Time-Cost Trade-Off Analysis in a Construction Project Problem: Case Study

ISSN (e): 2250 – 3005 || Volume, 06 || Issue, 10|| October – 2016 ||
International Journal of Computational Engineering Research (IJCER)
www.ijceronline.com Open Access Journal Page 32
Time-Cost Trade-Off Analysis in a Construction Project
Problem: Case Study
S. K. Biswasa
, C. L. Karmakera
, T. K. Biswasa
a
Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology,
Dhaka, Bangladesh.
I. INTRODUCTION
To stay competitive in the global market, completing the definite project compromising the cost and budget is
very challenging. Several factors may cause delays such as labor related delay, political issues, contractor delay
and some unseen delays which contribute to increase the uncertainty. So, proper planning and scheduling of all
activities/jobs required for the completion of the project on time and within budget play a vital role to solve the
problem. Project management can be defined as the process of utilizing resources, techniques etc. to get the job
done properly within a specified timeframe at the lowest possible cost. It also ensures the performance standards
to gain attraction to the buyers. Critical path method (CPM) and Project Evaluation and Review Technique
(PERT) are both used for proper project planning and scheduling of large projects. They help the project
managers in monitoring the progress of the stages. The major difference between them is that CPM considers
deterministic durations to schedule the jobs.
To expedite the execution of a project, project managers need to reduce the scheduled execution time by hiring
extra labor or using productive equipment. But this idea will incur additional cost hence shortening the
completion time of jobs on critical path network is needed. For real life projects, decision makers always
perform the trade-off between the time and cost of project through crashing/prolonging the duration of the
activities. According to several researchers, time-cost trade problem (TCTP) is considered as one of the vital
decisions in project accomplishment (Pour et al., 2012).
Research on the TCTP was first conducted by Kelly in 1961. Several researchers agreed that from 1961 the
research mainly focused on the deterministic cases (Mobinia et al., 2011; Phillips and Dessouky, 1977; Weglarz
et al., 2011). A variety of techniques were used to solve the time-cost trade problems which are classified into
two areas: mathematical programming method and heuristic methods. Mathematical programming method
includes linear programming, integer programming, and dynamic programming whereas heuristic methods use
genetic algorithm, cost-loop method etc.
The aim of this study is to develop a hybrid a model for identifying the optimum total cost associated with
project duration. A heuristic method named cost-loop method is used to find out the total crash costs at various
durations. The time costs relation is then analyzed by regression analysis to obtain the objective function. A
linear programming model has been developed and solved by using Matlab software.
ABSTRACT
In construction project, cost and time reduction is crucial in today’s competitive market respect.
Cost and time along with quality of the project play vital role in construction project’s decision.
Reduction in cost and time of projects has increased the demand of construction project in the
recent years. Trade-off between different conflicting aspects of projects is one of the challenging
problems often faced by construction companies. Time, cost and quality of project delivery are the
important aspects of each project which lead researchers in developing time-cost trade-off model.
These models are serving as important management tool for overcoming the limitation of critical
path methods frequently used by company. The objective of time-cost trade-off analysis is to
reduce the original project duration with possible least total cost. In this paper critical path
method with a heuristic method is used to find out the crash durations and crash costs. A
regression analysis is performed to identify the relationship between the times and costs in order
to formulize an optimization problem model. The problem is then solved by Matlab program
which yields a least cost of $60937 with duration 129.50 ≈130 days. Applying this approach, the
result obtained is satisfactory, which is an indication of usefulness of this approach in
construction project problems.
Keywords: Construction project; Critical path method; Trade-off analysis; Crashing

Time-Cost Trade-Off Analysis in a Construction Project Problem: Case Study
The rest of this study is arranged as follows: The second section presents the literature review on time-cost
trade-off analysis. Section 3 frameworks the developed methodology and provides a stepwise depiction of the
anticipated steps for shortening project execution time. A prototype example is given to visualize the
computational effectiveness in Section 4. And finally, in section five, results of the application are presented and
suggestions for the future studies are clarified. This section wraps up this study.
II. LITERATURE REVIEW
The objective of the time-cost trade-off problem (TCTP) is to reduce the original project duration obtained from
the critical path analysis, to meet a specific deadline with the minimum direct and indirect cost of the project.
Direct costs include costs of material, labor, equipment etc. whereas indirect costs are the necessary costs of
doing work which can‟t be related to a particular task. There are enormous research works in the arena of TCTP.
In 1991, Shouman et al. constructed a framework using mixed integer linear programming and CPM and
utilized in natural gas projects. The value of the study is that, by the use of it, minimum total cost is achieved
using crashing concept. A survey on forty seven papers conducted by Agarwal et al. (2013) revealed that about
41% work was performed in construction area during the 1990-2002. Liu et al. (1995) developed a hybrid
method using linear and integer programming for time-cost trade-off problem. Several researchers used dynamic
programming to adjust between two important aspects of the project (Hindelang et al., 1979; Prabuddha et al.,
1995; Arauzo et al., 2009).
Recently, different computational optimization techniques such as genetic algorithms (GA), Evolutionary
algorithms (EA), Particle swarm optimization (PSO) etc. have been used. Feng et al. (1997) adopted genetic
algorithms to solve construction time-cost trade-off problems. Li et al. (1999) designed machine learning and
genetic algorithms based system (MLGAS) in construction project and the system generated better results to
nonlinear TCTP. In 2003, Poonambalam et al. applied genetic algorithms for sequencing problems in mixed
model assembly lines of industrial arena and found better performance of GA. Genetic algorithm has been also
used to optimize multi-objective time-cost-quality trade-off problem (Shahsavari Pour et al. 2010). Azaron et al.
(2005) designed cost trade off problem as a multi-objective optimal problem consisting four objective functions
and used genetic algorithm to solve it. Several researchers developed hybrid model based on genetic algorithms
and other techniques and applied it to discrete TCTP problems (Azaron et al., 2005; Elazouni et al., 2007; Razek
et al., 2010).
To deal with problems having uncertainties, different researchers have used fuzzy logic. Pathak et al. (2007) and
Shahsavari Pour et al. (2012) applied fuzzy logic theory to consider affecting uncertainty in project quality.
Pathak et al. (2008) proposed ANN with MOGA (multi-objective genetic algorithm) approaches for solving
nonlinear TCTP for better project scheduling. In 2009, Chen et al. applied ant colony optimization algorithm in
project scheduling to optimize the discounted cash flows. Zeinalzadeh, 2011 demonstrated a mathematical
model using MILP-Lingo12 to minimize the total cost of a construction project.
The problem in this paper involves only deterministic time as a result dealing with uncertainty is avoided.
Firstly, critical path method (CPM) is applied to determine the critical path and critical activities. A heuristic
method named the cost-lope method is used to find out the total crash costs at various durations. The time costs
relation is then analyzed by regression analysis and an optimization problem is formulized which is solved using
Matlab software.
III. METHODOLOGY
At first, necessary data for construction problem are taken from a secondary source. CPM is applied to find out
the critical path and critical activities. The activities are shortened in order to get their lowest cost slopes using
the heuristic method. As the duration of the activities on the shortest path are shortened, the project duration is
also reduced. Eventually another path becomes critical, and a new list of activities on the critical path is
prepared. Using this way, optimum schedules are identified. The time costs relation is then analyzed by
regression analysis and an optimization problem is formulized which is solved using Matlab.
The procedure for shortening the project duration can be summarized in the following steps:
Step 1: Draw the project network.
Step 2: Perform CPM calculations and identify the critical path, using normal duration and costs for all
activities.
Step 3: Compute the cost slope for each activity.
Step 4: Start by shortening the activity duration on the critical path which has the least cost slope and not been
shortened to its crash duration.
Step 5: Reduce the duration of the critical activities with least cost slope until its crash duration is reached or
until the critical path changes.
Step 6: When multiple critical paths are involved, the activity to shorten is determined by comparing the cost
slope of the activity which lies on all critical path, with the sum of cost slope for a group of activities.

Step 7: Having shortened a critical path, adjust timings and floats.
Step 8: The cost increase due to activity shortening is calculated as the cost slope multiplied by the time units
shortened.
Step 9: Continue until no further shortening is possible, and then the crash point is reached.
IV. NUMERICAL EXAMPLE WITH CALCULATION
The proposed model has been applied on a construction project to demonstrate the practicality of the proposed
methodology. It needs an estimate of how much time each activity takes in the normal way in order to schedule
the activities in the network. It is required to crash the project duration from its original duration to a final
duration of 110 days. The project data of a construction problem provided by the project manager is shown in
table 1.Table 1 presents the details description of all activities required for the completion of the construction
project. Here, there are five activities and construction process starts with activity A and ends with activity F.
The associated cost in terms of dollar and required number of days to complete individual activity are
demonstrated in table 1.The first column represents the activity identification code, immediate predecessors of
each activity are shown in second column, third column shows the estimated normal cost and the fourth column
provides the activity duration in days. Daily indirect cost of the project is assumed to be $100.Table 2 depicts a
project with hypothetical normal time - cost data and crash time –cost data of necessary activities.
4.1 Computational steps
To determine the critical path consisting of activities with zero slack, different variables such as Earliest Start
(ES), Earliest Finish (EF), Latest Start (LS), Latest Finish (LF) and Slack are computed. Table 3 shows the
computation of determining the critical path of the project. Based on table 3 the total duration for the completion
of the project is 140 days and the critical path is B-C-D-E. Project total normal direct cost is equal to sum of
normal direct cost of all activities is $48300.
To expedite the project by reducing the expected project duration further down from 140 days, a process of
crashing the duration of activities has been anticipated. Reduction of project duration incurs the extra cost.
Project duration can be reduced by taking several measures such as overtime, hiring additional workers, using
special time-saving materials, and special equipment. Table 4 shows the calculation of the cost-time slopes of
the activities by a heuristic method named the cost-lope method. Both the cost slope and the crash ability are
shown beneath each activity in the precedence diagram in fig. 1.
Now, the steps for shortening the activity duration on the critical path based on least cost-time slope are given as
below:
1. Activity “D” has the lowest cost slope on the critical path and this activity can be crashed by 10 days. By
adjusting timing of the activities, the new critical path is B-F-E. New project duration is 130 days and the
project direct cost is increased by 10*60 = 600. Hence the project direct cost becomes 48300+600 = 48900.
2. As activity “E” lies on both critical paths, at this step this activity can be crashed. Activity “E” can be
crashed by 10 days. After this all activities has turned to critical activities.New project duration is 120 days
and the project direct cost is increased by 10*120 = 1200.Hence the project direct cost becomes
48900+1200 = 50100.

3. At this step, it is difficult to decrease one activity‟s duration and achieve decreasing in the project duration.
So, either to crash an activity on all critical paths, otherwise, choose several activities on different critical
paths. Activities “A” and “B” can be crashed together by 5 days which have the lowest cost slope
(100+200). New project duration is 115 days and the project direct cost is increased by 5*(100+200) =
1500. Hence the project direct cost becomes 50100+1500 = 51600.
4. In this final step, it is required to decrease the duration of an activity from path. “A” activity‟s duration can
be crashed to 110 days, “C” to 35 days and “F” to 55 days. New project duration is 110 days and the project
direct cost is increased by 5*(100+600+300) = 5000.Hence the project direct cost becomes 51600+5000 =
56600
Finally, different cost data associated with project duration are obtained using the heuristic method
which is presented in table 5. Figure 2 shows the scatter plot of different cost versus time required for
completing the construction project. To visualize the relationship between total cost and time, the regression
analysis is performed which is presented in figure 3. From figure 3, the obtained equation is Total cost (TC) =
15.44 x2
– 3999x +319875 where „X‟ represents the estimated duration (days) for the completion of project.
Now, the problem can be formulated as a linear programming model that has to be minimized. Here, Z
is the total cost of the construction project obtained from the regression analysis. The aim of this model is to
minimize the total cost (Z) subject to the constraint that the construction duration must be within 140 days to
110 days. The complete linear programming model can be given below:
Min
Subject to,
Using Matlab software the solution of the mathematical model is obtained as the total cost is $60937 with the
duration of about 130 days.
V. RESULT AND DISCUSSION
Crash times and crash costs are conflicting factors. Reducing one increases the other. The result shown in figure
2 indicates that total cost declines when project duration is increased. After some time, total cost reaches to its
minimum value then it starts to increases with increasing duration. This analysis shows the real behavior of
construction projects. This reveals the challenge of optimum resource utilization to compromise between
different and usually conflicting aspects of projects. The regression analysis shows the relationship between the
crash times and crash costs. The quadratic formula is best for representing the relationship. The time-cost trade-
off analysis of this project results in a minimum cost of $60937 with the duration of 129.50 ≈130 days.
In this research, only deterministic values of activity duration and cost are used. Uncertainty behavior of project
is avoided. For better prediction and result the parameter uncertainty can be considered.

VI. CONCLUSION
The aim of this research was time-cost trade-off analysis for a construction project. The analysis has been done
for an existing project. Critical path method (CPM) and a heuristic method have been used to find out the crash
times and crash costs. Regression analysis has been done in order to develop the relationship between the crash
times and the crash costs. The relation between crash times and crash costs has led to develop the optimization
model. Matlab program has been used to get the minimum total costs of the project with the minimum durations.
All these techniques utilized in this paper have shown a satisfactory result. The time-cost trade-off analysis of
this project results in a minimum cost of $60937 with the duration of 129.50 ≈130 days. This method is also
capable of producing a satisfactory result with varying project activities which implies the usefulness of this
approach presented in this paper.
REFERENCES
[1]. Arauzo, J.A., Galan, J.M., Pajares, J., and Paredes, A. lL., (2009).Multi-agent technology for scheduling and control projects in
multi-project environments- An auction based approach.Intelligence Artificial , 42, 12-20.
[2]. Ashtiani, B., Haghighirad, F., Makui, A., and ali Montazer, G., (2009). Extension of fuzzy TOPSIS method based on interval-
valued fuzzy sets. Applied Soft Computing, 9(2), 457-461.
[3]. Azaron, A., Perkgoz, C., and Sakawa, M., (2005).A genetic algorithm approach for time cost trade off in PERT networks. Applied
mathematics and computation, 168, 1317-1339.
[4]. Chen, W., Zhang, J., Chung, H.S., Huang, R., and Liu, O., (2009). Optimizing discounted cash flows in project scheduling- an ant
colony optimization approach. IEEE Transactions of System, Man & Cybernics.
[5]. Elazouni, A.M., and Metwally, F.G., (2007). Expanding finance based scheduling to derive overall optimized project schedules.
Journal of Constitution Engineering and Management, 133(1), 86-90.
[6]. Feng, C.W., Liu, L., and Burns, S.A., (1997).Using genetic algorithms to solve construction time cost trade-off problems. Journal of
Computing in Civil Engineering, 11(3), 184-189.
[7]. Hindelang, T.J., and Muth, J.F., (1979). A dynamic programming algorithm for decision CPM networks. Civil Engineering, 8(2),
113-124. Operations Research, 27, 225-241.
[8]. Kelley, J.E., (1961). Critical path planning and scheduling mathematical basis. Operation Research, 9, 296-320.
[9]. Li, H., Cao, J.N., and Love, P., (1999).Using machine learning and GA to solve time cost trade off problems. Journal of
Constitution Engineering and Management, 125(5), 347-353.
[10]. Liu, L., Burns, S.A., and Feng, C.W., (1995).Construction time cost trade off analysis using LP/IP Hybrid Method. Journal of
Constitution Engineering and Management, 121(5), 446-454.
[11]. Mobinia, M., Mobinib, Z., and Rabbani, M., (2011). An artificial immune algorithm for the project scheduling problem under
resource constraints. Applied Soft Computer, 11, 1975-1982.
[12]. Pathak, B.K., and Srivastava, S., (2007). MOGA-based time cost tradeoffs: responsiveness for project uncertainties. IEEE Congress
on evolutionary computation, 3085-3092.
[13]. Pathak, B.K., Srivastava, S., and Srivastava, K., (2008). Neural network embedded with multi-objective genetic algorithm to solve
nonlinear time cost trade-off problem of project scheduling. Journal of scientific and industrial research, 67, 124-131.
[14]. Phillips, S., and Dessouky, M.I., (1977). Solving the project time/cost trade off problem using minimal cut concept. Manage
Science, 24,393-400.
[15]. Poonambalam, S.G., Aravindan, P., and SubhaRao, M., (2003). Genetic algorithms for sequencing problems in mixed model
assembly lines. Computers and Industrial Engineering 45, 669-690.
[16]. Pour, N.S., Modarres, M., & Moghaddam, R.T., (2012). Time-cost-quality trade-off in project scheduling with linguistic
variables. World Applied Sciences Journal, 18(3), 404-413.
[17]. Prabuddha, D.E., Dunne, E. J., Ghosh, J. B. and Wells, C. E., (1995).The discrete time cost trade off revisited. European Journal of
Operational Research, 81, 225-238.
[18]. Razek, R.H.A.E., Diab, A.M., Hafez, S.M., and Aziz, R.F., (2010).Time cost quality trade-off software by using simplified GA for
typical repetitive construction projects. World Academy of Science, Engineering. & Technology, 61, 312-320.
[19]. Shahsavari Pour, N., Modarres, M. R., Tavakkoli-R.Moghaddam and Najafi, E., (2010). Optimizing a multi-objectives time cost
quality trade-off problem by a new hybrid genetic algorithm. World Applied Sciences Journal, 10(3), 355-363.
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Linguistic Variables. World Applied Sciences Journal 18 (3), 404-413.
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List of Tables
Table 1 Construction project data
Activity code Immediate predecessors Normal cost ($) Normal duration (days)
A - 12000 120
B - 1800 20
C B 16000 40
D C 1400 30
E D,F 3600 50
F B 13500 60

Table 2 List of normal & crash cost-time data
Activity
code
Immediate
predecessors
Normal cost
($)
Normal duration
(days)
Crash cost
($)
Crash duration
(days)
A - 12000 120 14000 100
B - 1800 20 2800 15
C B 16000 40 22000 30
D C 1400 30 2000 20
E D,F 3600 50 4800 40
F B 13500 60 18000 45
Table 3 Computation of critical path method
Activity
code
Earliest Start
(ES)
Earliest Finish
(EF)
Latest Start
(LS)
Latest Finish
(LF)
Slack
(LS-ES)
Critical
A 0 120 20 140 20 No
B 0 20 0 20 0 Yes
C 20 60 20 60 0 Yes
D 60 90 60 90 0 Yes
E 90 140 90 140 0 Yes
F 20 80 30 90 10 No
Table 4 Cost-time slope of the activities
Normal Crash
Activity
Code
Duration
(days)
Costs
($)
Duration
(days)
Costs
($)
Crash cost-
Normal cost (ΔC)
Normal time-
Crash time (Δt)
Cost slope
(ΔC/Δt)
A 120 12000 100 14000 2000 20 100
B 20 1800 15 2800 1000 5 200
C 40 16000 30 22000 6000 10 600
D 30 1400 20 2000 600 10 60
E 50 3600 40 4800 1200 10 120
F 60 13500 45 18000 4500 15 300
Table 5 Duration-Cost Data
Duration (days) Direct costs ($) Indirect costs ($) Total costs ($)
140
130
120
115
110
48300
48900
50100
51600
56600
14000
13000
12000
11500
11000
62300
61900
62100
63100
67600
List of Figures
Fig.1.Precedence diagram of activities
140135130125120115110
68000
67000
66000
65000
64000
63000
62000
time (days)
totalcost($)
Scatterplot of total cost vs time (days)
Fig. 2. Scatterplot of cost versus time

140135130125120115110
68000
67000
66000
65000
64000
63000
62000
61000
S 1201.43
R-Sq 87.4%
R-Sq(adj) 74.8%
time (days)
totalcost($)
Fitted Line Plot
total cost = 319875 - 3999 time (days)
+ 15.44 time (days)^2
Fig.3. Regression analysis between costs versus time

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