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Practical Tool for Development of Non-Dominated Optimum Front in Time–Cost Trade-off analysis

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Journal of The Institution of Engineers (India): Series A Aims and scope Submit manuscript


To overcome the limitations of critical path method (CPM) as a project network scheduling technique, various researchers have incorporated time–cost trade-off (TCT) to take care of the specified deadline and corresponding expenses. The results of an industry-wide questionnaire survey (Roofigari-Esfahan, N. (2011). Project Schedule Compression Considering Multi-objective Decision Environment (Doctoral dissertation, Concordia University).) revealed that despite the wide range of TCT analysis methods available in the literature; none of the respondents use these methods. The lack of specialized knowledge of mathematical modeling needed for defining objective function and constraint inequalities seems to be the main deterring in using these involved procedures. This necessitates developing a practical tool in the form of a simple user-friendly software capable of dealing with the rigor of optimization at the back end and entering a simple input at the front end. This paper presents a simple standalone software that requires input in the form of data defining the network precedence and activity time–cost relations. The objective function and constraints equations are automatically formed by the computer code and the mathematical model employing Linear/Integer programming is solved by an open-source solver integrated within the software itself. The program has been validated through implementing it on various case studies from the published literature. The implementation of developed software is illustrated with an example. The detailed results are then presented for a case study of small real-life project. The proposed software thus outweighs the current two stage procedure wherein a mathematical model is framed first and then some commercial solvers like Lingo (Zeinalzadeh in Aust. J. Basic Appl. Sci. 5:208–214, 2011), MATLAB are used to solve the model.

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Data Availability

The computer code developed in the present study is available as supplementary material in Online Resource.


α ij :

Cost slope for activity i-j

CC ij :

Cost of activity i-j at the crash point

CN ij :

Cost of activity i-j at the normal point

TC ij :

Duration of activity i-j at the crash point

TN ij :

Duration of activity i-j at the normal point

β ij :

Cost axis intercept of activity i-j

C ij :

Actual Cost of activity i-j

T ij :

Duration of activity i-j

TE i :

Event time of node i

TE j :

Event time of node j

T :

Predefined project duration

TE s :

Event time of start node

TE f :

Duration of project

C i :

Cost of activity i

β i :

Cost axis intercept

α i :

Cost slope for activity i

T i :

Duration of activity i

TS i :

Start time of activity i

TE j :

Early start time of activity j

TN i :

Duration of activity i at the normal point

ES s :

Early start time of start activity

ES f :

Early start time of finish activity

ES i :

Early start time of activity i

C :

Predefined budget

λ :

Indirect cost per day, considered in $/day

γ + :

Daily liquidated damages, measured in $/day

γ - :

Daily bonus for early completion, measured in $/day

D target :

Contract duration for calculation of liquidated damages /bonus


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Correspondence to Aditi Tiwari.

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Tiwari, A., Trivedi, M.K. Practical Tool for Development of Non-Dominated Optimum Front in Time–Cost Trade-off analysis. J. Inst. Eng. India Ser. A 102, 1073–1088 (2021).

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