limited to the theoretical approach of a project Table 1

indicates the notable differences between existing models and the

proposed model

As indicated inTable 1, the proposed model and procedure

makes it possible to solve the real problem by considering the

PQLC to be occurred during the execution of the project activities

Lowering the quality of individual activities in real life projects is

generally unacceptable The quality of each individual activity

can be classified as either conforming or nonconforming with the

project's requirements or specifications (Summers, 2005) An

activity that is classified as nonconforming requires additional direct costs for rework or modification Unlike previous approaches, the proposed model (in which the PQLC is considered) will be practical in real life project scheduling

4 Application of the model 4.1 Critical path determination

To perform a validity test of the model described inSection 3.2,

a robot type palletizing system installation (RTPSI) project for Y Company in South Korea was selected as an example Suppose this example project aims to increase the packaging productivity

of feminine care products by installing a RTPSI immediately after the current manufacturing process.Fig 1depicts the layout for the RTPSI

The business leader of the feminine care products division of this company appointed an engineering manager to complete the

Table 1

Comparisons between existing models and the proposed model.

Problem

focus

Base

formulation

Researcher Solution

method

Remarks (difference)

Time –

cost

flow

Present a theoretical base that incorporates sequence information, durations, costs, and crashing concept for project activities; have no consideration for the project activities' quality.

program

Develop nonlinear time/cost tradeoff models for solving an example; have no consideration for project quality.

may not be optimal because the project activities' quality is not considered.

et al., 1996

DP/B&B Propose the optimal procedures based on DP logic with a series –parallel network and a branch &

bound (B&B) search tree to solve a discrete time –cost tradeoff problem; may not be practical for solving a real-life problem and have no consideration on project activities' quality.

front

Develop a new algorithm and computer program for optimizing construction time –cost decisions; have no consideration for project activities' quality.

Chengen, 2009

GA Present an improved genetic algorithm to solve a multi-mode resource-constrained discrete time –cost

tradeoff problem; are applicable to special knowledge intensive projects and do not consider project activities' quality.

Chassiakos, 2004

MILP Provide an optimal project time–cost curve and a minimum cost schedule with the parameters

(generalized precedence relationships, activity planning constraints, external activity constraints, and late penalty/early bonus existence); have no consideration for project activities' quality.

duration but do not consider project activities' quality.

Debels, 2007

Heuristic search

Develop a new meta-heuristic procedure to provide near-optimal heuristic solutions for different problems but need to improve this procedure for the discrete time/cost tradeoff problem with time-switch constraints or net present value maximization; have no consideration for project activities' quality.

Time –

cost –

quality

Suresh, 1996

LP Develop linear programming models to study the interrelationship of three functions (time, cost, and

quality) and adopt the continuous scale to determine each activity quality This continuous scale at the activity level is inapplicable for solving real problems.

Myint, 1999

LP Apply the Babu-Suresh model to a real project and evaluate the applicability of their model; find the

limitations of continuous scale use in the process of activity quality inspection.

Taheri, 2006

IP Develop three inter-related (time, cost and quality) binary integer programming models and specify

project quality between 0.75 and 0.99 in increments of 0.05; may be inapplicable for the quality of a real project.

Taheri, 2007

IP/scatter search

Propose a meta-heuristic solution procedure for solving the time, cost, and quality tradeoff problem and complete a project with maximum quality at a given deadline; may be impractical in a real project because the maximum quality is ambiguous.

MILP the proposed MILP/PQLC Propose a MILP model and procedure that takes into account the potential quality loss cost in the

time –cost tradeoff problem This MILP and procedure makes it possible to solve the real problem of a project.

RTPSI project within 19 days, and assigned a project manager

who was responsible for satisfying the business leader's deadline

requirements while staying within the assigned budget The

project manager wanted to use crashing activities to shorten the

project duration and maintain nonconformance risk activity rate

for all project activities

each activity in the RTPSI project The cost (cj or c′j) of each

activity inTable 2includes expenses related to labor, materials,

and equipment The project manager was required to prepare a

practical and cost effective project schedule that would result in

the successful completion of the RTPSI project by the due date

An activity on node (AON) diagram is useful for

represent-ing precedence relationships among project activities

broken down into 18 individual activities They are A) surface

leveling, B) electric wiring for the conveyor, C) electric wiring

for the wrapping machine, D) electric wiring for the robot, E) installing the electrical panel for the conveyor, F) installing the electrical panel for the wrapping machine, G) installing the electrical panel for the robot, H) assembling the parts for the conveyor, I) framing the wrapping machine base, J) assembling the parts for the robot, K) installing the conveyor, L) installing the palletizer, M) installing the robot, N) setting up the robot program, O) testing the robot, P) testing for fabricated systems, Q) inspecting the engineering, and R) inspecting the process Activities B, C, and D inFig 2cannot begin until activity A is completed Activities K, L, and O must be completed before activity P is initiated

CPM is a useful technique for finding the longest path of planned activities on the AON diagram, which is necessary in order to determine the minimum time required for project completion There are three distinct paths describing the RTPSI project: path 1) A–B–E–H–K–P–Q–R, path 2) A–C–F–I–L– P–Q–R, and path 3) A–D–G–J–M–N–O–P–Q–R

Each path length indicated in Table 3 can be obtained by estimating the time tjinTable 2for each respective node in the RTPSI project network Of the three paths shown inTable 3, path 3 is the critical path that requires the longest time for the completion of the project

The activities along critical path 3 are used to determine the completion time for the RTPSI project and have zero flexibility The entire project duration may be reduced by crashing the time required to complete one or more of the activities in path 3 4.2 PQLC estimation

A systematic process for PQLC estimation that includes procedures, scale, and definition is divided into three steps: nonconformance risk identification and coding for project activities, nonconformance risk analysis for project activities, and PQLC estimation with nonconformance risk activity rate 4.2.1 Step 1: Nonconformance risk identification and coding for project activities

A nonconformance risk is defined as any uncertainty that would negatively affect project activity cost if it occurs after an activity is finished Three nonconformance risks for each activity

Fig 1 The RTPSI layout.

Table 2

Data related to the time –cost tradeoffs for individual activities.

Activity Immediate

predecessor

t j , days

c j ,

$100

t ′ j , day (s)

c ′ j ,

$100

R j , day (s)

E,

$100

m j ,

$100/

day

A – 3.0 17.88 2.0 20.11 1.0 2.23 2.23

B A 3.0 41.71 1.5 44.32 1.5 2.61 1.74

C A 4.0 69.41 2.0 89.37 2.0 19.96 9.98

D A 4.0 65.96 2.0 84.54 2.0 18.58 9.29

E B 3.0 138.10 1.5 170.06 1.5 31.96 21.31

F C 2.0 327.81 1.5 431.13 0.5 103.32 206.64

G D 3.0 189.99 1.5 210.22 1.5 20.23 13.49

H E 1.5 28.14 1.0 38.29 0.5 10.15 20.30

I F 2.0 16.83 1.0 22.08 1.0 5.25 5.25

J G 1.5 79.86 1.0 92.55 0.5 12.69 25.38

K H 6.0 123.86 3.0 167.37 3.0 43.51 14.50

L I 2.0 62.62 1.5 74.91 0.5 12.29 24.58

M J 4.0 625.93 2.0 655.86 2.0 29.93 14.97

N M 3.0 51.97 1.0 71.85 2.0 19.88 9.94

O N 2.0 14.90 1.5 20.11 0.5 5.21 10.42

P K, L, O 2.0 35.75 1.0 43.94 1.0 8.19 8.19

Q P 2.0 59.89 1.5 76.94 0.5 17.05 34.10

R Q 1.5 40.61 1.0 51.34 0.5 10.73 21.46

Total 1991.22 2364.99 373.77

were identified through brainstorming among experts and

stakeholders involved in the RTPSI project A code and

description for each nonconformance risk identified was specified

in the code and description register of nonconformance risks,

respectively The codes and descriptions are shown inTable 4

4.2.2 Step 2: Nonconformance risk analysis for project

activities

The probability and impact of each nonconformance risk

identified in Step 1 were assessed through interviews with

knowledgeable and experienced project team member(s) or expert

(s) from outside the project The previous experiences of experts

may be helpful for probability and impact assessment (

probability and impact of the nonconformance risk were assessed

with numerical scales: 0.10, 0.30, 0.50, 0.70, and 0.90 The

numerical scales are defined inTables 5 and 6, respectively

The numerical scales ofTables 5 and 6are used to develop the

probability and impact matrix ofTable 7 This matrix specifies

combinations of probability and impact that lead to scoring each

nonconformance risk identified in step 1, and is used to prioritize

nonconformance risks Numeric values inTable 7 are derived

from the nonconformance risk score; (NRS) = probability

(P) × impact (I)

The probability and impact matrix is useful at the beginning of

nonconformance risk analysis when an assessor has limited

information about the risks associated with an activity Individual

NRSs assessed by this matrix are shown inTable 8 If there is

more than one assessor, the sum of the NRSs from each assessor is

divided by the number of assessors to obtain the average score for

an individual nonconformance risk

To formulate a priority ranking of the individual codes based

on NRSs inTable 8, the NRSs were rearranged in descending order in Table 9 If there is more than one code in the same ranking row ofTable 9, priority is given to the nonconformance risk code of the activity with relatively high crash direct cost of them

The nonconformance risk analysis for project activities can

be a rapid and cost-effective means to prioritizing before the PQLC estimation

4.2.3 Step 3: PQLC estimation with nonconformance risk activity rate

The PQLC for nonconformance risk activity was estimated under the assumption that the rework or modification costs for a nonconformance risk activity are equivalent to its crash direct cost (c′j) The acceptable number of nonconformance risk activities is decided using Eq.(4) The RTPSI project PQLC is computed by inserting the nonconformance risk activities of related codes from

For the RTPSI project, the nonconformance risk activity rates from 5% to 25% were given in increments of 5%, and the PQLCs for each nonconformance risk activity rate candidate were estimated at 5%, 10%, 15%, 20%, and 25%, respectively 4.3 Computational results

The example was solved using LINGO software (version 6.01)

on a personal computer (Hewlett-Packard Compaq Intel® Centrino 2.0 GHz with 2 GB RAM and 80 GB hard disk) The estimated completion time of the RTPSI project according to the constraint Eq (3) was 17.5 days, which conformed with the desired project due date (D) Activities A, B, D, G, N, O, and P of the RTPSI project were identified as crashing activities that could influence the project due date

The estimation of the nonconformance risk activity rateα for the RTPSI project depends on the project manager's strategic approach regarding the business priorities of Y Company The number of nonconformance risk activities∑ Zjwas calculated according to the fourth constraint (4)

noncon-formance risk activity rate candidates The nonconnoncon-formance risk

Fig 2 Project network for RTPSI.

Table 3

Path length calculations.

Path Time estimation at each node Path length (days)

1 3 + 3 + 3 + 1.5 + 6 + 2 + 2 + 1.5 22.0

2 3 + 4 + 2 + 2 + 2 + 2 + 2 + 1.5 18.5

3 3 + 4 + 3 + 1.5 + 4 + 3 + 2 + 2 + 2 + 1.5 26.0

activities shown in Table 10 had higher NRS than the other

activities The RTPSI project PQLC was directly related to theα

value or to the number of nonconformance risk activities The

PQLC is visualized inFig 3

If no rework or modification occurs while executing

nonconformance risk activities, the PQLC is saved If any rework

or modifications occur during the execution of these activities, the

PQLC is payable in the budget Although the RTPSI project

requires excessive crashing for nonconformance risk activities,

cases in which preventive measures against rework or

modifica-tions can be taken allow the project manager to choose a lowα

value without concern about the PQLC

The information presented inTable 10andFig 3allowed the

project manager to complete the RTPSI project within the

assigned budget and due date in this real-life case

5 Conclusions

In this paper, we propose a mixed integer linear programming model that accounts for both the nonconformance risks and the PQLC of the project activities In a computational application of this model we found that the crashing activities were properly selected, and identified a need for special care regarding nonconformance risk activities By identifying these nonconfor-mance risk activities in the process of project scheduling, the project manager can take preventive actions that eliminate the need for rework or modification, which in turn facilitates the completion of the RTPSI project with minimum direct costs and before the due date Although rework or modification of nonconformance risk activities cannot be completely avoided during project execution, project cost overruns can be avoided because the direct cost already includes the PQLC This is similar

to a worst-case design concept in terms of reliability

In conclusion, we present a valid and practical model that can minimize PQLC influence on project cost due to excessive

Table 4

Code and description register of nonconformance risks.

Code Description of nonconformance risk Code Description of nonconformance risk

A1 Uneven floor when doing concrete work J1 Level error of suction disks

A2 Contaminated floor J2 Defectively assembled robot arm

A3 Low hardness of concrete floor J3 Inaccurate position where robot arm takes up box

B1 Reverse wiring between power supply cables K1 Loose bolts of supports for conveyor installation

B2 Poor contact of connectors or terminal blocks K2 Time interval error between conveyor sensors

B3 Interior wiring error of conveyor cables K3 Touching corner at turning point of L-shape

C1 Cables loosened while turning wrapping machine L1 Level error of magazine stand

C2 Poor contact of terminal blocks L2 Trouble related to pallet release from magazine stand

C3 Interior wiring error of wrapping machine cables L3 Incomplete operation of oil pressure, pneumatic brakes, and switches D1 Touch of flexible cables while moving robot arm M1 Programming error; robot position

D2 Poor contact of robot's terminal blocks M2 Readjustment of pattern; technical location

D3 Interior wiring error of robot cables M3 Malfunction of interlocking system

E1 Broken terminal blocks inside panel N1 Trouble in data processing system

E2 Damage to control unit inside panel N2 Inspection of programs related to each pattern

E3 Leakage of electricity due to accumulated dust N3 Preparing backup files

F1 Broken terminal blocks inside electrical panel O1 Inoperative box counter

F2 Damage to controller or drive inside electrical panel O2 Taking a long time to test number of boxes

F3 Inflow of dust into electrical panel O3 Test run data collection for long periods of time

G1 Broken terminal blocks inside of electrical panel P1 Trouble with oil pressure or pneumatic brakes

G2 Damage to control unit inside of panel P2 Trouble with conveyor transportation

G3 Leakage of electricity due to accumulated dust P3 Malfunction of bar code scanner

H1 Misaligned conveyor chains Q1 Loose cable connection

H2 Collision between boxes at junction of conveyor lines Q2 Rotation in the reverse direction

H3 Trouble with automatic reject system Q3 Trouble with interlocking systems

I1 Malfunction of wrapper-lifting system R1 Faulty connection between processes

I2 Collision with boxes during wrapper-lifting motion R2 Poor contact of safety devices

I3 Uneven space between wrapping arm and boxes R3 Incomplete operation of automatic control system

Table 5

The scale and definition of probability related to nonconformance risks.

Probability scale Definition (based on occurrence of rework or

modification after completion of an activity)

0.30 Possible

0.70 Highly likely

0.90 Almost certain

Table 6 The scale and definition of impact related to activity cost.

Impact scale Definition 0.10 b20% increase in activity cost 0.30 20 –40% increase in activity cost 0.50 40 –60% increase in activity cost 0.70 60 –80% increase in activity cost 0.90 N80% increase in activity cost

crashing activities In an example project, we determined that

quality is a significant factor in time–cost tradeoff problems when

project activities are excessively crashed When compared with

the previous models inTable 1, the proposed model will help

project planners develop practical project schedules, and is a meaningful approach in view of its possible utilization in real life projects Preventive actions for nonconformance risk activities may incur additional cost In future research, the proposed model may be extended to estimate the additional costs of preventative actions that are related to nonconformance risk activities and to use this information to formulate new approaches that incorporate quality concepts into project scheduling problems

References

Assaf, S., Al-Hejji, S., 2006 Causes of delay in large construction projects International Journal of Project Management 24, 349 –357

Atkinson, R., 1999 Project management: cost, time and quality, two best guesses and a phenomenon, its time to accept other success criteria International Journal of Project Management 17 (6), 337 –342

Avots, I., 1984 Information systems for matrix organizations in Cleveland In: David, I (Ed.), Matrix Management Systems Handbook Van Nostrand Reinhold, New York, pp 535 –537.

Babu, A., Suresh, N., 1996 Project management with time, cost, and quality considerations Journal of Operational Research 88, 320 –327

Brucker, P., Knust, S., 2006 Complex Scheduling Springer-Verlag Deckro, R.F., Hebert, J.E., Verdini, W.A., 1987 Nonlinear multiple criteria time/cost tradeoffs Proceedings of the Sixteenth Annual Western DSI Meeting, pp 134–137.

Deckro, R.F., Hebert, J.E., Verdini, W.A., 1995 Nonlinear time/cost tradeoff models in project management Computers &Industrial Engineering 28 (2),

219 –229

Demeulemeester, E.L., Herroelen, W.S., Elmaghraby, S.E., 1996 Optimal procedures for the discrete time/cost tradeoff problem in project networks European Journal of Operational Research 88, 50 –68

Elmaghraby, S.E., Salem, A., 1982 Optimal project compression under quadratic cost functions Applications of Management Science 2, 1 –39

Feng, C.W., Liu, L., Burns, S.A., 1997 Using genetic algorithms to solve construction time –cost tradeoff problems Journal of Computing in Civil Engineering 11 (3), 184 –189

Fulkerson, D., 1961 A network flow computation for project cost curves Management Science 7 (2), 167 –178

Goyal, S.K., 1975 A note on simple CPM time –cost tradeoff algorithm Management Science 21 (6), 718 –722

Hillier, F.S., Lieberman, G.J., 1995 Introduction to Mathematical Program-ming McGraw-Hill Inc, New York.

Icmeli-Tukel, O., Rom, W., 1997 Ensuring quality in resource constrained project scheduling European Journal of Operational Research 103,

483 –496

Kelley, J.T., Walker, M.R., 1959 Critical Path Planning and Scheduling: an Introduction Mauchly Associates, Ambler (PA).

Kelly, J.E., 1961 Critical-path planning and scheduling: mathematical basis Operations Research 9 (3), 296 –320

Kessler, E.H., Chakrabarti, A.K., 1999 Speeding up the pace of new product development Journal of Product Innovation Management 16, 231 –247

Table 7

Probability and impact matrix.

Probability 0.10 0.30 0.50 0.70 0.90

Impact

0.10 0.01 0.03 0.05 0.07 0.09

0.30 0.03 0.09 0.15 0.21 0.27

0.50 0.05 0.15 0.25 0.35 0.45

0.70 0.07 0.21 0.35 0.49 0.63

0.90 0.09 0.27 0.45 0.63 0.81

Table 8

NRS for each nonconformance risk code.

Code NRS Code NRS Code NRS Code NRS

A1 0.27 E3 0.20 J2 0.35 O1 0.28

A2 0.07 F1 0.09 J3 0.18 O2 0.20

A3 0.45 F2 0.40 K1 0.18 O3 0.14

B1 0.24 F3 0.20 K2 0.21 P1 0.30

B2 0.30 G1 0.15 K3 0.28 P2 0.18

B3 0.21 G2 0.45 L1 0.24 P3 0.32

C1 0.24 G3 0.12 L2 0.08 Q1 0.18

C2 0.25 H1 0.17 L3 0.21 Q2 0.30

C3 0.28 H2 0.31 M1 0.27 Q3 0.30

D1 0.37 H3 0.47 M2 0.27 R1 0.18

D2 0.25 I1 0.21 M3 0.24 R2 0.34

D3 0.21 I2 0.27 N1 0.27 R3 0.21

E1 0.15 I3 0.21 N2 0.14

E2 0.40 J1 0.24 N3 0.18

Table 9

Priority ranking of individual codes.

Ranking Code NRS Ranking Code NRS

1 H3 0.47 13 B1,C1,J1,L1,M3 0.24

2 A3,G2 0.45 14 B3,D3,I1,I3,K2,L3,R3 0.21

3 E2,F2 0.40 15 E3,F3,O2 0.20

4 D1 0.37 16 J3,K1,N3,P2,Q1,R1 0.18

9 B2,P1,Q2,Q3 0.30 21 F1 0.09

10 C3,K3,O1 0.28 22 L2 0.08

11 A1,I2,M1,M2,N1 0.27 23 A2 0.07

12 C2,D2 0.25

Table 10

PQLC for each nonconformance risk activity rate candidate.

Nonconformance risk activity H H,G H,G,A H,G,A,F H,G,A,F,E

PQLC, $100 38.29 248.51 268.62 699.75 869.81

Fig 3 PQLC increase related to αvalue.

Khang, D., Myint, Y., 1999 Time, cost and quality tradeoff in project

management: a case study International Journal of Project Management 17

(4), 249 –256

Martin, P.K., Tate, K., 2001 Getting Started in Project Management John

Wiley & Sons Inc, New York, pp 26 –27.

Meyer, W.L., Shaffer, L.R., 1963 Extensions of the Critical Path Method

Through the Application of Integer Programming University of Illinois,

Department of Civil Engineering.

Paquin, J.P., Couillard, J., Ferrand, D.J., 2000 Assessing and controlling the

quality of a project end product: the earned quality method IEEE

Transaction on Engineering Management 47, 88 –97

Patterson, J.H., Huber, D., 1974 A horizon-varying, zero-one approach to

project scheduling Management Science 20 (6), 990 –998

Perera, S., 1980 Linear programming solution to network compression ASCE

Journal of the Construction Division 106, 315 –327

Phillips, S., Dessouky, M.I., 1977 Solving the project time/cost tradeoff problem

using the minimal cut concept Management Science 24 (4), 393 –400

Robinson, D.R., 1975 A dynamic programming solution to cost –time tradeoff

for CPM Management Science 22 (2), 158 –166

Sakellaropoulos, S., Chassiakos, A.P., 2004 Project time –cost analysis under

generalised precedence relations Advances in Engineering Software 35,

715 –724

Schwindt, C., 2005 Resource Allocation in Project Management Springer-Verlag.

Scott-Young, C., Samson, D., 2008 Project success and project team

management: evidence from capital projects in the process industries.

Journal of Operations Management 26, 749 –766

Siemens, N., 1971 A simple CPM time –cost tradeoff algorithm Management

Science 17 (6), B354 –B363

Summers, D., 2005 Quality Management: Upper Saddle River Pearson Education, Inc., New Jersey.

Swink, M., Talluri, S., Pandejpong, T., 2006 Faster, better, cheaper: a study of NPD project efficiency and performance tradeoffs Journal of Operation Management 24, 542 –562

Tareghian, H., Taheri, S., 2006 On the discrete time, cost and quality tradeoff problem Applied Mathematics and Computation 181, 1305 –1312

Tareghian, H., Taheri, S., 2007 A solution procedure for the discrete time, cost and quality tradeoff problem using electromagnetic scatter search Applied Mathematics and Computation 190, 1136 –1145

Vanhoucke, M., Debels, D., 2007 The discrete time/cost tradeoff problem: extensions and heuristic procedures Journal of Scheduling 10, 311 –326

Vrat, P., Kriengkrairut, C., 1986 A goal programming model for project crashing with piecewise linear time –cost trade-offs Engineering costs production Economics 10, 161

Wateridge, J., 1998 How can IS/IT projects be measured for success? International Journal of Project Management 16, 59 –63

Wiest, J.D., 1963 The Scheduling of Large Projects with Limited Resources Unpublished PhD Thesis, Carnegie Institute of Technology, Pittsburgh Wiest, J.D., Levy, F.K., 1997 A Management Guide to PERT/CPM: Englewood Cliffs Prentice-Hall, Inc, New Jersey.

Wuliang, P., Chengen, W., 2009 A multi-mode resource-constrained discrete time–cost tradeoff problem and its genetic algorithm based solution International Journal of Project Management 27, 600–609

Zeng, J., An, M., Smith, N., 2007 Application of a fuzzy based decision making methodology to construction project risk assessment International Journal

of Project Management 25, 589 –600