The document reviews advanced linear and repetitive scheduling methods for construction projects, highlighting various approaches to optimize the scheduling process for repetitive tasks encountered in constructions such as high-rise buildings and highways. It categorizes scheduling techniques into exact, heuristic, and metaheuristic methods, emphasizing the importance of continuity in resource utilization and minimizing project duration. The paper also discusses optimization strategies, including genetic algorithms and different scheduling methods like Line of Balance and Repetitive Scheduling Method, while suggesting areas for future research.

1. A Review of Advanced Linear/Repetitive Scheduling
Methods and Techniques
Ali Ghavidel, Asad Ullah Malik, Susan Osorio and Ramil Taipov
Term Project – Spring 2019
CIVE 711 – Computer Aided Project Management
Submitted to: Prof. Tarek Hegazy
Submission Date: 18th July 2019

2. 1
Table of Contents
ABSTRACT ...........................................................................................................................2
1. INTRODUCTION...........................................................................................................2
2. BASIS OF THE PROBLEM...........................................................................................4
3. SCHEDULING METHODS...........................................................................................6
3.1 Repetitive Scheduling..............................................................................................6
a) Line of Balance (LOB) ............................................................................................6
b) Repetitive Scheduling Method (RSM) ....................................................................8
3.2 Linear Scheduling..................................................................................................10
4. SCHEDULE EVALUATION AND OPTIMIZATION METHODS...............................12
4.1 Repetitive Projects Evaluation and Review Technique (RPERT).........................12
4.2 Optimizing Strategy Software (OSS) ....................................................................14
4.3 Early Value Management (EVM)..........................................................................17
4.4 Genetic Algorithms (GA) / Soft Logic: .................................................................18
4.5 Learning and Forgetting Theory............................................................................20
4.6 Max-Min Ant System (MMAS) ............................................................................22
5. REVIEW OF NOVELTIES AND METHODS OF LINEAR/REPETITVE
SCHEDULING.....................................................................................................................24
6. CLASSIFICATION OF METHODS............................................................................36
7. ADVANTAGES AND DISADVANTAGES OF LINEAR/REPETITIVE
SCHEDULING TECHNIQUES...........................................................................................40
8. DISCUSSION ...............................................................................................................44
9. CONCLUSION.............................................................................................................45
10. REFERENCES..........................................................................................................46

3. 2
A REVIEW OF ADVANCED LINEAR/REPETITIVE SCHEDULING METHODS
AND TECHNIQUES
Ali Ghavidel, Asad Ullah Malik, Susan Osorio and Ramil Taipov
ABSTRACT
Over the past two decades, significant attention has been focused on the development
of advanced scheduling methods for repetitive/linear construction projects. Several
approaches have been proposed by various research groups in order to solve specific
problems in the scheduling of repetitive/linear construction projects such as high-rise
buildings, bridges, pipelines, and highways. Some of these approaches represent milestones
in the authors’ researches, and others provide a thorough solution implemented in computer
software. This paper is a review of several articles related to this topic, which have been
published in specialized journals since 1998. The solution methods for repetitive/linear
scheduling problems are various, extending from simple graphical techniques to complex
computational and optimization methods, such as genetic algorithms. The methods
underlying the different solutions can be divided into three groups: exact, heuristic and
metaheuristic. This paper presents an introduction into the different repetitive/linear
scheduling problems, outlines the optimization methods proposed, classifies the different
approach methods utilized and, finally, areas for future research are suggested.
Keywords: linear scheduling, construction management, repetitive units,
optimization, genetic algorithms.
1. INTRODUCTION
Repetitive construction projects are those that incorporate a number of similar
activities, which must be performed in a specific order, repeatedly, throughout the entirety
of the project. In this type of projects, the same crew executes a constant task
in different units by moving from one unit to another. Some common examples of these
projects are housing complexes, high-rise buildings, tunnels, highways, and pipeline
networks. Repetitive projects, were referred to as linear projects in the early literature;
however, these linear projects were later categorized into two groups: typical and non-typical
repetitive projects (Moselhi & El‐Rayes, 1993). A typical repetitive project is a project in
which activities have identical durations in all units, such as the construction of the model
houses in a housing complexes project. A non-typical repetitive project, on the other hand,
refers to a project in which repetitive activities have different durations. Highway and railway

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construction projects, where the excavation time for the base may vary due to different
geological characteristics throughout the alignment, are examples of this category.
Studies have demonstrated that repetitive projects can be significantly optimized and
improved by focusing on three main concerns (El-Rayes, 2001). First, applying resource
driven scheduling such that crew work is continuous, in order to minimize crew idle time and
maximize the efficiency of resource utilization. Second, scheduling and optimizing resource
usage so that the total duration of the project is minimized. Finally, given that the majority
of repetitive projects are comprised of both repetitive and non-repetitive activities, it is of
utmost importance to integrate the repetitive and non-repetitive scheduling techniques in an
efficient way. Therefore, vast amounts of studies have relied on these three main concerns
using different techniques and approaches to address them. The proposed approaches can be
summarized in five different groups (G. & I-Tung, 2016; R. Huang & Sun, 2005; Mattila &
Park, 2003). These groups are: (1) mathematical approach including critical path method
(CPM), program evaluation and review technique (PERT), and vertical production method
(VPM), (2) graphical approach including line of balance technique (LOB), linear scheduling
method (LSM), and repetitive scheduling method (RSM), (3) linear programming (LP), (4)
dynamic programming (DP) and (5) simulation.
The traditional mathematical approach, also known as network scheduling method or
bar charting, is considered a primary technique in scheduling construction projects. Among
the utilized methods within the mathematical approach, CPM is one of the most prevalent,
and has been widely used in linear construction scheduling. However, this method is
considered to be less effective for scheduling repetitive projects, mainly because it is not able
to maintain resource work continuity (Aziz, 2014b; H. R. B. & G., 1998; R. Huang & Sun,
2005). Nonetheless, due to the simplicity of mathematical methods, many researchers have
applied this approach in their studies, in an attempt to eliminate its deficiencies through
different functions and algorithms (García-Nieves, Ponz-Tienda, Ospina-Alvarado, &
Bonilla-Palacios, 2019; Ipsilandis, 2007; Lucko, 2009; Lucko, Asce, Orozco, & Asce, 2009;
Radziszewska-Zielina & Sroka, 2018).
As for the graphical approach, one of the most recognized methods for scheduling
repetitive construction projects is the line of balance technique (LOB) (Agrama, 2012; Arditi,
Tokdemir, & Suh, 1998; Gouda, Hosny, & Nassar, 2017). This method uses a simple
methodology for scheduling projects. The main shortage in LOB is considering a constant
production rate and maintaining work crew continuity. However, this method is combined
with other approaches to overcome these shortages. Tomar, A., and Bansal, V.K., (2019)
proposed a hybrid CPM/LOB method which considers both resource continuity using LOB
and logical dependencies using CPM (Tomar & Bansal, 2019). In their paper, the units do
not need to be numbered in order; instead, they just need to consider the successor and
predecessor. The advantages of combining CPM/LOB were applied to assess the delay risk
of repetitive construction (T. O. B., Huseyin, & Irem, 2019). This study presents a LOB

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schedule considering the target rate of delivery. It defines the risk scenarios arising from the
source of uncertainty of activities and finally qualifies risk using Monte Carlo simulation.
Mattila, K., and Park, A., (2003) compared LSM and RSM as two other methodologies within
the graphical approach (Mattila & Park, 2003). The study compares the LSM and the RSM
by analyzing their way of identifying the controlling activities and path. Two continuous full-
span linear activities are used to compare the methods; converging and diverging. The RSM
method relies on control points, whereas the LSM depends on control links.
However, because of simplifications such as considering a specific duration, equal
resource usage, and fixed production order, the above-mentioned techniques have implied
their limitations in optimal repetitive scheduling. Moreover, an important issue associated
with these techniques is that they cannot simultaneously address the four main factors
affecting optimal repetitive project scheduling. These four factors are: (1) minimizing crew
idle time, (2) minimizing the duration of the project, (3) considering crew work continuity,
and (4) considering repetitive and non-repetitive scheduling techniques collectively.
2. BASIS OF THE PROBLEM
For a construction project to succeed, it is fundamental to decide which are the
appropriate planning and scheduling techniques according to its attributes. Through precise
planning and scheduling, the probabilities of a given project to meet the determined deadlines
within its given budget, without disregarding the overall quality, increment significantly. The
critical path method (CPM), which is a network-based scheduling technique, has had a
noteworthy development in the past decades, expanding from graphical techniques and
manual calculations, to the currently leading software. This evolution is mainly attributed to
its popularity in the construction industry. However, in spite of its excellent applications to
intricate and divided projects, CPM has been proved deficient in capturing the necessities of
repetitive construction projects. Some of the reasons for this include its discretionary
distribution of repetitive activities, failure to display continuity of resources and current
location of the on-site works, and extensive amount of activities required to depict a linear
and/or repetitive project. Consequently, different scheduling methods must be applied
(Mattila & Park, 2003; Sharma, McIntyre, Gao, & Nguyen, 2009).
Linear scheduling method (LSM) and repetitive scheduling method (RSM) are other
forms of scheduling that have been present for the last decades; nonetheless, their
advancement has not been as significant, primarily because of the lack of commercially
feasible software. However, these techniques are superior in displaying the nature of
repetitive projects, given that they focus on production rates and work continuity rather than
the correlation among activities. Furthermore, this approach assures learning effect

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maximization and idle labor and equipment time minimization, a major concern in repetitive
construction projects (Duffy, Oberlender, & Seok Jeong, 2010; Long & Ohsato, 2009).
As the core concepts for linear and repetitive scheduling were resolved, the necessity
of optimization techniques became indisputable; therefore, several models have been
proposed. In an endeavor to overcome the shortages presented by previously developed
methods, metaheuristic and evolutionary techniques were developed (Altuwaim & El-Rayes,
2018; Georgy, 2008a; Hyari, El‐Rayes, & El‐Mashaleh, 2009). Different types of
optimization algorithms are used to analyze repetitive construction projects, including
genetic algorithms (GA), memetic algorithms (MA), particle swarm optimization (PSO), ant
colony optimization (ACO), and shuffled frog leaping algorithm (SFL) (Elbeltagi, Hegazy,
& Grierson, 2005). Among the mentioned algorithms, GAs are the most commonly used for
scheduling repetitive projects. Hegazi, T., and Nagib, W., (2001) proposed a computer-based
method for the scheduling of repetitive projects. The algorithm for this method achieved the
minimization of total construction cost using GAs for optimization (Tarek & Nagib, 2001).
GAs were also applied later to present a model for scheduling and optimization of high-rise
building construction projects (Hegazy & Kamarah, 2008). The GA computes crew numbers,
construction method, and interruptions that simultaneously minimize total cost and satisfy
the constraints.
Incidentally, approaches based on singularity functions have gained recognition for
their ability to mathematically model an otherwise graphic technique (Lucko, 2007), generate
minimum overall project duration acknowledging constraints (Lucko, 2009), accurately
calculate different types of floats in linear and repetitive schedules (Lucko et al., 2009),
provide resource leveled profiles (Lucko, 2010), among others. For instance, Lucko Gunnar
(2011) uses a GA approach to minimize the objective function, which, for repetitive/linear
construction projects, is a resource-leveled profile (Lucko, 2011). This study builds on
analyzing criticality of linear schedules with singularity functions. This new approach keeps
resources intact and derives one flexible equation for the complete resource profile of a
schedule, including any timing of resource rate changes. Moreover, a method for scheduling
repetitive construction projects has been developed with one or two objectives such as
minimum project duration, minimum project cost, or both of them, applying different
weights depending on the attribute’s importance (Long & Ohsato, 2009). In order to
minimize the mentioned objectives, the algorithm generates a set of suitable durations for
activities by genetic algorithm and then calculates suitable start times of these activities by a
scheduling algorithm. The method leaves to the scheduler to decide which of near-optimum
duration-cost solutions should be selected.

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3. SCHEDULING METHODS
As stated previously, traditional CPM does not address the specific requirements of
repetitive projects (i.e. maintaining continuity of crew work), which may result in
unnecessary idling of crews and equipment. Another significant disadvantage is that CPM is
unable visualize production rates.
Linear scheduling techniques are more convenient for repetitive construction projects.
They may be divided into two groups: techniques for repetitive construction scheduling
(activities that repeat in discrete units, i.e. tall buildings’ floors, model houses in a housing
complex) and techniques for linear construction scheduling (activities that are performed
continuously along the alignment, i.e. pipelines or highways).
3.1 Repetitive Scheduling
a) Line of Balance (LOB)
This technique was developed in the early 1940s by the Goodyear Company
(Arditi et al., 1998). It has been used for discrete repetitive units (floors of high-rise
buildings, individual houses, etc.), where these are represented in the Y-axis, and
time is represented in the X-axis. Activities on units are shown as bars with starting
and finishing times. Typically, it is assumed that repetitive activities have equal
duration on all units, so production lines linking start-to-start of the same type of
activity on adjacent units are parallel to finish-finish lines. Therefore, the slope of
the production line represents the activity production rate (units per time).
Determining the slope may not be as accurate for the case of variable duration of
activities throughout repetitive units, but the trend of production rate can be visually
recognized. Interruptions of crew work production (idle time) are also identified
from the plot. The advantage of LOB over network diagram is that LOB visualizes
production rate and duration in a graphical format (Fig. 1).

8. 7
Fig. 1. Line of balance technique on repetitive units (Hegazy & Wassef, 2001)
Dolabi and Afshar, (2016) have improved existing LOB based models and
presented a total cost optimization model which accounts for changes in production
rates, in addition to interruptions and construction methods for repetitive
projects. This has a positive impact on the optimal solutions and provides more
flexibility for planners and schedulers (Dolabi & Afshar, 2016).
Fig. 2. Defined modes for considering varying production rates and interruptions
(Dolabi & Afshar, 2016)
It must be noted that for the purpose of computer assisted scheduling and
optimization, LOB should be combined with a network technique (Arditi et al., 1998;
Hegazy & Wassef, 2001). Typically, the CPM method is applied to find a critical
path of the first unit in the series, and then the LOB technique is used for balancing
the production rates and resource usage (Hegazy & Wassef, 2001). Over the past

9. 8
two decades LOB based scheduling has been developed from a simple visual
technique to a highly intellectual software tool which will not only calculate duration
and cost, but also find the optimal composition of resources (number of crews,
interruptions between units, construction methods) in order to achieve minimum
duration and/or minimum project cost.
Genetic algorithms are one of the most widespread tools for the optimization
of LOB schedules when the optimal crew number, construction method and crew
work interruptions are determined by Excel Solver (Agrama, 2012; Aziz, 2013;
Damci, Arditi, & Polat, 2016; Hegazy & Wassef, 2001; Mathew, Paul, Dileeplal, &
Mathew, 2016; Hegazy & Kamarah, 2008).
Another example of evolutionary algorithms is the max-min ant system
(MMAS) algorithm (Dolabi & Afshar, 2016), where the minimum total cost is
achieved by MMAS in order to determine an optimal construction method, the
amount of interruptions and the variances in production rates. Furthermore, to
address discrete time-cost trade-off problem (DTCTP) in bridge construction, GAs
were combined with soft logic (Y. Huang, Zou, & Zhang, 2016). Through soft logic,
project duration can be shorted, not only by crashing critical activities but also by
changing the work sequence between units. Incidentally, fuzzy logic techniques were
employed (Arditi et al., 1998) to study of the effect of the learning curve on LOB
unit duration, evidencing that man-hours expended per unit decreased as the number
of repetitive units increased, when these units are typical. Monte Carlo simulation
was used for assessment of project delay risks (T. O. B. et al., 2019), when sensitivity
of project duration to uncertainties in man-hours required per unit is reviewed.
Finally, graph theory method implemented in MATLAB was employed to create
combined CPM/LOB algorithm for optimal crew routing (Gouda et al., 2017).
b) Repetitive Scheduling Method (RSM)
The RSM technique was introduced by Harris, R., and Ioannou, P. (1998) and
further developed by Ioannou, P., and Yang, T. (2016). It is a graphical technique,
which represents discrete repetitive activities as series of production lines. Duration
of a particular activity on repetitive units is presented on the X-axis, while the
progress of unit production (0 to 1) is shown on the Y-axis (Ioannou & Yang, 2016;
Harris & Ioannou, 1998). Slope of production line indicates an UPR - unit
production rate (units/day), as seen in Fig. 3.

10. 9
Fig. 3. Representation of activity in RSM format (bottom) versus network diagram
and bar chart (Harris & Ioannou, 1998)
The project’s activities are represented as a sequence of production lines (each
production line is an activity) on the X-Y plot. For vertical projects (i.e. high-rise
buildings) where the work progress is in units, the Y-axis represents the units, and
time is on the X-axis. Similarly, for linear projects where the work progress is
measured in length units (i.e. highways and pipelines), the X-axis represents the
length, whereas Y-axis shows time.
RSM was developed as a simple graphical tool intended for
positioning (rotating, shifting, aligning) of the unit production lines to ensure the
shortest duration and continuity of resource utilization. RSM determines control
points for rotation/shifting of production lines, and its controlling sequence is the
sequence of activities from start to finish which determines the project duration,
analogous to the critical path in CPM. However, while the RSM is convenient for
graphical scheduling and progress monitoring, mathematical formalization of this
method is quite cumbersome compared to LOB, reason why RSM is virtually not
employed nowadays in computer assisted scheduling (Ipsilandis, 2007). Some of the
available papers on this topic are:
• Multi-objective LP Scheduling Model for LRPs (MOLPS-LRP): this
paper combines CPM and RSM, employing a linear programming
algorithm for finding the optimal start and finish dates of activities. Its
objective function is to minimize project duration and cost (Ipsilandis,
2007).

11. 10
• Genetic algorithm model is used to find the optimal construction method:
this paper focuses on minimizing the project duration and cost (Long &
Ohsato, 2009).
It is worthwhile to mention that repetitive scheduling still has an extensive
area for further research to focus on, in order to appropriately implement it in the
construction industry. However, some of the most noteworthy computerized
scheduling techniques that have been developed over the last few years are mentioned
below:
• Genetic algorithm for optimization of cost and duration (Hegazy & Kamarah,
2008; Hegazy & Wassef, 2001)
• Fuzzy logic for determining crew production rate with consideration of
learning effect (Arditi et al., 1998)
• Minimum moment algorithm for resource leveling (Hassanein & Moselhi,
2005)
• Mixed-integer linear programming for TCTP (Time-cost trade-off problem)
(García-Nieves et al., 2019)
• Consideration of the learning rate in the duration of repetitive activities (Arditi
et al., 1998)
• Delay risk assessment Line-of-Balance scheduling and Monte Carlo
simulation (T. O. B. et al., 2019)
3.2 Linear Scheduling
Linear construction projects, such as highways and pipelines, have specific
features: construction activities are continuous, construction progresses along the
entire alignment, and the work sites are distributed horizontally. Thus, linear
schedules depict a time-location plot with distance units or stations on the X-axis, and
time on the Y-axis, as seen in Fig. 5. This plot visualizes location and production rate
of activities at every moment of time, making it intuitively clear for schedulers and
managers.

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Fig. 4. Linear schedule with controlling activity path as per Harmelink & Rowings, 1998
(Lucko & Orozco, 2009)
The linear construction activities scheduling technique frequently cited in literature
is the LSM – Linear Scheduling Method (Harmelink & Rowings, 1998). LSM is a graphical
technique, which allows finding the controlling path, which is the longest continuous path
through the sequence of activities. The controlling path is analogous to the critical path
described in CPM.
Some of the most noteworthy computerized scheduling techniques that have
been developed for linear scheduling over the years are mentioned below:
• Minimum moment algorithm for resource leveling (Hassanein & Moselhi,
2005)
• Singularity function for mathematical formalization of LSM method (Lucko,
2007)
• Singularity function for schedule analysis and optimization (Lucko, 2011;
Lucko & A., 2009)
• Metaheuristic evolutionary resource scheduler algorithm for linear scheduling
(Georgy, 2008)

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• Evolutionary algorithm with selection of fittest individual from population
and application of mutation (Hsie, Chang, Yang, & Huang, 2009)
• Minimum moment algorithm for resource leveling (Hassanein & Moselhi,
2005)
• Advanced linear scheduling program with varying production rates (Duffy et
al., 2012)
• Optimization of linear schedule with constraint programming (Tang, Liu,
Wang, Sun, & Kandil, 2018)
4. SCHEDULE EVALUATION AND OPTIMIZATION METHODS
4.1 Repetitive Projects Evaluation and Review Technique (RPERT)
This is a simplified software that will generate the expected project
completion probability of a specified duration (contract duration) (Aziz, 2013).
RPERT software is designed by a Java programming code system to provide a
number of new and unique capabilities. These capabilities include: (1) viewing the
expected project completion probability according to a set of specified durations per
each identical activity (optimistic time, most likely time, and pessimistic time) in the
analyzed project, and (2) providing seamless integration with available project time
calculations.
This software was developed using the Line of Balance technique (LOB) in
case of single or multiple crews integrated with the Program Evaluation and Review
Technique (PERT). PERT is a management tool for defining and integrating events
with coordinating moves for completing a project’s objectives on time; a process
which must be accomplished in time to assure completing project objectives on
schedule (Aziz, 2013). PERT was originally developed in 1957 by the U.S. Navy
Special Projects Office on the Polaris missile system to support the nuclear submarine
projects. PERT is one of the few managerial planning and controlling techniques
with powerful concepts like management of probabilities. Completion times of
activities are estimated using most optimistic, most pessimistic and most likely or
normal times.
Below are some of the most relevant specifications and qualities of PERT:
• Presents a comprehensive illustration of all major project activities and
their interdependencies.
• Provides time requirements needed for completing each
component activity.

14. 13
• Focuses managerial attention on those business activities most vital in
meeting the project completion date and identifies which resources could be
used more effectively if transferred to other phases of a project.
• PERT provides a scheme of the project as it occurs, thereby illustrating the
effects of managerial changes in the entire project.
• The ability of PERT to predict future performance and potential
future problems through frequency reporting, marked its major departure
from previous planning and control techniques which relied heavily on
historical data.
Fig. 5. Taxonomy of the existing planning techniques for construction projects
(Aziz, 2014)
Over time, many improvements have been made to the original method, which
include participative techniques like PACE (Programme Analysis, Control and
Evaluation) which are an enhanced version of PERT.
RPERT is implemented in four major modules including:
(1) User interface module to facilitate inserting the input of project data and
visualizing the output data. The present user interface module is designed to
implement the necessary interface functions in two main phases:
(a) An input phase that facilitates the input of project data details, project
activities, activities relations, and contract duration; and
(b) An output phase that allows the user to view the expected project
completion probability within a specified/certain duration.

15. 14
(2) A database module to facilitate data storage. The main purpose of this module is
to develop a relational database capable of storing necessary input data (e.g., project
data details, project activities, activities relations, contract duration) and storing
produced output data (e.g., expected project completion probability within a
specified/certain duration). This module is composed of main groups that are
designed to store the following construction planning details: (a) project data; (b)
holidays data; (c) exceptions data; (d) activities data; (e) relationships between
activities data; and (f) contract data (contract duration).
4.2 Optimizing Strategy Software (OSS)
OSS is a Genetic Algorithm based software for repetitive construction projects with
multi-mode resources developed by Aziz (2013). Like all GA based techniques, it was
developed based on the following basic steps (Aziz, 2013):
1. Generation of random population of “n” chromosomes (suitable solutions for
the problem).
2. Evaluation of fitness of each chromosome. Fitness determines the likelihood
of survival and reproduction of each solution in the following generations by
calculating four fitness functions based on four decision/optimization
variables.
3. Selection of parent chromosomes from the population based on better fitness
is done based on Elitism.
4. Production of offspring by Crossover and mutation
5. New offspring are accepted and replace less fit previous population.
6. The new population is then tested against the end condition criteria to return
the best solution in the current population to Step 2 and the loop keeps on
running.
OSS was designed for two main tasks: first, to incorporate and enable the optimization
of any repetitive construction project, and second, to enable available starting times for
all activities in the studied project and select the suitable start time of each activity within
its total float to get the best optimization scenario among large-scale solutions. These
activities have various numbers of resource mode options, each mode has its own
production rate (units/day), material cost, cost rate of labors and equipment and
subcontractor lump sum cost (Aziz, 2013).
Although the advantages, disadvantages and overview of OSS can be found in Table 1
and Table 3, some characteristics of its four modules are worth mentioning below (Aziz,
2013):

16. 15
• The project parameters include the following: (a) project size; (b) activity
precedence information; and (c) available resource utilization options for each
activity.
• The required GA parameters for the initialization phase include the following: (a)
string size; (b) number of generations; (c) population size; (d) mutation rate; and
(e) crossover rate.
• The string size is determined by the model, considering the total number of
construction activities (K) included in the analyzed project. The number of
generations (G) and population size (U) are identified based on the selected string
size in order to improve the quality of the solution.
• The mutation rate and crossover rate are determined considering the population
size and the method of selection employed by the algorithm, respectively.
• The Population generation phase in the running module calculates the optimal
rank of each solution generated by the Initialization phase in the same running
module. First, this is done by ranking the solutions in the population according to
their highest net present value and lowest duration, price, and maximum working
capital; this is called Pareto optimal domination of solutions, where a solution is
identified as dominant if it is better than all other solutions in all of the considered
optimization objectives simultaneously.

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Fig. 6. Main modules and their respective sub-sections, and the function they perform in
OSS (Aziz, 2013)

18. 17
4.3 Early Value Management (EVM)
EVM (Earned Value Project Management or Earned Value Performance Management
(EVPM)) is a project management technique for measuring project performance and progress
in an objective manner and forecast it as well. Project control takes place against the cost
baseline using a technique called “Earned Value” (Roseke, 2018). Lee (2016) has used this
method to forecast and illustrate the ripple effect of disruptions on repetitive construction
activities (Lee, 2016). Disruption can be defined as any change in the method of performance
or planned work sequence contemplated by the contractor at the time the job was tendered
(Halligan, Demsetz, Brown, & Pace, 1994). Ripple effect is the notion that a single action
has an effect over several different entities (G. N., 2019).
Fig. 7. Impact on the estimated final cost (Aziz, 2013)
Similar to the Measured Mile Method, the loss of productivity in EVM is calculated
as the difference between the productivity actually observed and the productivity that might
reasonably have been expected if not for the unanticipated conditions. In practical projects,
if project activities are interrupted for owner-related reasons, contractors can file for
“Inefficiency Claims”. However, to do that under the umbrella of EVM, they would have to
perform the following basic tasks:
1. Identify and define impacted work (Output → CPIi = impacted cost performance
index)
2. Identify the impacted and not impacted time periods and project locations (Output
→ CPIu = not impacted cost performance index)
3. Carefully evaluate the difference between the 2 periods. (Output →∑(𝐶𝑃𝐼 𝑢 −
𝐶𝑃𝐼𝑖))
4. Locate and assemble job-cost records (Output → ACWPi = actual cost of work
performed for impacted period)
5. Determine whether they will base the analysis on hours or dollars. (Output → LR =
labor rate (labor costs/total costs))

19. 18
6. Calculate the loss (Output → D = damages due to lost labor productivity)
𝐷 = ∑(𝐶𝑃𝐼 𝑢 − 𝐶𝑃𝐼𝑖). 𝐴𝐶𝑊𝑃𝑖. 𝐿𝑅
Finally, Cost Performance Indexes are calculated in the following manner:
𝐶𝑜𝑠𝑡 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 𝐼𝑛𝑑𝑒𝑥 (𝐶𝑃𝐼) =
𝐵𝑢𝑑𝑔𝑒𝑡𝑒𝑑 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑊𝑜𝑟𝑘 𝐶𝑜𝑚𝑝𝑙𝑒𝑡𝑒𝑑 (𝐵𝐶𝑊𝑃)
𝐴𝑐𝑡𝑢𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑊𝑜𝑟𝑘 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑒𝑑 (𝐴𝐶𝑊𝑃)
4.4 Genetic Algorithms (GA) / Soft Logic:
In computer science and operations research, a genetic algorithm (GA) is a
metaheuristic method inspired by the process of natural selection, which belongs to
the larger class of evolutionary algorithms (EA). GAs are commonly used to generate
high-quality solutions for optimization and search problems by relying on bio-
inspired operators such as mutation, crossover, and selection. John Holland
introduced GAs in 1960 based on the concept of Darwin’s theory of evolution;
afterwards his student David E. Goldberg extended GAs in 1989.
Huang, Zou, and Zhang (2016) have developed a mathematical model based
on a genetic algorithms and linear programming approach considering the work
sequence as a variable (.i.e. soft logic) to address discrete time-cost trade-off problem
(DTCTP) in repetitive construction projects (Y. Huang et al., 2016). This
programming approach differs from other optimization methods which often assume
only one work sequence between various repetitive units when determining optimum
crew formation and interruption strategies for each activity in all the units (Ezeldin &
Soliman, 2008; Hyari et al., 2009; Reda, 2007; Senouci & Eldin, 2010; Terry &
Lucko, 2012). The computation results of Huang, Zou and Zhang’s (2016) models
validate the enhanced flexibility in minimizing project duration and cost while
scheduling by applying soft logic.
In general, the objective of DTCTP is divided into 3 parts:
1. Deadline problem
2. Budget problem
3. Time-cost curve problem

20. 19
Fig. 8. Example of position-based crossover (Y. Huang et al., 2016)
Fig. 9. Example of mutation (Y. Huang et al., 2016)

21. 20
Fig. 10. Mechanism of GA (Y. Huang et al., 2016)
4.5 Learning and Forgetting Theory
Learning theory refers to the experience gained by an employee/worker/crew by
doing a particular task repeatedly, which leads to reduction in duration of each subsequent
repetitive task. The use of the learning theory in the construction industry is limited. This
is owed to the varying conditions of work and the inability to provide the crews with the
opportunity of conducting uninterrupted works while performing technologically
homogenous processes in the consecutive stages of construction (Biruk & Rzepecki,
2019). Therefore, it is more suitable to develop a model for scheduling repetitive tasks
using Learning and Forgetting theory simultaneously. In forgetting theory, the effect of
forgetting is proportional to the duration of intervals/interruptions, for example, when the
crew either stops working or is assigned to some other task, which is not similar to the
ones being performed prior to the interruption.

22. 21
Fig. 11. The knowledge of acquisition and forgetting on the work efficiency (Jaber &
Bonney, 1997)
Although a considerable amount of research has been done for learning theory and
forgetting theory separately, Biruk and Rzepecki (2019) proposed a method in an attempt
to bring them together. This method utilizes Wright’s (2012) exponential model of
learning, as well as the forgetting model prepared by Globerson and Levin (1987),
together to give the duration of the individual repetitive construction processes, which
may provide an advantage at the stage of submitting bids in tenders (Biruk & Rzepecki,
2019).
Below the Learning Expression developed by Wright (2012) is shown (Wright, 2012):
𝑡 𝑛 = 𝑡1. 𝑛−𝑙
where: tn – process duration in a unit, n, t1 – process duration in the first construction unit,
n – the number of process repetitions (number of the next unit), and l – reduction
parameter, which determines the shape of the logarithmic curve.
Similarly, the Forgetting Expression developed by Globerson and Levin (1987) is shown
below (Globerson, 1987):
𝑡 𝑏 = 𝑡1 − [𝑡1 − 𝑡 𝑤]. (𝑎. ∆𝑡 + 1). 𝑒−𝑎.𝑡

23. 22
Where, tb = time in which loss of learning effect occurs, ∆t = duration of interval, tw –
duration of the subsequent process, if an interval does not occur, a – forgetting
coefficient, and e – the base for natural logarithms.
4.6 Max-Min Ant System (MMAS)
Max-Min Ant System falls under the category of Ant Colony Algorithms Family. Ant
colony optimization (ACO) algorithms evolve not in their genetics but in their social
behavior (Elbeltagi et al., 2005). The method originally developed for computer science
applications has found its applications in advanced scheduling of linear and repetitive
projects as well.
As the name indicates, MMAS adds maximum and minimum pheromone amounts.
Dolabi and Afshar (2016), have taken this concept, improved the existing LOB- Based
models, and presented a Total Cost Optimization Model for LRPs by varying production
rates, giving construction planners additional flexibility. Similar to maximum and
minimum pheromone amounts, the proposed model has imposed upper and lower limits
on construction methods, modes for each activity, interruption days for each activity and
number of outsourced and omitted crew for each activity (Dolabi & Afshar, 2016). In
contrast with other ACOs, the proposed MMAS model uses a two-stage optimization
model since Dolabi and Asfhar (2016) concluded this it surpasses the one-stage MMA
optimization model.
MMAS takes the following as inputs:
• Number of ants
• Termination criteria
• Maximum and minimum limit of pheromone information
• Heuristic information
• Evaporation rate
• Relative influence of pheromone trails and heuristic information, algorithm
exploration and exploitation parameter
• Pheromone updating information

24. 23
Fig. 12. Procedures of two-stage MMAS optimization model for optimizing total project
cost (Dolabi & Afshar, 2016)

25. 24
5. REVIEW OF NOVELTIES AND METHODS OF LINEAR/REPETITVE
SCHEDULING
With the intention of introducing a comprehensible review of the novelties
and methodologies proposed by all the papers reviewed, the main points of each paper
are presented in Table 1.
Table 1: Linear/Repetitive Scheduling Techniques’ Novelties and Methodologies
No
Authors
NameofPaper
Year
Novelty
Specifications/Methodology
1
Anjul Tomar ·
V. K. Bansal
Scheduling of repetitive
construction projects
using geographic
information systems
2019
Combining critical path method and
line of balance (LOB) techniques to
schedule both non-repetitive and
repetitive projects simultaneously.
This hybrid method also uses
geographic information systems
(GIS) environment to decreases the
duration of projects.
The program is developed using Python
along with the usage of ArcGIS for
graphical interpretations.
2
Onur B.
Tokdemir,
M.ASCE;
Huseyin Erol;
and Irem
Dikmen
Delay Risk Assessment
of Repetitive
Construction Projects
Using Line-of-Balance
Scheduling and Monte
Carlo Simulation
2019
LOB used schedule considers the
target rate of delivery in the study. It
also defines the risk scenarios arising
from the source of uncertainty of
activities and finally qualifies risk
using Monte Carlo simulation in the
model.
The delay risk assessment method in
this paper consists of four steps: 1-
LOB calculations, 2- Risk factors are
analyzed using stochastic simulations,
3- A sensitivity analysis is conducted to
formulate effective risk response, 4-
Risk responses are developed and
project risks are re-analyzed.
3
"Juan Diego
García-
Nieves1, José
Luis Ponz-
Tienda,
Angélica
Ospina-
Alvarado,
Mateo Bonilla-
Palacios"
Multipurpose linear
programming
optimization model for
repetitive activities
scheduling in
construction projects
2019
a) the simultaneous implementation
of multiple executions with
controlled execution shifts,
accelerating or deaccelerating the
sub-activities respect the previous
sub-activity b) the possibility of
considering multiple crews, fully
integrated with repetitive activity
scheduling, resource-constrained
scenarios, time-cost analysis and
discretional continuity restrictions
The model developed a linear
mathematical model to handle activities
in repetitive projects.
4
Slawomir
Biruk, Lukasz
Rzepecki
Scheduling Repetitive
Construction Processes
Using the Learning-
Forgetting Theory
2019
Although a considerable amount of
research has been done in Learning
Theory and Forgetting theory
separately; this paper proposes a
method in which Wright’s
exponential model of learning as
well as the forgetting model prepared
by Globerson and Levin are applied
together to give the duration of the
individual repetitive construction
processes which may provide an
Implementation plan of repetitive
construction processes was made for a
multi-storey building and by taking into
account the impact of learning and
forgetting effect in MS Excel due to
unavailabity of any other commercially
available software which could cater for
learning and forgeeting coefficients.

26. 25
advantage at the stage of submitting
bids in tenders.
5
Ayman
Altuwaim1 and
Khaled Rayes
Optimizing the
Scheduling of
Repetitive Construction
to Minimize
Interruption Cost
2018
Simultaneously minimizes project
duration, crew work interruptions,
and interruption costs. The novelty
of the model is that it is capable of
considering and minimizing
interruption costs along with other
affecting parameters.
The model uses a two step procedure:
first, the model uses a newly developed
heuristic scheduling model using GA to
generate a wide range of schedules that
minimize both project duration and
crew work interruptions. In the second
step, the model minimizes the
interruption cost using a single
objective optimization model.
6
Elżbieta
Radziszewska-
Zielina and
Bartłomiej
Sroka
Planning repetitive
construction projects
considering
technological
constraints
2018
Considering technological
constraints in a flexible way in
repetitive construction projects
In the model, tasks can not be
interrupted. Start time and duration of
each task are considered as input. Both
constraints and goal functions are
linear. Therefore, the solution is Linear
programming. The author used Python
programming language with Simplex
algorithm to analyze the model.
7
J. D. Garc´ıa-
Nieves, J. L.
Ponz-Tienda &
A. Salcedo-
Bernal
The Multimode
Resource-Constrained
Project Scheduling
Problem for Repetitive
Activities in
Construction Projects
2018
Considering activity acceleration
routines and resource consumption
in an efficient manner, which
commonly are not considered in
traditional resource-constrained
project scheduling problems.
The model takes into account two
different objective functions; the project
makespan and the project tardiness.
Both objective functions represent the
project duration.
8
Ayman
Altuwaima,b,
Khaled El-
Rayes
Minimizing duration
and crew work
interruptions of
repetitive construction
projects
2018
Minimize the duration and crew
work interruptions of repetitive
construction projects by allowing
selected work interruptions while
maximizing work continuity.
This model is developed in four main
phases: early schedule computation
phase, work-continuity float
calculation, strict work continuity, and
performance evaluation.
9
"Yuanjie Tang,
Rengkui Liu
and Futian
Wang,
Quanxin Sun,
Amr A.
Kandil"
Scheduling
Optimization of Linear
Schedule with
Constraint Programming
2018
Constrained Programming (CP)
based algorithm is proposed for
linear scheduling of transportation
projects, e .g. railways. Discrete
modes of activity (construction
methods) are used to describe
relationships between production
rate/duration, resource requirements,
and cost. Method is verified on three
case studies.
Scheduling module is written in ILOG
OPL language (IBM Corp., 2009)
integrated with IBM ILOG CPLEX
Optimization Studio. To dicretize
continuous variables, authors introduce
a notation of "Mode of activity", which
is a combinatuon of {resource
requirements, rate, cost, crew index}
for linear activities and {resource
requirements, duration, cost, crew
index} for block activities. Mode of
activity is similar to Construction
method. Number of modes is finite. A
constraint system includes seven types
of constraint: logical constraints (e. g.
time and distance buffers), production
rate, construction continuity, resource,
duration, cost, max crews number.
Model can be solved for various
Objective functions: min duration, min
cost, resource leveling,
optimal resource utilization. Desision
variables include Mode (Construction
method), Crew number, Start date of
activity.
10
Xin Zou,
Ph.D.1; Shu-
Cherng Fang2;
Yuan-Sheng
Huang3; and
Li-Hui Zhang4
Mixed-Integer Linear
Programming Approach
for Scheduling
Repetitive Projects with
Time-Cost Trade-Off
Consideration
2017
Minimizing the total cost in given
deadline without formulating such
that unit assignment strategy does
not produce a negaive effect on
projectec cost and duration and
changing the logic sequence of
different units will not result in
shorter project duration or cost.
TCTP model is mathematical based and
used for medium sized projects, while
TCTP-Approximation method is
appropriate for large-sized projects.
TCTP-Approximation is able to solve
the same size problem faster than TCTP

27. 26
11
Ahmed Gouda
a, Ossama
Hosny b,
Khaled Nassar
Optimal crew routing
for linear repetitive
projects using graph
theory
2017
Assigns multitasking skilled crews to
more than one activity for optimizing
the crews routing such that attempts
to enhance the LOB implementations
on breaking down the activities and
formulating, assigning multitask
crews in linear projects, and crew
routing optimization using a new
method.
Methodology: Uses graph theory for
searching and hybrid CPM/LOB
method to minimize the total resource
usage of a linear project. Objective:
First, assign multitasking skilled crews
to the different activity instead of only
one activity, second, minimize the
number of resources. Variables: The
number of crews, crews formulation,
and routing of each crew. Constraints:
Start and finish date of activities,
activity production rate, overall project
completion date, number of available
crews, and logic relationships among
activities. "
12
Yuansheng
Huang, Xin
Zou, Lihui
Zhang
Genetic Algorithm-
Based Method for the
Deadline Problem in
Repetitive Construction
Projects Considering
Soft Logic
2016
This study develops a mathematical
model considering soft logic to
address the discrete time-cost trade-
off problem (DTCTP) in repetitive
construction projects. The objective
is to select a set of activity modes,
start times, and work sequences
between units such that the total cost
is minimized while meeting a given
deadline. A targeted genetic
algorithm is also presented, in which
only the activity modes and work
sequences between units are
encoded, and suitable start times of
all subactivities are then determined
using a linear programming
approach.
Objective function is to minimize
project cost with precedence relation
constraints as finsih to start with zero
lag time between activities. The soft
relation constraints ensure that the start
time of each activity in sucessor unit is
larger than or equal to the sum of the
finish time of preceeding unit and the
resource-transferring time between the
succesor and predecossor unit of this
activity if second unit is scheduled to
start after first unit. The deadline
constraint ensures that the project
duration is not longer than the allowed
deadline. The main motivation for
using a GA to attack the problem lies in
the power of GAs in searching for high-
quality solutions for the DTCTP.
13
Hamid Reza
Zolfaghar
Dolabi, Abbas
Afshar
Cost Optimization of
Repetitive Projects with
Varying Production
Rates using a Max-Min
Ant System
2016
This paper addresses the exisiting
limitation of constant rate of
production lines in each unit by
aiming to improve existing LOB-
based models and presents a total
cost optimization model which
accounts for changes in production
rates, in addition to interruptions and
construction methods. Proposed
model uses the max-min ant system
(MMAS) algorithm.
Objective function is used to minimize
Direct, In-direct, Incentive,
Interruption, Basic-crew and
Outsourcing-crew cost. A two stage
optimization model is used, where the
first stage defines the construction
methods based on various inputs like
activity properties, number of units,
stated project deadline and various
other tunable parameters of the MMAS
model like maximum and minimum
limit of pheromone information,
algorithm exploration and exploitation
parameter and pheromone updating
information etc; the second stage is
designed to determine the remaining
decision variables.
14
Photios G.
Ioannou, I-
Tung Yang
Repetitive Scheduling
Method: Requirements,
Modeling, and
Implementation
2016
This paper presents the necessary
requirements that scheduling
systems should address to meet the
needs and complexities of repetitive
projects in practice and have
proposed a unified scheduling
framework called Repetitive
Scheduling Method (RSM).
Repetitive. RP2, a computer program
developed by the authors to validate
the proposed scheduling approach, is
used to develop the production
The computer program .i.e. RP2
focuses on the development of a
scheduling system that minimizes
project duration while maintaining
resource work continuity to minimize
un-forced idleness. A fundamental new
scheduling concept introduced in RSM
is the controlling sequence, which is the
chain of activities that currently
determines the duration of the target
schedule and which results from
scheduling activities to achieve

28. 27
diagrams and tabular reports of the
target schedule for a complex of
four-story apartment buildings for a
low-income housing project.
resource work continuity. A set of
requirements was compiled to serve as
design criteria based on obervations
from the authors' research and that of
the others. A computerized system like
RP2 is an ideal tool for performing a
what-if sensitivity analysis, because it
can generate complete graphical and
tabular reports almost instantly
15
Jeeno Mathew,
Brijesh Paul,
Dileepal J,
Tinjumol
Mathew
Multi Objective
Optimization for
Scheduling Repetitive
Projects using GA
2016
This study will help to develop a
method for scheduling repetitive
projects with objectives of
minimizing project duration, project
cost and both of them with
constraints of precedence
relationships between activities,
constraints of precedence
relationships between units and
constraints of the due date in which
work should be complete. In this
work a penalty cost is added to the
total project cost in a situation where
a particular activity is not completed
in the due date of that activity in a
unit. In this work a penalty cost is
added to the total project cost in a
situation where a particular activity
is not completed in the due date of
that activity in a unit.
Objective TC is computed using
planner-specified weights that reflect
the relative importance of project
duration and project cost respectively.
Durations per unit quantity of work of
activities are the decision variables
which is assumed to be the genes of the
chromosome in the populations.
Chromosome size is depend on the
difference between the maximum
durations per unit quantity of work of
activity and minimum durations per
unit quantity of work of activity of all
the resources in an activity. In this work
a penalty cost is added to the total
project cost in a situation where a
particular activity is not completed in
the due date of that activity in a unit.
The method consider the constraints of
precedence relationships between
activities, constraints of precedence
relationships between project units and
constraints of due date in which work
should complete for each activity in
every unit. The proposed method will
help the project manager to select the
best crew options to optimize the
project duration and project cost in
repetitive project works.
16 Jae-Seob Lee
Estimating Cumulative
Damages due to
Disruptions in
Repetitive Construction
2016
The original contribution of the
paper is summarized as (1)
application of Earned Value
Management (EVM) and resource
continuity to the topic of
cummulative damage calculations
due to changed process sequence and
(2) development of a method to
assess the ripple effect as well as the
direct effect of disruptions on project
productivity performance (in specific
labor productivity) by Cost
Performance Indexes and comparing
it with Measured Mile analysis. The
unique value of this study lies in its
EVMbased hybrid approach to
addressing the time-varying
uncertainty issue on performance
change due to disruptions common
to construction projects experiencing
changes requiring resequence of
works.
The method for estimating cumulative
damages in Repetitive Construction is
proposed based on the assumption that
the damages are mainly incurred by (1)
idle time of resources, (2) lost
productivity, and (3) ripple effect,
which eventually impact on the project
final cost. Damages on Resource
Utilization is done analytically by
calculating daily loss in labor cost from
the work interruption period i.e. lag
between acticities. Damages due Lost
labour productivity are calculated by
the earned value analysis which
implicitly compares planned
productivity (unimpacted cost
performance index) with actual
productivity (impacted cost
performance index) in the same
impacted periods to determine the loss
of productivity. EVM is again used to
cater for ripple effect which effects
labor productivity of the unchanged
work in addition to its impact on the
changed work. In earned value claims
analysis, the measured mile is analyzed
using earned value methods rather than
by the simple extrapolation of work
hours. Consequently, the total cost of
impacted and nonimpacted activity
costs will be compared to EAC
(Estimate At Completion) based on the

29. 28
measured mile. The productivity
multiplier (actual job hours/earned job
hours) is obtained by comparing earned
job hours or costs for measured mile
activities to actual job hours or costs for
the same activities. The difference
between each ETC (Estimate To
Complete) is the value of the cost
impact due to ripple effects.
17
Atilla Damci,
David Arditi,
Gul Polat
Impacts of Different
Objective Functions on
Resource Leveling in
Line-of-Balance
Scheduling
2016
The paper studies how the selection
between 10 different objective
functions impacts the resource
leveling profile (Number of workers
vs time curve) in LOB scheduling.
GA algorithm is used to identify
optimum crew size and number of
crews. Result: in small pipeline
project resource distribution is the
same for either objective function.
Future study direction: to investigate
the impact of objective function on
complex projects with different
precedence order, parallel activities
and multiple resources.
Ten objective functions were applied to
GA algorithm: The sum of the absolute
deviations in daily resource usage The
sum of only the increases in daily
resource usage from one day to the next
The sum of the absolute deviations
between daily resource usage and the
average resource usage The maximum
daily resource usage The maximum
deviation in daily resource usage The
maximum absolute deviation between
daily resource usage and the average
resource usage The sum of the square
of daily resource usage The sum of the
square of the deviations in daily
resource usage The sum of the square
of the deviations between daily
resource usage and the average resource
usage The sum of the idle and
nonproductive resource days during the
entire project duration. All these
objective functions resulted in the same
schedule and daily resource usage
profile.
18 Gunnar Lucko
Temporal Constraints in
Linear Scheduling with
Singularity Functions:
Case of Calendarization
2014
This paper develops new theory in a
novel application of singularity
functions, which are flexible range-
based mathematical expressions, to
perform a complete and transparent
calendarization. It solves the
challenges of incorporating leap
years, distinguishing weekdays, and
inserting nonworking holidays into a
schedule.
A five-step algorithm is provided for
linear schedules, which explicitly
contain more information than network
schedules and thus have more analytical
potential. The new model is validated
with commercial software. It enables an
integrated treatment of different types
of constraints and can lead toward
improving algorithmic optimization
approaches for planning construction
projects. Three research objectives are
addressed to create the foundations for
a comprehensive calendarization: •
Review calendar elements, including
weekdays versus weekends, holidays,
leap years, and day-month-year dates,
and derive a complete model for them
based on singularity functions; •
Integrate model with existing
scheduling methodology for constraint
satisfaction applications to create a
functional calendarization algorithm
that is transparent, general, and
customizable; and • Verify its
correctness and validate it with a
detailed example from the literature by
comparing its calculated dates with
calendar constraints against those
generated by software products. The
remainder of the paper is organized as
follows: It defines the basic term and
principles of using singularity
functions, establishes detailed
objectives for calendar functions,
reviews rules for calendar elements,
develops a five-step calendarization

30. 29
algorithm, analyzes an example of a
linear schedule, and validates the
accuracy of the algorithm.
19
Remon Fayek
Aziz
RPERT: Repetitive-
Projects Evaluation and
Review Technique
2013
This paper focuses on the calculation
of expected completion probability
of any repetitive construction project
within a specified/certain duration
(contract duration) by using Line Of
Balance technique (LOB) in case of
single or multiple number of crews
integrated with Program Evaluation
and Review Technique (PERT).
Repetitive-Projects Evaluation and
Review Technique (RPERT), which
is a simplified software, will
generate the expected project
completion probability of a
specified/certain duration (contract
duration). RPERT software is
designed by java programming code
system to provide a number of new
and unique capabilities, including:
(1) Viewing the expected project
completion probability according to
a set of specified durations per each
identical activity (optimistic time,
most likely time, and pessimistic
time) in the analyzed project; (2)
Providing seamless integration with
available project time calculations.
The system is developed in four main
modules: (1) A user interface module to
facilitate inserting the input of project
data and visualizing the output expected
project probabilities solutions; (2) A
database module to facilitate data
storage and retrieval of data; (3) A
running module can be defined as a
class of programming code system and
is designed to allow different
calculation runs; and (4) A processing
module can be defined as a class of
programming code system, especially
java coding and its applications that is
designed to communicate and exchange
data from available modules with a
seamless integration.
20
Remon Fayek
Aziz
Optimizing strategy
software for repetitive
construction projects
within multi-mode
resources
2013
This paper focuses on how to
calculate tender data using
Optimizing Strategy Software
(OSS), which is superior to existing
optimization algorithms, for
repetitive construction projects with
identical activity’s duration in case
of single number of crew such as:
project duration, project/bid price,
project maximum working capital,
and project net present value of the
studied project. A simplified multi-
objective optimization software
(OSS) is presented that creates best
tender data to contractor compared
with more feasible options generated
from multi-mode resources in a
given project. OSS is designed by
java programing code system using
eclipse software to provide a number
of new and unique capabilities,
including: (1) Ranking the obtained
optimal plans according to a set of
planner specified weights
representing the relative importance
of duration, price, maximum
working capital and net present value
in the analyzed project; (2)
Visualizing and viewing the
generated optimal trade-off; and (3)
Providing seamless integration with
available project management
calculations.
In order to provide the novel
capabilities of OSS, the system is
implemented and developed in four
main modules: (1) A user interface
module; (2) A database module; (3) A
running module; (4) A connecting
module. However, while formulating
this model Precedence Diagram Method
(PDM) and Line of Balance (LOB) is
used to represent each stage of the
project and activity schedule at all
stages in the project time plan
respectively. The running module i.e.
the proposed model is further
implemented in three major phases: (1)
Initialization phase that generates an
initial set of possible solutions; (2)
Fitness evaluation phase that calculates
the project (duration, price, maximum
working capital, and net present value)
of each generated solution; and (3)
Population generation phase that seeks
to improve the fitness of solutions over
successive generations
21 F. A. Agrama
Multi-objective genetic
optimization of linear
construction projects
2012
This paper presents a multi-objective
genetic algorithm optimization
model for scheduling linear
construction projects. The model
developed enables the generation of
optimal/near optimal construction
The model's methodology consists on:
crew synchronization calculations,
interruption calculations, schedule
calculations, optimization through
weighting sum approach and genetic
algorithms method and finally multi-

31. 30
plans that simultaneously minimize
project duration, crew work
interruptions and the number of
synchronized crews.
objective function. Finally, a LOB chart
for each path is presented.
22
G. Duffy, A.
Woldesenbet,
D. H. S. Jeong,
and G. D.
Oberlender
Advanced linear
scheduling program
with varying production
rates for pipeline
construction projects
2012
The program developed allows the
evaluation of the impact of various
routes or start dates in the schedule.
It also has the ability to incorporate
data such as weather and terrain
information in schedule prediction.
Additionally, the program visualizes
the obstacles in the project through
the Activity Performance Index
(API)
"For the program's development,
multiple regression analysis was
utilized to check for variables affecting
production rate. Then, through Velocity
1.0, the user completes the following:
1) input tab: general information,
activities and their relationships, and
production rates 2) activity tab:
activities that take place in the project
3)others tab: holidays or other non-
working days. Based on the last three,
the output tab produces a linear
schedule showing production rate
variance. "
23 G. Lucko
Integrating Efficient
Resource Optimization
and Linear Schedule
Analysis with
Singularity Functions
2011
This papes focuses on resource
leveling and investigates a novel
resource model and its efficient
optimization towards a leveled
profile. An important contribution of
this papes is that its entire
formulation uses the same
mathematical approach, singularity
functions.
The methodology for the genetic
algorithm developed consists of: 1)
Linear Scheduling: the first generation
is initialized with genes. Parallel
schedule calculations for a bandwith of
4 chromosomes are performed. 2)
Reproduction and Selection: the
moment determines the fitness of a
chromosome as the relative probability
to survive into the next generation. 3)
Crossover: The probability of crossover
between parents was set to a 0.6 in
order to retain any existing positive
traits and possibly amplify them in new
combinations. Only one crossover
could occur per iteration. 4) Mutation:
the probability for mutation in any gene
was set to 0.05 to infuse diversity
without causing individual iterations to
fluctuate excessively. Several mutations
could occur per iteration.
24
G. A. Duffy,
G. D.
Oberlender,
and D. H. Seok
Jeong
Linear Scheduling
Model with Varying
Production Rates
2010
The research focuses on expanding
the capabilities of linear scheduling
to account for variations in
production rates. The model
developed aims to present a
framework for linear scheduling that
accounts for variance in production
rates when and where the variance
occurs, as well as enhance the visual
capabilites of linear scheduling.
The model's methodology consists on
determining its production variables,
which can be divided in general, time,
location or time-location. Then, it
divides de project's time-location chart
(TLC) in working windows (WW).
Calculations such as distance remaining
(DR), time remaining (TR), and
distance traveled in time remaining
(DTTR) are done for the WW. Finally,
the activity performance index (API) is
added to the WW.
25
Machine Hsie,
Ching-Jung
Chang, I-Tung
Yang, Chun-
Yen Huang
"Resource-constrained
scheduling for
continuous repetitive
projects with time-based
production units"
2009
Minimizing the project duration by
automatically searching; using
evolutionary strategies, for optimal
set of production rates of crews in
different periods of time. The
novelty of proposed model can be
addressed in three real life situation;
considering variable production rate
of crews, strating and finishing in
different locations for crews, and
multiple predecessors and successors
for acitivities.
It considers resource limit, work
continuity, lead-distance and lead-time
between operations. The evolutionary
strategies, proposed here, include six
steps; population initialization,
individual fitness value computation,
the best parent selection, performing
mutation to produce offsprings, coming
back to the second step, and finally
stopping when the termination criterion
is met. This model used evolutionary
estrategies (ES). Chromosomes are
representing the selection of production
rates, and genes are the choice of
production plans for individual
activities.

32. 31
26
K. H. Hyari, K.
El-Rayes, and
M. El-
Mashaleh
Automated trade-off
between time and cost
in planning repetitive
construction projects
2009
A bi-objective optimization model
for resource optimization is
developed. The model optimizes
simultaneously the two main
objectives in repetitive scheduling:
minimizing project duration and
minimzing project cost.
The model development consists of
four modules: scheduling module,
direct cost module, multi-objective
optimization module and total project
cost module. The scheduling module’s
objective is to generate a schedule
based on resources for repetitive
construction projects. The direct cost
module evaluates the fitness of any
planning option generated by the multi-
objective optimization module in the
cost segment of the time-cost
optimization problem by calculating the
total project direct cost. The multi-
objective optimization module is the
heart of the model and its main purpose
is to generate and identify a set of
optimal/near optimal resource
utilization solutions that provide
optimal/near optimal time-cost trade-
offs for repetitive construction projects.
The stages comprising this module are:
initialization and population evolution.
The total project cost module’s
objective is to compute project total
cost for each optimum trade-off
solutions obtained previously.
27
H. Sharma, C.
McIntyre, Z.
Gao, and T.-H.
Nguyen
Developing a Traffic
Closure Integrated
Linear Schedule for
Highway Rehabilitation
Projects
2009
This paper introduces a traffic
closure integrated linear schedule
technique that integrates associated
traffic closure issues during work
progress to the traditional linear
scheduling.
The development of TCILS for
highway rehabilitation projects consists
on five phases: 1) Phase I: workzone
and construction sequence, 2) Phase II:
preliminary linear schedule (PLS), 3)
Phase III: least closure-time linear
schedule (LCLS), 4) Phase IV: traffic
closure setup and removal on LCLS, 5)
Phase V: final traffic closure integrated
linear schedule (TCILS).
28 G. Lucko
Productivity Scheduling
Method: Linear
Schedule Analysis with
Singularity Functions
2009
This paper introduces a
mathematical model of linear
schedules based on singularity
functions, in which the analytical
algorithm needs only algebra and
basic calculus. The method is
flexible and expansible, yet precise
and inclusive.
The methodology steps for the
development of the algorithm are as
follows: 1) Capture Schedule Data:
create activity list with names, ranges
across time and productivity,
precedence and time/buffer values. 2)
Initial Activity and Buffer Equation:
follow precedence, write inital activity
and buffer equations. 3) Differences of
Activities and Buffers: follow
precedence, calculate pairs of
differences between predecessors
time/buffers and successors. 4)
Differentiation of Differences:
differentiate pairs of differences,
evaluate them to find locations of
minimum values. 5)Final Activity and
Buffer Equations: follow precedence,
subtract minimum values of differences
from activity and buffer equations.
29
G. Lucko, A.
M. Asce, A. A.
P. Orozco, and
S. M. Asce,
Float Types in Linear
Schedule Analysis with
Singularity Functions
2009
This paper applies singularity
functions to activities and buffers for
a complete criticality analysis. It
enables calculating when and where
activities can compensate for delays.
To develop the model, several case
distinctions are evaluated. It must be
distinguished what created the float in a
linear schedule, either time or location
buffers. Neighboring activities must be
compared to reveal whether the
predecessor has a productivity that is
larger than, equal to, or smaller than the
productivity of its successor. Convex
and concave activities must be
identified. The potential float, which is
the white area between activities in the

33. 32
LSM, diagram is calculated. The free
float is calculated as the distance
between the minimum equation of any
succesor and the buffer equation of the
current activity. The total float is
calculated after the free float. The
iterfering float is calculated as the
difference between the total and free
float equations. The independent and
safety floats are calculated. Finally, the
float equations are developed.
30
Luong Duc
Long, Ario
Ohsato
A genetic algorithm-
based method for
scheduling repetitive
construction projects
2008
GA model for repetitive schedule
solved for 1 or 2 objectives such as
min duration, min cost, or both of
them with tunable weights. GA
finds a set of near-minimum
durations for activities, then a
scheduling algorithm calculates
suitable start times of these
activities. Output data represents a
set of near-optimum schedules, so
that scheduler can make informed
decision.
Method utilizes GA where decision
variables in chromosome represent
activity durations in form of binary
strings. Crossover or mutation
operations are applied to create
offsprings. The fitness function may be
considered as the project duration–Tp,
or the project cost–Cp, or both of them–
TC (where Tp and Cp contribute with
different weights set by user). Time-
cost relationship between crew
productivity and cost for particular
activity may be specified either as an
array of options {0.4; 180.0}, {0.6;
160} (i. e. various construction
methods), or as a formula. Type of
activity is to be specified by user: type
Alpha activities will be continuously
performed to maintain the work
continuity of crews (resources); type
Beta activities allow work interruptions.
Method typically considers the “finish
to start” relationship between activities
(immediate or with addition of lag).
31 Maged Georgy
Evolutionary resource
scheduler for linear
projects
2008
GA model for resource leveling in
linear projects. Resource leveling is
performed via minimizing either the
day-to-day fluctuations in resource
usage or the daily deviations from
the average resource usage.
Implementation of algorithm is done
in AutoLISP programming language
under AutoCAD 2002.
Standard GA with one-point crossover
and mutation. Solved variable is daily
resource usage for particular activity.
Neither productivity of crew nor
interruption times are included in
solutions domain. Sample problem is
employed to demonstrate the advantage
of GA over Linear Programming.
32
Tarek Hegazy,
Ehab Kamarah
Efficient Repetitive
Scheduling for High-
Rise Construction
2008
GA model particularly focused on
high-rise buildings construction.
Algorithm allows setting vertical
constraints between floors, considers
specifity of structural core activities.
Different work amount can be set for
different floors. GA computes crews
number, construction method, and
interruptions that minimize total cost
and satisfy with constraints.
Effectiveness of method is
demonstrated using a case study
project of 13-story building.
Algorithm involves 6 steps: 1) Critical
path calculation for single floor;
2) Scheduling of activities related to
structure core (columns, beams, slabs);
3) Determination of floor progress rate
(floors/day) that is required to meet the
project deadline; calculation of number
of crews required to ensure that
progress rate; 4) Vertical constraints
between floors (e. g. lags); 5) Setting
the designed work interruptions;
6) Optimization of total cost by means
of GA finding minimum of objective
function which is total cost (sum of
direct and indirect costs, late
completion penalties, early completion
incentive). Variables are: construction
method, number of crews, work
interruptions at the floors.

34. 33
33
Pandelis
G.Ipsilandis
Multiobjective Linear
Programming Model for
Scheduling Linear
Repetitive Projects
2007
Multiobjective linear programming
algorithm for scheduling of linear
repetitive projects. Model generates
a set of schedules to support the
manager in finding a trade-off
between minimizing the project
duration (reducing the penalties for
late completion) and minimizing the
interrupts between activities (i. e.
reducing the amount paid for
resource idle time).
Algorithm seeks minimum of objective
function being mainly a sum of two
components: 1.Penalties for the
completion delay; 2. Cost expended for
resources idling due to interruptions
between activities. Relative importance
of each term is controlled through
weight coefficients set by user.
Learning effect is taken into account for
crew production rate, however the crew
numbers, initial crew production rate
and cost per time unit are the input
constants, so the slope of production
line is not a subject of optimization.
Algorithm 'plays' only with start and
finish dates to meet project constraints
and minimize objective function. No
resource leveling is provided.
34 Gunnar Lucko
Computational Analysis
of Linear and Repetitive
Construction Project
Schedules with
Singularity Functions
2007
The article proposes a method of
mathematical formalization of LSM
- graphical technique offered by
Harmelink and Rowing, 1998. The
singularity function is employed for
modeling of linear shedule, finding
critical points and critical path.
The singularity functions approach for
mathematical formalization of linear
schedules is developed in analogy to
methods used in structural mechanics.
Every activity can be described by a
singularity function if a) the input data
is known: activity start and finish
dates&locations, productivity rate,
activity type (continuous or
intermittent; linear or bar or block) ; b)
time or distance buffer constraints
between activities are set. Model can
find critical points, intersections
between activities, and determine the
critical path according to algorithm of
Harmelink and Rowings, 1998.
35
A. Hassanein
and O. Moselhi
Accelerating linear
projects
2005
Method developed to accelerate
delivery of linear projects, such as
highways and pipelines. Algorithm
analyzes the existing schedule and
project constraints, identifies activity
to be expedited, and applies several
expediting strategies to find how it
would reduce the project duration
and affect cost. Report is generated
with a set of schedules along with
associated costs (tabular and
graphical views). The best suitable
expediting method is to be selected
by user. Thus, the method provides
schedulers with the flexibility to
make informed decision.
A two stage iterative process is
employed: 1. The 'controlled' activity
(the activity least balanced with its
predeccessors/successors) is identified
using the minimum moment algorithm
for resource leveling. 2. The following
expediting strategies: a) working
overtime; b) working double shifts; c)
working weekends: d) changing
number of crews; e) relaxing activities
(assigning a smaller, less productive
crew to an activity) - are examined. The
whole schedule is recalculated, and the
strategy that results in minimal project
duration is determined. Each iteration
incrementally reduces project duration
until either deadline is met or the
project duration cannot be further
reduced. Method is implemented in a
prototype software (Visual C++ for
code and MS Access for crew data).
Model takes into account both the
positive effect of 'learning curve' and
the negative effect of extended working
hours on crew productivity.
36
K. G. Mattila
and A. Park
Comparison of Linear
Scheduling Model and
Repetitive Scheduling
Method
2003
This paper discusses basic linear
scheduling techniques and the
calculation of critical activities of
basic linear scheduling elements
using the linear scheduling method
and the repetetitive scheduling
method.
The paper compares the LSM and the
RSM by analyzing their way of
identifying the controlling activities and
path. Two continuous full-span linear
activities are used to compare the
methods, first when converging; second
when diverging. The RMS method
hinges on control points, whereas the
LSM depends on control links. LSM

35. 34
and RSM identified the same
controlling activity path.
37
David Arditi,
Onur
Tokdemir,
Kangsuk Suh
Effect of learning on
line-of-balance
scheduling
2001
The paper proposes to take learning
effect into account in Line-of-
Balance (LOB) scheduling, and
proposes an approach to formulate
learning rates. Traditional LOB
schedule assumes that production
rate for repetitive activities is equal
in all subsequent units. In fact, due
to ""learning effect"", the man-hours
expended per unit decrease as the
number of repetitive units increases,
which means that overall duration of
activity or number of workers may
be reduced.
Based on proportion between manual
labor and machine-paced labor, authors
assume LR=80% for labor intensive
activities (75% of manual labor),
LR=85% for unit labor/machine ratio
and LR=90% for machine intensive
activities (75% of machine-paced
labor). Further authors introduce the
adjustment factors that affect learning
rates, and determine their weights:
Worker learning, i.e. having skilled and
trained workers (40%), Construction
method (20%), Managerial support
(15%), Quality of design (15%), Others
- job conditons, weather etc. (15%). To
quantify the adjustment factors it was
proposed to use natural language
definitions (e. g. ""Simple"",
""Moderate"", ""Complex"") and use
fuzzy logic with S-type membership
function. - Paper includes Example
project which demonstrates that with
inclusion of learning effect in LOB
schedule, project duration may be
reduced from 87 to 73 days. - In
conclusion authors say that further
research is required, which might
include: validating the fuzzy model by
experts; carrying out case studies with
field data to calibrate the initial learning
rates and adjustment factors for various
typical construction activities."
38
Tarek Hegazy,
Nagib Wassef
Cost Optimization in
Projects with Repetitive
Nonserial Activities
2001
Scheduling of repetitive projects to
achieve the minimization of total
construction cost using GA.
Distinctive features: - Integration of
CPM and LOB methodologies to
achieve the continuity of work and
synchronisation of parallel crews; -
Finding near-optimal solution being
a combination of the following
variables: construction method (cost,
duration, max. crew number
constraint), number of crews,
interruption times with objective to
ensure minimization of total project
cost; - Use of Genetic algorithm for
optimization; - Implementation in
Microsoft Excel spreadsheet (for the
time of publication that was not a
widespread approach); - Support of
export/import to MS Project.
The proposed method has the following
distinctive features: Integration of CPM
and LOB methodologies to achieve the
continuity of work and synchronisation
of parallel crews. Finding near-optimal
solution being a combination of the
following variables:construction
method (cost, duration, max. crew
number constraint), number of crews,
interruption times with objective to
ensure minimization of total project
cost. Optimization tool - genetic
algorithm solved in Evolver (add-on to
Microsoft Excel). Overall
implementation is done in Microsoft
Excel spreadsheet (for the time of
publication that was not a widespread
approach). Input data can be imported
from, and optimized schedule can be
exported to Microsoft Project. The
objective function (total cost) includes
direct and indirect cost, penalties for
late completion, incentive for early
completion, as well as fictious penalties
for additional crews and for work
interruptions.
39
Robert B.
Harris, Photios
G. Ioannou
Scheduling Projects
with Repeating
Activities
1998
Authors present their own
scheduling technique called
Repetetive Scheduling Method
(RSM) which can ensure continuous
resources utilization. RSM is a
simple graphical tool which allows
scheduler to handle repetitive and
linear projects. The paper introduces
a concept of controlling sequence
Project activities are represented as a
sequence of production lines (each
production line is an activity) on X-Y
plot. For vertical projects (e. g. high-
rise building) where work progress is in
units, theY-axis represents the units,
and time is on X-axis. For linear
projects where work progress is
measured in length units (highways,

36. 35
which is the sequence of activities
from start to finish which determines
the project duration, like critical path
in CPM.
pipelines etc.), X-axis represents the
lenght, and Y-axis is time. The design
of RSM schedule employs the
positioning (rotating, shifting,
aligning) of the unit production lines by
using the concept of control points.
Authors also demonstrated the paradox
when under some conditions an
increase in production rate
may increase the project duration
instead of reducing it.
40
David J.
Harmelink,
James E.
Rowings
Linear Scheduling
Model: Development of
Controlling Activity
Path
1998
The paper introduces LSM -
graphical method which aims to
determine a controlling activity path
for linear schedule (longest
continuous path through the
sequence of activities). Method itself
is not an optimization tool, it is
considered to form a basis for
computerized scheduling algorithms
for linear construction.
The procedure involves three steps: 1)
creating activity sequence list; 2) doing
upward pass to find potential
controlling segments 3) doing
downward pass to identify the parts
of potential controlling segments
which are located on the
actual controlling path."

37. 36
6. CLASSIFICATION OF METHODS
With the intention of introducing a comprehensible classification of the
methods proposed by all the papers reviewed, the main points of each paper are
presented in Table 2.
Table 2: Classification of Methods
No
NameofPaper
Year
ProjectType
Graphical
Representation
Exactsolution
Heuristicsolution
Metaheuristic
solution
Others
Repetitive
Linear
CPM/LOB
PDM
LSM
RSM
Graphical
Analytical
EVM/MMA
LinearProg.
ConstraintsProg.
SingularityFunctions
Min.moment
LSMVPR
RPERT
TCTP
MRCRSP
GA
MMAS
MonteCarlo
FuzzyLogic
1
Scheduling of repetitive
construction projects
using geographic
information systems
2
0
1
9
Y Y Y
Y
2
Delay Risk Assessment
of Repetitive
Construction Projects
Using Line-of-Balance
Scheduling and Monte
Carlo Simulation
2
0
1
9
Y Y Y
3
Multipurpose linear
programming
optimization model for
repetitive activities
scheduling in
construction projects
2
0
1
9
Y Y
4
Scheduling Repetitive
Construction Processes
Using the Learning-
Forgetting Theory
2
0
1
9
Y Y Y
5
Optimizing the
Scheduling of
Repetitive Construction
to Minimize
Interruption Cost
2
0
1
8
Y Y
6
Planning repetitive
construction projects
considering
technological
constraints
2
0
1
8
Y Y
7
The Multimode
Resource-Constrained
Project Scheduling
Problem for Repetitive
Activities in
Construction Projects
2
0
1
8
Y Y

38. 37
8
Minimizing duration
and crew work
interruptions of
repetitive construction
projects
2
0
1
8
Y Y
9
Scheduling
Optimization of Linear
Schedule with
Constraint
Programming
2
0
1
8
Y Y Y
10
Mixed-Integer Linear
Programming Approach
for Scheduling
Repetitive Projects with
Time-Cost Trade-Off
Consideration
2
0
1
7
Y Y
11
Optimal crew routing
for linear repetitive
projects using graph
theory
2
0
1
7
Y Y Y Y
12
Genetic Algorithm-
Based Method for the
Deadline Problem in
Repetitive Construction
Projects Considering
Soft Logic
2
0
1
6
Y Y
13
Cost Optimization of
Repetitive Projects with
Varying Production
Rates using a Max-Min
Ant System
2
0
1
6
Y
14
Repetitive Scheduling
Method: Requirements,
Modeling, and
Implementation
2
0
1
6
Y Y Y
15
Multi Objective
Optimization for
Scheduling Repetitive
Projects using GA
2
0
1
6
Y Y
16
Estimating Cumulative
Damages due to
Disruptions in
Repetitive Construction
2
0
1
6
Y Y Y
17
Impacts of Different
Objective Functions on
Resource Leveling in
Line-of-Balance
Scheduling
2
0
1
6
Y Y Y Y

39. 38
18
Temporal Constraints in
Linear Scheduling with
Singularity Functions:
Case of Calendarization
2
0
1
4
Y Y
19
RPERT: Repetitive-
Projects Evaluation and
Review Technique
2
0
1
3
Y Y
20
Optimizing strategy
software for repetitive
construction projects
within multi-mode
resources
2
0
1
3
Y Y Y
21
Multi-objective genetic
optimization of linear
construction projects
2
0
1
2
Y Y Y
22
Advanced linear
scheduling program
with varying production
rates for pipeline
construction projects
2
0
1
2
Y Y Y
23
Integrating Efficient
Resource Optimization
and Linear Schedule
Analysis with
Singularity Functions
2
0
1
1
Y Y Y Y
24
Linear Scheduling
Model with Varying
Production Rates
2
0
1
0
Y Y Y Y
25
"Resource-constrained
scheduling for
continuous repetitive
projects with time-
based production units"
2
0
0
9
Y Y
26
Automated trade-off
between time and cost
in planning repetitive
construction projects
2
0
0
9
Y Y
27
Developing a Traffic
Closure Integrated
Linear Schedule for
Highway Rehabilitation
Projects
2
0
0
9
Y Y Y
28
Productivity Scheduling
Method: Linear
Schedule Analysis with
Singularity Functions
2
0
0
9
Y Y Y
29
Float Types in Linear
Schedule Analysis with
Singularity Functions
2
0
0
9
Y Y Y
30
A genetic algorithm-
based method for
scheduling repetitive
construction projects
2
0
0
8
Y Y Y
31
Evolutionary resource
scheduler for linear
projects
2
0
0
8
Y Y Y

40. 39
32
Efficient Repetitive
Scheduling for High-
Rise Construction
2
0
0
8
Y Y Y
33
Multiobjective Linear
Programming Model
for Scheduling Linear
Repetitive Projects
2
0
0
7
Y Y Y
34
"Computational
Analysis of Linear and
Repetitive Construction
Project Schedules with
Singularity Functions"
2
0
0
7
Y Y Y
35
Accelerating linear
projects
2
0
0
5
Y Y Y
36
Comparison of Linear
Scheduling Model and
Repetitive Scheduling
Method
2
0
0
3
Y Y Y Y
37
Effect of learning on
line-of-balance
scheduling
2
0
0
1
Y Y Y
38
Cost Optimization in
Projects with Repetitive
Nonserial Activities
2
0
0
1
Y Y Y
39
Scheduling Projects
with Repeating
Activities
1
9
9
8
Y Y Y
40
Linear Scheduling
Model: Development of
Controlling Activity
Path
1
9
9
8
Y Y Y

41. 40
7. ADVANTAGES AND DISADVANTAGES OF LINEAR/REPETITIVE
SCHEDULING TECHNIQUES
Finally, with the intention of introducing the benefits and limitations of the
techniques proposed by all the papers reviewed, the main points of each paper are
presented in Table 3.
Table 3: Advantages and Disadvantages of Linear/Repetitive Scheduling Techniques
No Name of Paper Year Advantages Disadvantages
1
Scheduling of
repetitive
construction projects
using geographic
information systems
2019
It considers both resource continuity using
LOB and logical dependencies using CPM.
The units do not need to be numbered in
order; they just need to consider the successor
and predecessor. The developed tool provides
visual presentation of the schedule in the
form of 4D model.
-
2
Delay Risk
Assessment of
Repetitive
Construction Projects
Using Line-of-
Balance Scheduling
and Monte Carlo
Simulation
2019
It uses the advantages of combining
CPM/LOB together and considers delay risk
evaluation.
The relation between the risk factors and duration
of tasks are not constant for all projects. All units
are assumed to be affected from same source of
risk but in fact, each individual unit could have
different risk events. Due to focus on duration,
changes in resources are underestimated.
3
Multipurpose linear
programming
optimization model
for repetitive
activities scheduling
in construction
projects
2019
Realistic conditions are taken into account: 1)
the four traditional relationships (FS,SF,SS,
FF), 2) discretional continuity between sub-
activities established by the scheduler, 3)
multiple execution modes for the activities, 4)
accelerating and deaccelerating routines
inside each activity, 5) controlled maximum
shifts in the execution of the activities, and 6)
the possibility of establishing multiple crews
for an activity.
Model does not handle several calendars. Only
linear and non-interruptible sub-activities are
considered. The number of crews is an input
variable and cannot be optimized. Only traditional
SS, SF, FS, FF relationships are considered. If the
number of sub-activities increase, it will face with
computational limits.
4
Scheduling
Repetitive
Construction
Processes Using the
Learning-Forgetting
Theory
2019
It enables a more precise estimation of
realization times for construction projects.
The conducted studies indicate that taking
account of this effect leads to a significant
reduction of the expected directive time of a
project, even in the case of the lack of
continuity in the works of construction crews
and partial loss of acquired experience. The
observed effect of performance boost leads to
reaching the same goals with the engagement
of lesser means.
The usefulness of the gathered data may be
limited, as the learning effect is highly dependent
on the construction realization conditions i.e.
workers’ tiredness, absence from work, lack of a
motivational remuneration system, high personnel
fluctuation and frequent changes within
construction crews, increased workloads related
to the transportation of products to higher levels
or use of improper tools. It is crucial to take
account of the constant technological and
organizational progress being made in the field of
construction as well.
5
The Multimode
Resource-
Constrained Project
Scheduling Problem
for Repetitive
Activities in
Construction Projects
2018
It provides a more realistic MRCPSP model
for repetitive activities. Controlled activity
acceleration routines are incorporated to the
model. It introduces an easy criterion to
implement scheduling problems.
The study does not consider soft logic scheduling
optimization, non repetitive activities, or negative
acceleration routines. Only minimal SS, SF, FS,
and FF relationships are allowed. High
computational effort due to a large number of
activities (it is not metaheuristic).
7
Scheduling
Optimization of
Linear Schedule with
Constraint
Programming
2018
Comprehensive model for linear construction
(pipeline) based on LSM technique, employs
powerful optimization software package IBM
ILOG CPLEX Optimization Studio.
As a direction for future work, authors identify
the application of proposed algorithm to the LOB
based schedules for repetitive construction.

42. 41
8
Optimal crew routing
for linear repetitive
projects using graph
theory
2017
Considering multitasking skilled crews to
linear construction projects among different
activities
The issue of learning phenomenon has to be
accounted, as this may be one of the
disadvantages of moving same crew over
different “sub-activities.
9
Genetic Algorithm-
Based Method for the
Deadline Problem in
Repetitive
Construction Projects
Considering Soft
Logic
2016 -
An important assumption adopted in this paper is
that all activities are only performed by one crew.
Therefore, for those projects that employ more
than one crew to perform the same activity, the
proposed model can only serve as a reference.
This is the main limitation of the model, and the
authors will attempt to overcome it in future
studies. Moreover, it is suggested that more
construction projects can be investigated to
examine the structures of resource transferring
cost in order to broaden the application of the
proposed model in practice.
10
Cost Optimization of
Repetitive Projects
with Varying
Production Rates
using a Max-Min Ant
System
2016
Unlike previous models, the proposed model
calculates the real amount of interruption for
each crew monetarily and its time interval
and uses the crew allocation modules to find
the best crew distribution associated with the
least cost for individual activities by
introducing penalty cost of basic crew
distribution and additional cost of
outsourcing crew. Moreover, it also considers
liquidated damages for delays and a bonus for
early completion of the project.
Similar to maximum and minimum pheromone
amounts, the proposed model has imposed upper
and lower limits on construction methods, modes
for each activity, interruption days for each
activity and number of outsourced and omitted
crew for each activity. In addition to that,
production rates could only be considered from
the turning unit and the previous
limitations/assumptions of LOB still govern as it
acts as the scheduling subroutine for the proposed
model.
11
Repetitive
Scheduling Method:
Requirements,
Modeling, and
Implementation
2016
RSM recognizes that activity production lines
may have different slopes (unit production
rates) in different units because of differences
in work quantities or changes in resource
production rates
Not ideal for scheduling repetitive projects
because it does not achieve resource work
continuity.
12
Multi Objective
Optimization for
Scheduling
Repetitive Projects
using GA
2016
Unlike previous methods which either
maintain work continuity to maximize
learning effect, minimize idle labour and
equipment time or maximize the net present
value of the project, this method uses multi
objective programming which optimizes
multiple objectives.
-
13
Estimating
Cumulative Damages
due to Disruptions in
Repetitive
Construction
2016
1. In summary, the proposed method seeks to
provide a robust means of estimating
cumulative damages due to disruptions. The
value of the proposed method is that different
perspectives on the estimation of cumulative
damages might identify and consider the
same events in distinctly dissimilar ways,
especially in terms of the cumulative effect of
disruption in repetitive construction. 2.
Highly accurate time and cost forecasts can
be obtained by applying the EVM
methodology. 3. The previous methods did
not consider that the estimated costs for the
work remaining could differ from the original
planned budget in terms of timing and
financial cost due to performance change,
even after the completion of disruptions.
Therefore, the proposed method has
incorporated the idle time of resources, the
lost productivity, and the feasible change of
estimated costs for the work remaining after
disruptions. This can minimize the
shortcomings of the previous methods.
1. The feasibility analysis in this case study was
run on a limited set of empirical data assuming
the situation that productivity would not recover
even though the change is removed. Therefore,
the proposed method poses difficulties for
application in general situations. 2. This method is
proposed based on the case where disruptions will
cause, or be caused by, lost productivity during
the impacted period, with the assumption that
other causes are negligible. 3. This method also
assumes that the expected productivities will be
achieved, that conditions in calculating revised
estimated costs for the work remaining will
change even after the completion of disruptions
and that past project progress is representative of
future progress. 4. In addition, learning curve
effects are not considered in the production rates
of activities (i.e., constant production rates for
simple purposes of demonstration) 5. The
proposed method has a limitation in that it can be
applied to the cases where the productivity is not
recovered due to resequencing of activities, even
though changes are removed. Thus, the suggested
method poses difficulties for application in
general construction project situations.

43. 42
14
Impacts of Different
Objective Functions
on Resource Leveling
in Line-of-Balance
Scheduling
2016
For simple projects without parallel activities
and floats, selection of objective function
does not affect the final schedule and
resource usage profile.
The effect of objective function on more complex
schedules with parallel activities needs to be
studied. In addition, the "Construction method"
should be included in decision variables.
15
Temporal Constraints
in Linear Scheduling
with Singularity
Functions: Case of
Calendarization
2014
Its contributions to the body of knowledge
are threefold:
(1) It has opened a new avenue to constraint
satisfaction whereby singularity functions
express intricate temporal constraints; (2)
provided equations to calculate leap years,
calendar dates, and improve upon previous
weekday approaches with marker days; and
(3) developed an algorithm that inserts
weekends and different types of holidays to
calendarize linear schedules, and verified and
validated these elements.
1. Hard constraints always had to be fulfilled in
the example. In practice, however, soft constraints
are considered, which may be violated in cases of
strong need, e.g., to accelerate a project with
overtime work.
2. Functional limitations are that the approach in
its current form can only map the linear schedule
onto a single calendar, whereas a real-world
project will likely entail multiple resources with
individual calendars.
16
RPERT: Repetitive-
Projects Evaluation
and Review
Technique
2013
1. One of its most powerful concepts is the
management of probabilities. 2. PERT
presented a comprehensive illustration of all
major project activities and their
interdependencies. In fact, it even provided
time requirements needed for completing
each component activity. 3. It focused
managerial attention on those business
activities most vital in meeting the project
completion date and identified which
resources could be used more effectively if
transferred to other phases of a project. 4.
PERT provided a scheme of the project as it
occurred, thereby illustrating the effects of
managerial changes in the entire project. 5.
PERT diagrams are available to eliminate the
estimating process and make PERT a more
useful and convenient tool.
1. No idle time is allowed for employed crews;
thus, once a crew starts working on an activity at
the first stage, it will continue working with the
same production rate until finishing the work at
the last stage 2. If an activity duration needs to be
changed to meet a particular feasible project
duration, then an equal change must be made to
the activity duration per all stages 3. The learning
phenomenon, whereby the actual duration of an
activity is reduced as repetition increases, is
neglected 4. The work on each activity is
conducted by one unit at a time per all stages 5.
The project under study is not disturbed by
incidents during constructing.
17
Optimizing strategy
software for
repetitive
construction projects
within multi-mode
resources
2013
OSS is intended to give more scenarios,
which provide practical support for typical
construction contractors who need to
optimize resource utilization in order to
minimize project duration, project/bid price,
and project maximum working capital while
maximizing its net present value
simultaneously.
1. Does not account for multiple crews in
repetitive construction projects. 2. No idle time is
allowed for employed crews; thus, once a crew
starts working on an activity at the first stage, it
will continue working with the same production
rate until finishing the work at the last stage; 3.
The learning phenomenon, whereby the actual
duration of an activity is reduced as repetition
increases, is neglected 4. Materials’ prices are
kept to be fixed during the contract fulfillments;
5. Mobilization advance of a contract is neglected
6. Overheads of the project under study are
constant and unchangeable with time and project
progress.
18
Multi-objective
genetic optimization
of linear construction
projects
2012
Planners can generate near optimal
construction plans that establish trade-offs
between project duration, total crews and
total interruptions. Lag and overlap times can
be introduced.
The model does not take into account the total
cost related to each solution presented.
19
Advanced linear
scheduling program
with varying
production rates for
pipeline construction
projects
2012
The program developed is able to clearly
predict and visualize changes is production
rates, as well as when and where they will
occur along a given pipeline route.
Model is only effective for pipeline construction
projects and is not useful for any other kind of
location-based repetitive project (alignment) or
point-based repetitive projects (tall buildings).
20
Integrating Efficient
Resource
Optimization and
Linear Schedule
Analysis with
Singularity Functions
2011
The developed model effectively optimizes
resource allocation. It converges quickly,
maintains the association between resources
and their activities, effectively models shifts
and resources, and reduces the required
number of variables and constraints.
The optimization of this model consists on
reducing required buffers, however using the total
float of an activity could be and improvement to
the optimization approach.

44. 43
21
Linear Scheduling
Model with Varying
Production Rates
2010
The program demonstrated that variations
caused by time and location variables could
be predicted for future construction projects.
The model also allows the scheduler to
analyze the impact of various routes and start
dates in the schedule.
Model is only effective for location-based
repetitive projects (alignments) and is not useful
for point-based repetitive projects (tall buildings).
22
Resource-constrained
scheduling for
continuous repetitive
projects with time-
based production
units
2009
Crews can maintain the same size and
composition in each time period. Production
units can directly match the time-based
payment schedule to save unnecessary
administrative work.
Random selection of parents and crossover
operation are not used. The fittest individuals
(elitists) becomes a parent, and only mutation is
applied to create offspring.
23
Automated trade-off
between time and
cost in planning
repetitive
construction projects
2009
Planners can evaluate a set of near optimal
trade-off solutions and select a construction
plan that simultaneously minimizes project
duration and cost.
The model does not take into account other
important objectives in repetitive construction
projects such as quality and safety. Also, it cannot
quantify the impact of construction planning on
project objectives.
24
Developing a Traffic
Closure Integrated
Linear Schedule for
Highway
Rehabilitation
Projects
2009
The TCILS properly addresses the issues
related to traffic that help identify and avoid
the conflicts with traffic closure and work
progress in highway rehabilitation projects. It
also reduces unwanted idle time of both
plants and equipment involved.
The model does not take into account the
optimization of work zones. Interruption in
production rates are not considered. Cost and
resources are not taken into account either.
25
Productivity
Scheduling Method:
Linear Schedule
Analysis with
Singularity Functions
2009
The algorithm of the PSM automatically
calculates the configuration that minimizes
the overall project duration under
consideration of all constraints from
time/buffers. This analysis approach is also
computationally efficient.
Further research must be conducted to include
different types of float, probabilistic activity
durations and resource allocation and leveling to
the PSM algorithm.
26
Float Types in Linear
Schedule Analysis
with Singularity
Functions
2009
The developed model proved that singularity
functions are a uniquely flexible way to
model complex behaviors of a dependent
variable. Therefore, the floats at any location
on a noncritical segment of a linear schedule
can be determined exactly, and planners can
determine how their linear o repetitive project
is impacted by delays.
The model does not take into account issues like
interruptability.
27
A genetic algorithm-
based method for
scheduling repetitive
construction projects
2008
This was one of the first executions of genetic
algorithm utilizing Excel functionality.
Only activity durations for unit are sought by GA.
The other parameters that contribute to overall
project duration and cost (crew number,
interrupts, extended hours) are not involved into
optimization. Project cost does not account for
incentives and penalties.
28
Evolutionary
resource scheduler
for linear projects
2008
The methods offers some automation of LSM
which natively was a graphical technique.
1. Method does not cover intermittent activities,
varying resource rates, multiple-resource leveling,
which are left for future studies. 2. Total project
cost is not calculated, only the duration.
29
Efficient Repetitive
Scheduling for High-
Rise Construction
2008
Comprehensive method covering wide range
of applications. In fact, criteria of
optimization may be easily modified to
minimum project duration, or minimum
interruption time if required. Genetic
algorithm finds a global optimum and does
not stick to a local optimum.
It would be beneficial to add a function of
import/export schedule to Microsoft Project.
30
Multiobjective Linear
Programming Model
for Scheduling Linear
Repetitive Projects
2007 -
This model is applicable only for the projects with
fixed crew number and production rate. It could
be much more functional, if crew numbers, initial
production rates, cost per time unit were the
decision variables.
31
Computational
Analysis of Linear
and Repetitive
Construction Project
Schedules with
Singularity Functions
2007
Technique can partially automate scheduler's
job. Scheduler enters initial schedule in
tabular form, and algorithm can check it for
crashes, identify control points and control
path.
It is not an optimization tool. It still requires
scheduler's decision in positioning of production
lines, i. e. allocation of resources, delays and
interruption times. Costs are not taken into
consideration at all. This is the first approach of
development the LSM quantitative basis. Author

45. 44
does not claim it to be comprehensive and leaves
a space for further development.
32
Accelerating linear
projects
2005
Algorithm takes into account differences in
crew productivity caused by to learning effect
and extended working hours.
1. Method does not allow several options for
construction method (sets of cost, resources and
duration). 2. When algorithm solves a schedule
for different expediting strategies, it simply tries
all possible strategies without using optimization.
This may lead to very long solving time for bigger
projects.
33
Comparison of
Linear Scheduling
Model and Repetitive
Scheduling Method
2003
Its advantageous to understand how LSM and
RSM work and that either of them will
provide you with the same results regarding
the project's controlling path.
The paper's analysis only focuses on multiunit
projects, rather than physically linear projects.
While the analysis provides satisfactory results,
these techniques must be computerized to become
useful.
34
Effect of learning on
line-of-balance
scheduling
2001
Accounting for the learning curve effect
allows more effective scheduling of repetitive
projects, mainly reduction of duration of
activities at the construction of latter units in
series.
1. It is not logical to reduce number of workers in
the crew after the crew has gained experience as a
team, because the learning effect may cease. 2.
Cumulative units number X in learning rate
equations shall be divided by number of crews,
otherwise for the activity including 20 units and 5
crews (i.e. each crew produces only 4 units), the
man-hours expended for unit #20 would be the
same as if there was only one crew.
35
Cost Optimization in
Projects with
Repetitive Nonserial
Activities
2001
Comprehensive method covering wide range
of applications. In fact, criteria of
optimization may be easily modified to
minimum project duration, or minimum
interruption time if required. Genetic
algorithm finds a global optimum and does
not stick to a local optimum.
Due to limitations of software and hardware used
at the time of publication, optimization running
time might reach several hours. Simplified model
(production rate is constant within activity; all
units require equal amount of work).
36
Scheduling Projects
with Repeating
Activities
1998
"Easy visual method. In contrast to bar chart,
unit production rates are visualized on a plot
through production line slopes. This article is
frequently cited in the papers studying
repetitive/linear scheduling. The
methodology, described in this paper
triggered an interest of researchers to
develop numerical solutions."
Purely manual visual technique without any
automation. Scheduler has to perform laborious
calculations to decide how to change the resource
production rate (changing crews number, adding
shifts, extending working hours, technology etc.).
The total cost of project is not calculated.
37
Linear Scheduling
Model: Development
of Controlling
Activity Path
1998
Visual tool without any mathematical
equations for schedule checking. Provides
some guidelines for researchers who are
going to describe the method mathematically.
Tool is good for checking, however does not
explain what actions can be taken to minimize the
duration of project.
8. DISCUSSION
While a significant amount of research has been accomplished for scheduling
repetitive/linear construction projects, there are still many uncertainties that need to
be further addressed. Thus, some limitations of current papers that could be taken into
account for future research are discussed below:
• Increasing the number of activities due to dividing them into sub-activities
has been an issue for some researchers. Further research could be completed
to enhance the proposed algorithms in order to address this issue. However,
there is still a challenge in computational capabilities for solving the repetitive
projects with a large number of sub-activities.

46. 45
• One of the main limitations of studies utilizing the TCTP method is that this
method is incapable of considering more than one mode for activities in non-
typical repetitive construction projects, such as highways and railways.
• In real life, crew size could be changed for activities, however, this input is
usually considered constant in the models. Changing the formation of crews
or using a multi-skilled workforce can be taken into account in future studies.
• Considering several calendars along with other premises is one of the main
shortages for many of the reviewed methodologies.
• Unlike conventionally utilized methodologies such as CPM, novelty models
are capable of acknowledging and minimizing crew interruption cost, project
duration, work interruptions, and cost, simultaneously. However, future
research in this area can focus on considering serial and non-serial repetitive
activities, and enable the utilization of multiple crew formations to platform
repetitive activities.
• It would be interesting to make a comparative study how different
optimization algorithms could solve the same problem taken from a real
construction case. For example, research (Damci et. al, 2016) presents how
the selection of different objective functions influences the resource leveling
profile (number of workers vs time curve) in LOB scheduling. Finally, all ten
objective functions resulted in the same resource utilization profile. The test
case was quite simple: seven activities, no parallel activities and floats. As a
future goal, research should focus on the impact of objective function on more
complex project cases with different precedence order, parallel activities and
multiple resources.
• Most of the papers evaluated utilized several software packages (Excel, Java,
Python, etc.) when rendering schedules. However, to ensure the
implementation of repetitive schedules in the construction industry, the
export-import to commonly used scheduling software (MS Project,
Primavera) should be considered.
9. CONCLUSION
The construction industry develops continuously, and for a construction project
to succeed, it is fundamental to decide which are the appropriate planning and scheduling
techniques according to its attributes. While CPM has had a noteworthy development in
the past decades, it has been proved deficient in capturing the necessities of repetitive
construction projects. This paper described the novelties, methodologies and techniques
of repetitive/linear scheduling described in literature from the past two decades,
consisting on forty articles published in peer-reviewed journals. It also presents the

47. 46
shortages encountered among the papers reviewed, along with suggestions on how to
overcome them. Primarily, the purpose of this paper is to present the current development
of research in this topic and encourage its expansion.
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