Scheduling optimization with line of balance and start-finish relations / Ricardo Viana Vargas, Felipe Fernandes Moreira.

Ricardo Viana Vargas – United Nations (UNOPS) – Universidade Federal Fluminense

Felipe Fernandes Moreira – Universidade Federal do Ceará

The “start-finish” relationships between activities are often misunderstood. Part of it is due to the lack of comprehension of the true meaning of logical relationships. A Guide to the Project Management Body of Knowledge (PMBOK® Guide) – Fifth Edition lists the “start-finish” relationship only to represent the complete list of possible links (PMI, 2013). The first and second editions state that typically only professional scheduling engineers use the “start-finish,” warning that the usage of relations other than the most common (“finish-start”) may produce unexpected results. The same goes for the Line of Balance Scheduling Method, which is used in the civil construction industry and is absent from the PMBOK® Guide. This article, which has the objective of studying some usages of the “start-finish” relationship and its unexpected results, shows the usage of the Line of Balance scheduling method with the sequencing of repeating tasks; on the just-in-time sequencing of activities; on the scheduling of milestones and supporting activities; and on backward planning.

Introduction

Part of the planning effort in a project is directed to determining the sequence of the activities in such a way that the execution goes on in the most efficient way possible. This sequencing is modeled using relationships between activities, called dependencies, which may be “finish-start” (“FS”), “start-start” (“SS”), “finish-finish” (“FF”) and “start-finish” (“SF”). This link establishes a relationship between activities, where one of them is the predecessor (the activity that comes before logically), and the other is the successor (the activity that comes after logically), (PMI, 2013).

The PMBOK® Guide (2013) defines the “SF” logical relationship as: “the completion of the successor activity depends upon the initiation of the predecessor activity.” It is important to notice that, with the “SF” relation, the predecessor is the activity that happens chronologically after, while the successor is the activity that happens chronologically before.

Also in the PMBOK® Guide (2013), the listing of the “SF” relation is only to represent the complete list of the Precedence Diagramming Method, since the guide considers this particular relation as rare. The description of the “SF” as a rare kind of link is on every version of the PMBOK® Guide (1996, 2000, 2004, 2008, and 2013). In addition, the first and second editions (1996 and 2000), however, state that typically only professional scheduling engineers use the “SF” relationships. These editions even warn that the usage of relationships other than the most common (“finish-start”) may produce unexpected results, since their implementation is not consistent.

The Line of Balance Scheduling Method (LBSM) is also a technique absent from the PMBOK® Guide since its first release (1996, 2000, 2004, 2008 and 2013). Civil construction companies from Brazil, Finland, and Australia are satisfactorily using the LBSM (Henrich & Koskela, 2006). Employing this technique is majorly related to the effort for incorporating to their project management systems, the basic concepts of Lean Construction (Bernardes, 2003), more precisely with the Last Planner® production system, developed by Glenn Ballard and Greg Howell, founders of the Lean Construction Institute® (LCI).

The U.S. Navy initially used the concept of Line of Balance as a technique for planning the execution of activities of the industry in 1942 (Kenley & Seppänen, 2010). General Electric, later, working for the U.S. Navy, used it not only as a planning tool, but also as a control tool in the United Kingdom; the method was adopted by the Nation Building Agency.

The preference for the Line of Balance scheduling method for developing the project schedule is due to the fact that the “unit of production x time” configuration, instead of the usual Gantt chart configuration (“activities x time”), results in better visualization for the link between the flow of work of the different crews (Bernardes, 2003). This allows a different perspective for the control of the project activities – with the Line of Balance, the focus of control is the rate of production of the working crews and not the control of individual discrete activities, which is the focus of the Critical Path Method that is largely used (Kenley & Seppänen, 2010).

Objectives

The definition of predecessors and successors as logical relationships at the Precedence Diagramming Method section appears only upon the release of the PMBOK® Guide – Fifth Edition (PMI, 2013). Up until then, the definition of logical relationships appears only in the glossary. Even in the fifth edition, the PMBOK® Guide does not clearly distinguish logical relation from chronological relation. Moreover, it does not represent the “SF” relation on its example of Precedence Diagramming Method, something that would help the understanding. In addition, the LBSM remains out of the PMBOK® Guide, despite its use in the civil construction industry.

The present article has the objective to show the applications of the “start-finish” (“SF”) relationship to model schedules and the capability of the LBSM to optimize schedules. It is also an objective of the paper to discuss and investigate the unexpected results of the use of the “SF” relation and to propose solutions.

Line of Balance Scheduling Method

The Line of Balance proposes that the planning of activities should be according to a rate of production, or cycle, meaning the number of production units delivered by a working crew, by a unit of time (Henrich & Koskela, 2006). Such a concept is similar to the concept of takt-time from the Toyota Production System (Ohno, 1988).

Next, an example showing a comparison of the regular Gantt chart and the Line of Balance for scheduling three tasks repeating themselves continuously along four floors (Exhibit 1). The assumption is that the next task initiates when the working crew ends the task on the precedent production unit.

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Exhibit 1: List of activities.

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Exhibit 2: Schedule using the Gantt chart.

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Exhibit 3: Schedule using the LBSM.

The rate of production, or cycle, is the angular coefficient of each line (Exhibits 2 and 3). For Task 1, the cycle is 0.25 units per unit of time; for Task 2, the cycle is 0.50 units per unit of time; and for Task 3, the cycle is 0.33 units per unit of time. The analysis of these cycle times allows the management team to balance the lines to optimize the use of resources and achieve a reduction of the time needed to complete the project. Exhibit 4 is the result of reducing the amount of resources of Task 2 by half (in other words, reducing its cycle time to 0.25, the same value of Task 1, and increasing the task duration to four days).

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Exhibit 4: Balancing lines to achieve a schedule reduction.

The line balancing of these two activities allowed the finishing of the project to happen one day earlier with the reduction of the resources used on Task 2 only – the remaining tasks were left untouched. The comparison of the Gantt chart and the Line of Balance also shows a significant reduction of lines displayed on the schedule (from 12 in the Gantt chart to four in the Line of Balance). The large reduction on the example shows the potential to simplify the schedule chart of a real project that contains several repetitive processes like, for example, a building with 100 floors with “n” different kinds of tasks on each floor. The simplification factor is the number of tasks inside each repetitive process (also called production unit). If you have 100 km of road and 20 tasks for each km, by using the Line of Balance, you are reducing the number of lines of your Gantt chart by 20 (Exhibit 5).

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Exhibit 5: Simplification factor.

It is important to note that even though the example used, cycle of tasks, it is possible to model a Line of Balance with process cycles, deliverables, and sub-nets of precedency diagrams (Kenley & Seppänen, 2010). In addition, the example used floors, but it can also be used for houses, apartments, locations of a story, sections of a highway, or pipeline, etc.

In the civil construction industry, the repetition of activities is commonly scheduled continuously (Kenley & Seppänen, 2010). Exhibit 6 shows the activities listed in Exhibit 1 modeled without the constraint of continuous repetition.

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Exhibit 6: Line of balance without the continuity of repetition.

On the resulting Line of Balance, the sequence of tasks is finishing on the 21st day (three days earlier). However, it is important to notice that this is not always a good practice. For example, in a construction project where a skyscraper is the product, or in a smaller-scale real estate project, the deliverables cannot be transferred in a “first in-first out” routine. They are transferred to the final client in a single lot. Therefore, the measure showed on Exhibit 6 would increase the inventory of completed work. It is possible to see, while examining Exhibit 6, that the first floor would wait 12 days, while the second and third would wait 8 and 4 days respectively, which results in a total of 24 days. The Line of Balance of Exhibit 3 has a total of 18 days, or 25% less.

Another relevant consequence of breaking the continuity is that resources will remain (for a longer amount of time) allocated on the project. On Exhibit 6, the resources of Task 2 would be dedicated to this project for 14 days, while at Exhibit 3, the total time is only 8 days (about 43% less). For Task 3, the modeling pattern of Exhibit 6 results in 15 days of its resources, while the modelling of Exhibit 3 results in 12 days (20% less). This would imply a larger human resources cost for the project. In Brazil, the average labour cost for residential buildings is about 50%, according to indexes published by the Brazilian Chamber of Construction Industry (CBIC, 2014). Popescu, Phaobunjong, & Ovararin (2003) inform that construction projects’ labour costs range from 30 to 50%.

The management team has carefully studied the consequences of breaking the repetition continuity in order to decide what the best option for the project schedule is.

Utilization of “SF” Relation on Continuous Sequencing of Tasks

On Exhibit 3 it is possible to observe a peculiarity. Task 1 has four days of duration and its successor, Task 2, has two days, which means that the Task 1 progression has a smaller linear coefficient than the Task 2 progression (it is slower). Modeling the cycle of the continuous repetition of Task 1 goes by using the “FS” (finish-start) relation, since the next task initiates when the working crew ends the task on the precedent production unit.

To allow the same continuity for Task 2, it is necessary to base the modeling of its cycle at the end of the last repetition of Task 1. Task 1, on the fourth floor, already has a “FS” relation with Task 2 on the fourth floor. This way, the start date of Task 2 at the fourth floor is well-defined on time. The whole scheme is detailed below (Exhibit 7).

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Exhibit 7: Network diagram with the logical relationship between tasks.

Modeling the remaining repetitions of Task 2 using the “FS” relationship is not sufficient to ensure the continuity of all repetitions. The only way to automatically ensure this is by using another kind of linkage, one that can transfer the constraint defined by the cycle of repetition of Task 1 “downward” from Task 2 on the fourth floor to Task 2 on the first floor. Therefore, with the definition by PMI (2013), the predecessor in this case is Task 2 on the fourth floor, despite the fact that this is the last repetition in the schedule; it offers the time constraint for the sequence of tasks. The successor is, then, Task 2 on the third floor – a task that happens earlier than its predecessor does, but has its timing defined by the task that comes next on the time schedule.

This relationship between these two tasks is different; the start of the task that happens later in time is connected to the end of the task that happens immediately before. It is a legitimate “start-finish” relation. The result is that the start of Task 2 on the fourth floor is linked to the end of Task 2 on the third floor, that has its start linked to the end of Task 2 on the second floor, that has its start linked to the end of Task 2 on the first floor (Exhibit 8).

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Exhibit 8: SF relation between the repetitions of task 2.

Continuing the modeling of the network diagram, the fourth floor is no longer the time constraint for the cycle of the next set of tasks. From Exhibit 3, it is possible to perceive that the Task 3 progression has its angular coefficient smaller than the Task 2 progression (in other words, it is slower). To keep the continuous progression for Task 3, it must proceed from the end of Task 2 on the first floor “upwards” (from the first until the fourth floor). This sequence is modeled by using the “FS” relation, connecting the end of Task 3 on the first floor with the start of Task 3 on the second floor, which has its end linked with the start of Task 3 on the third floor. Finally, Task 3 on the third floor has its end linked with the start of Task 3 on the fourth floor.

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Exhibit 9: Complete network diagram for the example.

Another peculiarity appears when modeling this network diagram using a schedule management software in order to identify the critical path. The result displayed by the software states that every single task on the network is part of the critical path, and this is not true. Analyzing the progression of Task 2, it is true to say that every task has a free float of zero (which means that any delay on any task will delay the next one). However, there will be no delay on the project end date if Task 2 on the second floor has a one-day delay. The same if Task 2 on the third floor has a two-day delay or Task 2 on the fourth floor has a three-day delay (which means that the total float is not zero) (Exhibit 10).

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Exhibit 10: Total float for the repetitions of task 2.

It is notable that the inclusion of the “SF” relation on network diagrams reveals a flaw in schedule management software. Apparently, they consider every single task with a free float equal to zero as a critical task, not taking into consideration the total float.

Utilization of “SF” Relation On Optimization of Resources (Just in Time)

Consider the table of activities (Exhibit 11) for the next example.

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Exhibit 11: Activities list.

The example consists of a sequence of activities. As observed on the following network diagram, two parallel paths come out from Task A. The path with Tasks A, B, C, and D is the critical path, and Task E has a free float of 12 days. “ES” and “EF” are the early start and early finish, respectively, for every task. The free float of Task E is the result of the subtraction of EF from the ES of its successor (Task D).

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Exhibit 12: Network diagram.

An analysis of the diagram from the resource usage point of view reveals that executing Task E by the thirteenth day of the project is too early – its deliverable has to wait for 12 days until used by the next task. This is overproduction, one of the “seven wastes of production systems” (Ohno, 1997 and Shingo, 1996). More precisely, overproduction in anticipation; the task was executed much earlier than necessary – quantified by its free float of 12 days.

Employing the SF relation can remove this anticipation. To do so, it is necessary to remove the FS relation between Task E and Task A, replacing it by a SF relation with Task D as the predecessor and Task E as the successor (remembering that predecessor and successor are logical concepts, not referring to time scale) (Exhibit 13). This schedules Task E as late as possible.

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Exhibit 13: New network diagram with the SF relation.

In this arrangement, the path formed by tasks A, B, C, and D fixes the finishing date of the project. The SF relationship serves as a pulling mechanism for the execution of Task E. Breaking the logical bond between Task A and Task E does not influence the whole model because Task D is dependent of Task C, that is also dependent of Task B, and further depends on Task A. Therefore, by the time Task E has to start, Task A is already finished. This is true for every duration of Task E that is lower than the sum of the tasks in parallel. This happens because if the duration of Task E was equal or superior to the sum of its parallel tasks, Task E would be part of the critical path.

It is important to notice some implications of this new approach. The first is that such an arrangement has Task E as part of the critical path – there is no free or total float on the resulting sequence. This results, therefore, in a higher level of risk for the whole project. The project manager should evaluate the impact of this change on the network structure. To mitigate this risk, the project manager can insert a buffer between Task D and Task E.

Removing the link between Task A and Task E may cause communication flaws between the teams responsible for executing each task. The project manager should keep in mind that this change in the logical structure might hide the need for interaction between both teams. An example for this would be Task E being dependent on some sort of deliverable resulting from Task A.

Utilization of the SF Relationshipas Milestones and for Support Activities

This utilization is, in truth, a consequence of the other two utilizations already mentioned. As it could be seen, the main idea behind the first utilization is to subordinate a sequence of tasks to an imposed time constraint. In the example given, the finishing date of the cycle of Task 1 imposes a fixed date to the end of the cycle of Task 2. In the second utilization, the SF relationship assured the scheduling of activities for exact time with no anticipation.

With milestones, a practical example would be finishing a sequence of painting activities for a building by the end of the sixth month of the project, or the completion of the management plan should be by the third month after the project approval. Assuming that milestones in a network diagram are tasks with zero duration and with a fixed start date, the modeling of one of the examples is presented on Exhibit 14.

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Exhibit 14: Milestones and SF relation.

Exhibit 14 shows that Milestone 1 subordinates the end of the workflow of the painting activities. This way, the continuous use of SF relationships between the tasks’ repetitions “downwards” will result in the necessary start date for the workflow. Just like the last utilization, this results in a higher level of risk.

The same applies for scheduling contract obligations or management activities; for example, some dates for control meetings, dates for the distribution of reports, dates for paying suppliers or contractors, and many more. Going deeper on the given examples, for a report distribution, some management activities have to be completed: the gathering of data, the data analysis, completing the report, and delivering the report. The delivery of a report is a milestone and the modeling can go on the same as in the other example.

Utilization of the SF Relation on “Backward Planning”

It is possible to generalize the utilization of SF relations to subordinate activities to a certain milestone to all tasks of a project. In other words, subordinate all of them to a milestone that represents the end of the project. This model will allow the design to move “backwards,” from a required end date until the necessary start date. The name of this procedure is backward planning, as introduced by Kishira (2009) as tool for the Critical Chain Project Management (CCPM).

It is possible to see that the CCPM is quite similar to the Drum-Buffer-Rope Scheduling (DBRS), a method for scheduling any manufacturing process (Cox & Spencer, 2002). The DBRS designs the production system subordinating every process step to the process bottleneck, known as the process constraint. In order to reduce the work in progress, the scheduling demands that the steps behind the process constraint produce only what the bottleneck's capacity can manage.

The CCPM uses the same idea. The project's major constraint is its deadline (Goldratt, 1996). Accordingly, in order to subordinate all activities of the project to its constraint, the deadline serves as the starting point of the scheduling process.

The inconvenience of this methodology is the already exposed fact that commercial schedule management software has an algorithm that mistakenly calculates the critical path for networks designed with SF relations. Modeling a sequence of tasks using the backward planning logic will result in a critical path composed by the last task of the path – no matter how long the sequence is – when, in fact, every single one of them is critical (a fact confirmed when modeling the same sequence using the traditional way).

In truth, the use of this technique to design a network diagram will cause the same effect observed on the just-in-time item: none of the tasks will have a float. This effect is consistent with the CCPM, since the methodology has the objective of removing every trace of individual slack inserted in the schedule and transfer it to the project buffer at the end of the critical chain (that protects the deadline) and to feeding buffers in the convergent paths (to protect parts of the critical chain).

Conclusion

This paper proposed utilizations of the Start-Finish (SF) relationship to develop project schedules – particularly with the Line of Balance method. Initially, the SF relation showed how to integrate the sequence of repetitive tasks. Then, the SF relation served as a “pulling mechanism” for activities, removing any unnecessary anticipation, inspired by the just-in-time concept from the Toyota Production System. In addition, combining both utilizations already mentioned, the SF relationship subordinated tasks to milestones and was able to help on the scheduling of support and project management tasks. Lastly, the SF relation can be a powerful tool for backward planning, part of the Critical Chain Project Management.

The paper also analyzed some relevant impacts of the method and the challenges of using it with traditional schedule management. The downside of the technique relates to the increase on the level of risk due to the removal of the floats and the additional risk of communication problems with the new network diagram structure.

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This material has been reproduced with the permission of the copyright owner. Unauthorized reproduction of this material is strictly prohibited. For permission to reproduce this material, please contact PMI or any listed author.

© 2015, Ricardo Viana Vargas and Felipe Fernandes Moreira
Originally published as a part of the 2015 PMI Global Congress Proceedings – London, UK

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