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NICMAR
ASSIGNMENT
ON
LINEAR PROGRAMMING CHART
PRESENTED BY :
PATEL JAYENDRA - 231133
PATEL SHILPAN - 231134
SHEKHAR JHA - 231077
VISHRUT KALMANDE - 231082
TAPAS GANGULY - 231114
ASSIGNMENT
CONTENTS
I. LINEAR SCHEDUALING METHOD
1. HISTORY
2. INTRODUCTION
3. HOW LSM IS DIFFERENT
4. FEATURES
5. LIMITATIONS
6. ADVANTAGES & DISADVANTAGES
7. DIFFERENCE OF LSM AND NETWORK ANALYSIS
8. NON-LINEAR AND DESCRETE CONSTRUCTION ACTIVITIES
9. BIBLOGRAPHY
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LINEAR PROGRAMMING CHART
HISTORY
The LPC method of scheduling is well suited to projects that are composed of
activities of a linear and repetitive nature. The objective of this study is to set down the basic
principles that can be used in the development of a computerized LPC scheduling system that
overcomes the problems associated with existing systems and creates solutions to problems
encountered in the implementation of repetitive-unit construction. The challenges associated
with LPC scheduling include developing an algorithm that handles project acceleration
efficiently and accurately, recognizing time and space dependencies, calculating LPC
quantities, dealing with resource and milestone constraints, incorporating the occasional
nonlinear and discrete activities, defining a radically new concept of criticalness, including
the effect of the learning curve, developing an optimal strategy to reduce project duration by
increasing the rate of production of selected activities, performing cost optimization, and
improving the visual presentation of LPC diagrams.
In simple terms, the time chainage diagram, or location time chart
refer to by Cormican (1985), is combination of bar chart and line of balance scheduling
formats and it is from these programming techniques that time chainage principles have been
developed. The time chainage form of presentation enables the time dependencies between
activities to be shown together with their order and direction of progress along the job. These
diagrams are most usefully employed as the planning tool on projects such as motorways and
major highway works, pipelines, railway track work, tunnelling etc. Project of this nature can
be viewed as mainly linear in nature. In other words construction starts at one point and
proceeds in an orderly fashion towards another location. This would be typified on a highway
project by activities such as fencing, drainage, road surfacing, and road marking. To some
extent this type of work calls for a different planning technique because bar charts would not
be useful in giving locational information and precedence/ arrow diagrams would not reflect
the time /location relation ship which clearly exists on such projects. In this respect, most
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operations take place on a forward travel bases with the gang starting at one point or chainage
and moving along the job. As one activity leaves a particular location then other activities can
take their place. This ensures the correct construction sequence and avoids over intensive
activity in one location.
Linear construction consists of a group of operations that involve
repetitive ‘‘units’’ of construction elements. Highways, high-rise buildings, tunnels, and
pipelines are good examples that exhibit repetitive characteristics where the same basic unit is
repeated several times. Multiple-dwelling, multiple-floor, or linearly progressive
projects allow construction to proceed in a repetitive fashion, allowing for
cost and time efficiencies. To achieve these possible efficiencies, it is necessary to balance the
crews. By such scheduling, a construction manager achieves continuity in the placement of all
repetitive elements, thus maximizing the productivity of labor and equipment ~Ashley 1980!.
INTRODUCTION
WHAT IS LINEAR SCHEDULING?
Linear scheduling is a unique means of resources leveling or allocation with a simple
graphic display of time-space interaction. This technique is known by a number of other titles,
including the vertical production method, time-space scheduling method and repetitive-unit
construction. The term linear scheduling has become more widely accepted in recent years.
The exact origin of linear scheduling is unknown, but it stems from efforts in
manufacturing work to prevent delays or bottlenecks. In the manufacturing industry a related
scheduling technique is more widely known as the line of balance.
The development of a linear schedule for a project is similar to any other scheduling
process. The first three steps, familiar to most scheduler, are:
1. Identify activities.
2. Estimate activity production rates.
3. Develop activity sequence.
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In accomplishing these three steps, one must determine whether the linear schedule
method is the most appropriate. As a rule, the project will work well in linear sched¬uling it
the vast majority of the activities can be grouped as a family of repetitive and nearly identical
tasks. The activities should be defined in a level of detail comparable to that found on a bar
chart.
The fundamental aspects of the use of linear schedules eta fee described
Through the use of some examples. Figure 14.3 shows a simple linear schedule that Consists
of the layout of the centerline of the fence; Activity B consists of auguring the post holes,
installing the posts and attaching the boards; and Activity C consists of painting the fence. In
Figure 14.3, the vertical axis represents the station position or distance along the fence. Since
the horizontal axis is lime, the slope of the activities represents the rate of production
(distance/time). That is, the steeper the
Slope, the faster the activity is accomplished. In this example, it should be obvious
That erecting the fence itself will take longer than laying out fence or painting the fence.
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As noted earlier, with the linear schedule there is no need to think in terms of an early-
start schedule or a late-start schedule. Rather, the linear schedule is generally more akin to the
expected schedule, which is some form of compromise between the early and late schedules,
is the linear schedule deterministic or probabilistic? At first glance, the linear schedule would
appear to be deterministic; however, a closer examination will reveal that it too is a reflection
of the probabilistic approach.
It display time and space graphically on the same instrument. This allows the cost
engineer to visually deconflict production activities on the project space representation.
Additionally, instead of being activity-based, they are production- based and allow the cost
engineer to synchronize the schedule with the same assumed production rates that were used
in the project cost estimate. This furnishes a method for seamlessly transitioning from project
planning to project execution schedules.
HOW LPC IS DIFFERENT
“Linear schedules are simple charts that show both when and where a given work
activity will take place. Because they put time and space together on one chart, linear
schedules allow us to see how the pieces of the project fit together. Enhanced with color,
varying shades, or patterns they also communicate types of work and crew movement. This
is something neither bar charts nor CPM schedules can do....”
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All the interviewees agreed that LSM scheduling is superior to the
CPM when scheduling projects of a repetitive nature; and these projects capitalize and make
use of many of LSM scheduling benefits. One of the interviewees explained how in repetitive
projects, LSM scheduling is more beneficial in areas like managing the project resources,
visualization of the project schedule, creating schedules more efficiently, managing and
updating the schedule, and decreasing the chance of scheduling errors. He believes that for
projects of a non-repetitive nature, CPM and LSM are equally suitable and usable. Another
interviewee believed that scheduling projects with a less percentage of repeated activities is
one of the weaknesses of LSM scheduling. Even though, it is possible to schedule them using
LSM, he still faced hardships doing so. A scheduling practitioner commented that LSM
scheduling is more practical when used to schedule projects with a repetitive nature, however
on other types of projects LSM loses many of its advantages. Another scheduling practitioner
discussed how the LSM technique is better in scheduling repetitive and non-repetitive projects
alike, because it allows for easier tracking of productivity rates through inspection of the
scheduled activities‟ slopes. Furthermore, he discussed how LSM permits enhanced
management and tracking of sub-contractors' work on the project site. The academician
explained how the strength of LSM is its ability to schedule repeated activities with the same
crews or resources over various locations, and if the repetition of the activities did not exist,
then LSM scheduling loses its edge. The academician stated “If you don’t have a lot of
repetitive activities, than Line of Balance doesn’t make sense, because its strength is in how
you could optimize your resources over different locations or zones. If I've got a project
where each crew is only going to do one thing and show up one time, than Linear scheduling
method doesn’t make much sense. I can just use a CPM and optimize the use of my
resources.”
FEATURES OF LPC
The study also attempted to investigate various advantages and limitations of applying
LSM scheduling to construction projects, and how it compares with CPM. Some of LSM
scheduling advantages discussed by the interviewees are listed below:
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Clearly shows the amount of work taking place in a certain area at a specific
time of the project.
Has the ability to show and optimize the resources used for large number of
repeated activities, executed in several zones or locations.
Easier cost and time optimization analysis because of all the information
available for each activity in the project.
Ease of setup and its superior presentation and visualization.
Easier to modify, update and change the schedule.
Better managing of all the various sub-contractors in the project.
Allows for simpler and clearer resource management and resource
optimization functions.
Better consideration of the site space which enhances the management of the
crews and resources involved in a certain spot at a certain time of the project.
Visualization of productivity and location of crews.
Generates schedule forecasts, based on the information of the “actual built”
productivity rates.
The major disadvantages they discussed include: the difficulty to schedule soft
activities (like procurement or milestones activities), activities could only be divided by
locations and not by systems or any other classification or grouping, and LSM scheduling
inability to generate a clear critical path for the project. Below, is a table presenting the
interviewees comments and opinions regarding the limitations of LSM scheduling.
In the case of projects which are mainly containing the repetitive kind of activities, the
precedence diagram in the figure below shows the comparison between the LSM and Activity
based diagram.
In the below diagram the work of simple multistoried building frame is shown in
figure.
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Another comparison is shown in Figure 14.2 where a simple highway is presented as a
precedence diagram and also as a linear schedule. The precedence diagram shows a finish-to-
start relationship between activities, while the linear schedule not exhibit such a clear
distinction between the completion of one activity and the of the next. It should become clear
that the linear schedule is a more accurate portrayal of the actual construction of the highway.
For example, there will be a point in the last portion of the fill work is being done that
finishing grading is well underway and paving work will have started. There are other
differences between precedence diagram and linear scheduling. While the precedence diagram
may use the beginning of-day convention this has no meaning in the linear schedule. Since the
project duration is shown as a continuum in the linear schedule, there is no need to think in
terms of beginning-of-day or end-of –day convention as the entire day is portrayed in the
linear schedule.
Where is the critical path in the linear schedule? This is not an easy question to
answer. The linear schedule itself does not identity the critical activities, in linear schedules,
the level of detail is such that most, of the activities, will be critical In the example only two
activities are not critical, namely,, striping the pavement and performing the signage work,
These activities will take place as the landscape work is performed.
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a graphic depiction of the float. What does the vertical distance between two contiguous
activities represent? It simply represents the physical distance between two activities at a point in
time, also known as a space buffer. It essentially shows how close together two contiguous
activities are. A vertical line extended fully through the linear schedule at any selected time
represented on the horizontal axis will intersect all activities that are scheduled to occur
at the time. It is worthwhile to examine this relationship. Even if an activity has ample float, the
operation of one activity might be too close to another operation to effectively accomplish both at
the same time. Considerably below that which is anticipated and at other times will far exceed
the expected production rate? It is practical to portray it as a straight line and include a
sufficient time buffer to accommodate for the hour-to-hour or day-to-day fluctuations in
productivity.
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As shown in Figure 14.3, the horizontal distance between two activities is a graphic
representation of the free float of the earlier activity at that location. It is evident that the float for
the activity may change for different locations along the fence. The layout work must begin
promptly so that the fence installation can commence. At this point in time (start of the layout
work), the layout activity has very little float, but as the layout work nears completion, its float is
considerable. Thus, the layout work must begin promptly in order to keep the project on schedule,
while a delay at layout completion may not have an adverse impact on the project duration.
Once the linear schedule format is understood, it is easy to grasp the nature of a project. As
mentioned, the horizontal distance between two contiguous activities is a graphic depiction of the
float. What does the vertical distance between two contiguous activities represent? It simply represents
the physical distance between two activities at a point in time, also known as a space buffer. It
essentially shows how close together two contiguous activities are. A vertical line extended fully
through the linear schedule at any selected time represented on the horizontal axis will
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intersect all activities that are scheduled to occur at the time. It is worthwhile to examine this
relationship. Even if an activity has ample float, the operation of one activity might be too close to
another operation to effectively accomplish both at the same time.
Conflict between the activities would indicate that two activities are occurring
concurrently at the same location, generally an irreconcilable conflict (see Figure 14.4). It should be
evident that there might be some activities that might actually appear to be able to occur at the same
place at the same time. For example, one activity might show that the sign-age is being installed at a
particular station or location along a roadway. Another activity, painting the centerline stripe of the
roadway, might take place at the same station at the same time. While these activities might actually
cross when portrayed on a linear schedule, in reality they are not in conflict. It is only because of
the lack of sufficient detail that there is a visual, but no actual, conflict.
One interesting feature of linear schedules is their simplicity. It is easy to grasp the
operations that are taking place and it is also easy to see the impact of making modifications to the
schedule. For example, suppose it is desirable for the fence project to be completed earlier than
originally scheduled. The activity that warrants immediate focus is the fence construction activity,
as this activity (Activity B) essentially drives the schedule (see Figure 14.3). One way that the
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schedule can be reduced is to add a second crew for this activity. This second crew will begin the
work later than the first crew and it will begin at a considerable distance from the first crew. The
schedule compression is readily observable when this is done (see Figure 14.5). Note that
Activity B now appears as two different activities that have the same production rate as seen by the
slope of the line.
LPC LIMITATIONS:
The early start and finish times in the first and last units should be calculated for each and
every activity on all possible paths between the origin and terminal nodes of the unit network.
To do this, an LPC analysis must be conducted in the following way.
Once the first activity in the first unit starts at time zero, the production rate of the
succeeding activity should be compared with that of the first activity. If the production rate of
the first activity is faster than that of the succeeding activity, the succeeding activity in the
first unit can start right after the first activity in the first unit is finished. Otherwise, the
succeeding activity cannot start until sufficient lead time is provided, to prevent a conflict in
the logical relationship between the two activities. Therefore, the early start time of the
succeeding activity of the first unit can be derived from the early start time of the succeeding
activity in the last unit, which can start right after the first activity in the last unit is finished .
The same procedure can be applied to all of the consecutive activities, until the early start and
finish times of all activities in every path are determined in every unit. If there is an activity
that belongs to more than one path, it is called a bottleneck activity. The start time of this
activity is the latest one among the early start times that are obtained by analyzing the
different paths. Paths that share a bottleneck activity should be appropriately adjusted
according to the bottleneck activity’s start and finish times.
Dealing with Constraints
Successful scheduling should include proper sequencing of activities, comprehensive
understanding of interdependent activities, and flexible linking of services that flow
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simultaneously. The resource requirements for each activity are to be analyzed and estimated,
preferably in detail. If resources are limited, the activity start and finish times and the
resource-based logic may be changed because resource analysis.
Resource Aggregations
The distribution of resources during the course of the project is of particular importance to
construction managers. Not only do managers have to make sure that the resources they
allocate to the activities do not exceed availabilities, but they would also want to see as
smooth a distribution as possible in order to avoid the disruption of hiring and firing crews
during the course of the project. The proposed approach that is borrowed from work allows
for the generation of resource histograms superimposed on LPC diagrams. The resource
distribution for a single activity is presented. The area under the histogram represents the
man-hours ~or equipment hours! necessary to perform that activity. It should be possible to
combine distributions plotted for individual activities that make use of the same type of
resource and plot a single histogram that shows the distribution of that particular type of
resource over the life of the project.
Resource Limitations
To produce a realistic schedule, it is necessary to incorporate into the system a
procedure that can handle resource constraints that may exist in some activities. In that
respect, the activities that are performed by the same crew or equipment should be identified.
Those activities cannot be carried out simultaneously because of their exclusive use of the
same crew or equipment. The LPC analysis should be modified when determining the start
and finish times of these activities. Regardless of rates of production, the start time of such an
activity in the first unit should be determined by calculating the finish time of the preceding
activity ~that makes use of the same resources! in the last unit. The concept of the modified
LPC analysis.
Contractual Milestones
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In addition to limited resources, contractual milestones can be important parameters to
be considered in scheduling a project using the LPC technique. If the completion date of a
particular activity and/or of a particular unit is specified in the contract, this
information should be taken into consideration in LPC calculations. Since the target rate of a
project has little meaning in LPC calculations, scheduling capabilities that can meet the
requirements of partial delivery are essential. The proposed procedure of incorporating
milestones in LPC calculations makes use of an optimization process that compresses
activities. Once an optimized schedule is obtained that satisfies the contract duration, the
calculated date of the milestone activity is compared with the required milestone on the
specified unit. If any compression is required, the production rates of relevant activities
preceding the milestone activity are accelerated
until the requirement is met. The activities succeeding the milestone activity are not
considered in the optimization process performed on a time basis.
Resource Limitations
To produce a realistic schedule, it is necessary to incorporate into the system a
procedure that can handle resource constraints that may exist in some activities. In that
respect, the activities that are performed by the same crew or equipment should be identified.
Those activities cannot be carried out simultaneously because of their exclusive use of the
same crew or equipment. The LSM analysis should be modified when determining the start
and finish times of these activities. Regardless of rates of production, the start time of such an
activity in the first unit should be determined by calculating the finish time of the preceding
activity ~that makes use of the same resources! in the last unit.
Resource Aggregation
The distribution of resources during the course of the project is of Particular
importance to construction managers. Not only do managers have to make sure that the
resources they allocate to the activities do not exceed availabilities, but they would also want
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to see as smooth a distribution as possible in order to avoid the disruption of hiring and firing
crews during the course of the project.
Interdependencies among Activities
LSM scheduling can be performed easily, based on a combination of network
technology and the basic concept of LSM. Usually, a network diagram called the ‘‘unit
network’’ is prepared to represent the logical sequences of individual activities in one of the
many units to be produced. This unit network shows the interrelationships and/or
interdependencies among activities ~Fig. 2!. However, organizing activities in a chronological
order is not always adequate in representing interdependencies. Sometimes, special
characteristics of particular activities can also have a crucial impact in defining
interdependencies among activities. For example, when using the time data generated by a
unit network, the use of early starts ~or late starts! across the board for all activities without
exception may create workflow problems. Care must be taken to make sure that network
floats are not used arbitrarily or indiscriminately in the preparation of the LSM schedule. The
following are two special cases that illustrate this condition.
Time Dependency
When an activity must be carried out right after the preceding activity, these
two activities are characterized as activities with time dependency. In highway projects, for
example, primecoating activities should immediately follow the sweeping of the base course.
Therefore, a time-dependent activity does not have the freedom to be performed at its own
rate of production. Its rate of production is governed by the rate of production of its time
dependent counterpart activity. In LSM calculations, time-dependent activities should be
assigned the same rate of production in order not to provide an undesirable time gap between
the two activities as the number of units increases. The unified rate of production of time
dependent activities can be decided by taking the production rate of whichever of the two
activities is the dominant one. The other activity whose rate of production is adjusted will
inevitably suffer idle times for its crews and/or equipment, since the adjusted rate of
production will cease being a multiple of its natural rhythm
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Space Dependency
The phenomenon of space dependency is encountered mainly in high-rise building
construction. The typical example for this kind of dependency is the sequence formwork-
reinforcements concrete. These three activities have to proceed at rates of production that are
very close to each other, and yet the precedence relationships have to be strictly adhered to.
Otherwise, schedulers run the risk of prescribing formwork on the upper floor while the
concrete on the lower floor has not been poured yet. In this case, a dependent activity does not
have the freedom to be performed at its own rate of production and will have to wait until the
other dependent activities within the same unit are completed. It is therefore inevitable that
space-dependent activities have idle time.
In LSM calculations, the individual space-dependent activities should be considered as
a combined activity whose unit duration is calculated by adding up the unit duration of each
space dependent activity.
ADVANTAGES OF LPC:
The advantages of LPC Technique are:
1. Clearly shows the amount of work taking place in a certain area at a specific time of
the project.
2. Has the ability to show and optimize the resources used for large number of repeated
activities, executed in several zones or locations.
3. Easier cost and time optimization analysis because of all the information available for each
activity in the project.
4. Ease of setup and its superior presentation and visualization.
5. Easier to modify, update and change the schedule.
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6. Better managing of all the various sub-contractors in the project.
7. Allows for simpler and clearer resource management and resource optimization functions.
8. Better consideration of the site space which enhances the management of the crews and
resources involved in a certain spot at a certain time of the project.
9. Visualization of productivity and location of crews.
10. Generates schedule forecasts, based on the information of the “actual built” productivity
rates.
DISADVANTAGES AND LIMITATION OF LPC:
1. Inability to generate a clear critical path of the project schedule relative to one provided by CPM schedules.
2. It can only be divided by location.
3. In CPM scheduling the user could divide project by location and other systems like trades, in LOB only location.
4. Productivity rates in LOB schedule do not include the effect of crews‟ learning curve, or if the individuals working in the crews changed.
COMPARISON BETWEEN LPC & NETWORK ANALYSIS:
Technique Planning uses Programme uses Progress Control Uses
LOB Repetitive work (Houses, Precast Concrete production, Multi storey buildings)
1) Good communicating tool2) Demonstrates trade interference
1) Useful planning tool2) Difficult to show a lot of detail clearly3) Illustrates general pace of work and trade interference
Network Analysis
1) Project Management2) Contracts3) Design Management
1) Poor communicating tool2) In network form3) Usually converted to bar chart for general use
1) Powerful controlling tool for large numbers of contractors 2) Forms basis of computer.
EFFECT OF LEARNING IN LPC S CHEDULING:
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Learning rates are generated by modifying historical learning rates of typical construction
activities and by incorporating the impact of relevant factors such as number of operations in
one unit, activity complexity, and job and management conditions. Fuzzy set theory is used
to develop production rules to treat both factual and uncertain information. An S-type
membership function is used to interpret the fuzzy data and to produce adjustment factors that
are in turn used to modify consecutive learning rates until an adjusted learning rate is
obtained. The adjusted learning rate is then used to calculate expected worker-hours and
activity durations at each unit. A final LPC diagram is generated using this information.
Different pairs of curves represent the start and the finish times of each activity in sets of units
that make use of different numbers of crews. Learning reduces project duration and resource
requirements. The proposed approach demonstrates the potential for formalizing the
inclusion of learning effects into the LPC scheduling of repetitive-unit construction.
NONLINEAR AND DISCRETE CONSTRUCTION PROCESS:
Repetitive construction process may contain some nonlinear and non-repetitive (discrete)
activities.
(a) Nonlinear activities
In a high way project, earthwork will vary from section to section due to differences in the
terrain, which is defined by nonlinearity in most literatures. A nonlinear activity is
characterized by repetitive operation where the output of operations is not uniform at every
unit. The nonlinear activities cannot be treated like the linear and repetitive activities in LOB
calculations because the outputs in these activities differ from unit to unit.
(b) Discrete activities
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In a high way pavement project, the posting of the occasional sign structure is de fined a
discrete activity, which does not repeat itself in every unit. The discrete portions of the project
cannot be scheduled directly by the LOB method either, because these activities are not
included in the typical network. Yet, both nonlinear and discrete activities may interfere with
the scheduling of adjacent activities and, consequently, with the critical. Therefore, the
schedule of the entire project cannot be produced until these nonlinear and discrete activities
are scheduled and coordinated with the linear and repetitive.
CONCLUSION
The research has shown that most of the Line of Balance (LOB) scheduling
practitioners interviewed are satisfied with the scheduling technique and prefer using it over
the Critical Path Method (CPM). They all discussed a myriad of LOB scheduling advantages
and demonstrated how it helps in improving the planning and managing processes of
construction projects. LOB scheduling is effective in applying changes in job progress,
resource allocations, performing schedule changes efficiently, and simplicity and clarity of the
whole project schedule. They also discussed how, after some study of the schedule, the user
should be able to understand the flow of work through the project and comprehend the
reasoning for performing the work in the illustrated manner. Most of these advantages were
part of the scheduling practitioners‟ experience and were mentioned in their replies to the
interview questions.
BIBLOGRAPHY
Harmelink, D. J., and Rowings, J. E. ~1998!. ‘‘Linear scheduling model: Development of controlling activity path.’’ J. Constr. Eng. Manage.,124~4!, 263–268
D.B. Ashley, "Simulation of Repetitive-Unit Construction," J. Constr. Div.,ASCE, Vol. 106 (2), pp. 185-194 (1980).S.M. Hafez, “Survey of the-State-of-the-Art: Scheduling Projects with Repetitive Construction Process,” AlexandriaEngineering Journal, Egypt, Vol. 43 (4)(2004).
Lutz, J. D., and Halpin, D. W. ~1992!. ‘‘Analyzing linear construction operations using simulation and line-of-balance.’’ Proc., Transportation Research Board 71st Annual Meeting, Transportation Research Record 1351, Transportation Research Board, National Academy Press, Washington, D.C., 48–56.
Moselhi, O., and El-Rayes, K. ~1993!. ‘‘Scheduling of repetitive projects with cost optimization.’’ J. Constr. Eng. Manage., 119~4!,681–697.
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Thabet, W. Y., and Beliveau, Y. J. ~1994!. ‘‘HVLS: Horizontal and vertical logic scheduling for multistory projects.’’ J. Constr. Eng. Manage.,120~4!, 875–892.
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NATIONAL INSTITTE OF CONSTRUCTION
MANAGEMENT AND RESEARCH
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