Scheduling activities of linear and repetitive projects, the linear scheduling method [19], with various names (line of balance, construction planning technique, vertical production method, time-location matrix model, time space scheduling method, disturbance scheduling, horizontal and vertical logic scheduling for multistory projects, time versus distance diagrams, linear balance charts, and velocity diagrams) being annotated in one previous study [20], attempts to optimize construction productivity and resource continuity. The scheduling problems encountered by linear and repetitive projects can be regarded as special instances of conventional construction projects. The similar concept of floats was broadly used in linear scheduling approaches.

As discussed in linear scheduling methods, the location and time buffers (time floats) were defined and used in indicating how close activities can become while being conducted [13, 21]. The rate float, representing the amount that the production rate of a non-controlling linear activity can be lowered before the activity will become a controlling segment, is used to evaluate the impact of a delay on the project completion [22]. The time float, representing the amount of time a particular activity can be delayed without affecting the scheduled project date, is used to calculate the difference between either the starts or the finishes of an activity and its direct successor [23]. Based on the float definitions of the traditional CPM, a previous study defined potential floats, including TF, FF, INTF, INDF and SF, for linear schedules by using singularity functions to provide a tool to determine how linear or repetitive construction projects were impacted by delays [13].

Above linear scheduling methods adopted the traditional CPM as a basis for developing innovative approaches to solve the particular problems in linear and repetitive projects. Therefore, the floats used in the traditional CPM can be used in linear scheduling approaches. That is, no obvious difference exists between the floats used in the traditional CPM and linear scheduling approaches.

The resource-constrained scheduling method is another scheduling technique to minimize project duration, whereas the resource-leveling technique targets to level/smooth resource requirement profiles. Compared to the traditional CPM that assumes unlimited resources, the resource-constrained scheduling method attempts to arrange activities while considering resource availability and limitations.

With considering resource conflict, a previous study defined current float to represent the finish float available with respect to the float’s latest finish time in original network computations. The current float can be regarded as an abstract concept and may take negative values to indicate that the activities are already behind schedule [24]. Furthermore, in considering the resource availability, scheduled total float and scheduled free float were defined to replace original TF and FF in the traditional CPM [4]. In solving implementation problems in resource-constrained scheduling, a previous study identified the problem of the difference between the theoretically remaining TF and the real remaining TF, termed as the phantom float, and proposed an innovative resource-constrained critical path method (RCPM) technique to identify the resource dependency and to keep track of the activity’s late finish time by considering both technological relationships and resource dependencies. Similar to the basic concept of TF shared for activities on the same chain in the traditional CPM, the RCPM technique had an approach to determining which activities (might not be in the same chain) share total floats [25].

Resource-constrained scheduling methods focused on solving resource-constrained problems that the traditional CPM encountered. That is, resource-constrained scheduling methods extend the CPM’s ability in more complicated situations. Similar to the situation of floats in linear scheduling approaches, resource-constrained scheduling methods used not only the floats developed for the traditional CPM but also employed evolution floats to represent specified activity flexibility.

The critical chain scheduling (CCS) technique derived from the Theory of Constraints (TOC) in the project management domain is an innovative technique to scheduling activities by considering both logic relationships and resource availability [26] and removing some management pitfalls (for example, student syndrome). The CCS technique proposed a new leveled critical path (termed critical chain) instead of the traditional critical path to handle critical activities [27].

Similar to the concept of float in the traditional CPM, many types of buffer were defined: project buffer, feeding buffer and resource buffer [27, 28]. Buffers are designed quantities of time for a project schedule to protect what is important to project success. For improving the robustness of project baseline schedules under CCS, the strategy of choosing appropriate buffer sizes is important and discussed elsewhere [29].

The use of buffers in CCS differs from the use of floats in the traditional CPM due to their fundamental purposes: the former one is used for proactive project management and the latter one is used for reactive project management. However, some commercialized CCS software packages, for example the ProChain^® Project Scheduling software [30], integrated the functions of CCS and CPM and provided the float values for activity control and the buffer values for project management. Thus, there is no conflict between the use of floats and the use of buffers in CCS for the same project.

In developing an innovative scheduling method for construction projects, the chronographic method, six new types of float were proposed: complete float, start float, finish float, partial complete float, partial start float and partial finish float [3]. Combined with the four popular floats in traditional CPM, the chronographic method derived twenty-four floats, although most of them are theoretically based outcomes, to help schedule an optimized project schedule. The newly developed floats can be regarded as the subclass of traditional CPM floats [3].

For solving several problems (for example, if the level of duration detail is rough) in the traditional CPM, the critical path segments (CPS) approach was developed for better schedule analysis. Based on the CPS approach, the total float in the traditional CPM can be calculated accurately for better schedule management, although the developed approach was not mature [31].

The floats in three major approaches (linear scheduling, resource-constrained scheduling and critical chain scheduling) have been reviewed for capturing constructive information for better schedule management. Notably, excluding the popular floats in the traditional CPM, the floats in specific advanced scheduling approach are only suitable for the project types specified in particular approach.

In sum, the innovative floats in advanced scheduling approaches are derived from the popular floats in the traditional CPM. Thus, no completely new float was proposed in the discussed scheduling approaches. While using the advanced scheduling approaches, understanding all floats in the traditional CPM is necessary.

Based on practical implementation perspective, manually calculating all float values for a construction project is tedious, time-consuming and even impossible. Commercial PMSs are usually employed to obtain required float values. There are many diversified professional PMSs available now, and many web sites for software review and comparison are also reachable. This study discussed the definition and functionality of floats in the latest version of three popular systems for construction projects: Microsoft^® Office Project, Oracle^® Primavera^® P6^TM and Deltek^® Open Plan^TM, which were selected and discussed in a textbook introducing the CPM for construction management [32]. Basic information of floats in discussed PMSs is summarized in Table 1.

The Microsoft^® Project name for “float” is “slack.” As noted in Microsoft^® Project’s reference file, the behavior of TF can differ depending on the link type. For example, if a user works with a start-to-start relationship, TF can be changed when the user enters progress on the predecessor activity. With progress entered in the predecessor, the start date of the successor is known and becomes part of the total float calculation [33].

Excluding the TF and FF, Microsoft^® Project defines start and finish floats for better schedule control. The smaller of the start float and finish float amounts determines the amount of free float available, that is, the amount of time an activity can be delayed without affecting the start date of a successor activity or the project finish date. Notably, if an activity has an actual start date and a deadline, the start float is zero and the finish float is the difference between the activity’s finish date and deadline date [33].

Note that Microsoft^® Project 2010 provides a field, the negative slack (negative total float), to display the amount of negative total float for an activity on the Gantt Chart. The negative float indicates that there is not enough time scheduled for the activity and is usually caused by constraint dates or activity dependencies; therefore, the field indicates the amount of time that must be saved so that successor activities are not delayed [33].

Primavera^® P6^TM uses TF, FF, start float and finish float for representing the time buffer for delay activity/project. For providing a consistent value for TF, it allows the user to select one of three options: (1) start float; (2) finish float; and (3) the smallest of start float and finish float [34]. The TF might be different to others’ when complicated logical relationships are used.

In determining critical activities, Primavera^® P6^TM allows the user to define activities either on the longest path or with total float less than or equal to a customized time. Moreover, Primavera^® P6^TM provides a new function of float path for the user to manage the most critical path (and sub-critical float paths) in a project schedule by considering TF/FF values. Notably, in calculating multiple critical float paths, critical activities that are not part of a critical float path remain tagged as critical [34].

Based on a general float definition, the number of time periods by which an activity can be delayed without affecting other activities in a project, Deltek^® Open Plan^TM, uses TF, FF, finish TF, finish FF, relationship TF and relationship FF for flexible schedule management. Notably, it defines that the relationship TF is the amount by which the lag in a relationship would have to be increased to either cause a delay in the project completion or a late target date; the relationship FF is the amount by which the lag in a relationship would have to be increased to cause the delay of a successor activity [35]. Therefore, the schedule manager can use the relationship TF/FF to determine which relationship is responsible for controlling the critical status of the successor activity.

Note that Open Plan^TM calculates a scheduled float for an activity when resource scheduling is executed. The scheduled float is the difference between the late finish date and the scheduled finish date of the activity. In some circumstances, scheduled float may be shared with other activities in the logical flow of the project [35].

Through reviewing all float information in three major commercial PMSs (Microsoft^® Office Project, Oracle^® Primavera^® P6^TM and Deltek^® Open Plan^TM), this study finds that only TF and FF in the traditional CPM are common used in discussed PMSs. The definitions of TF and FF summarized in Table 1 are similar. Furthermore, all PMSs drive start and finish TF/FF for facilitating logical relationships of start-to-start and finish-to-finish used. It is interesting that every PMS develops its own unique attribute/function as Table 1 shown for better schedule management.

In sum, all PMSs provide easy-to-use float management functions. Notably, compared to Microsoft^® Project and Primavera^® P6^TM, Open Plan^TM provides more complicated float values for the user to control complex project schedules. However, Open Plan^TM increases use complexity and might cause wrong use, and even decision making faults if the user employs complicated floats but does not understand them correctly.

Based on the perspective of managing schedules by controlling floats, this study discussed five managerial essentials those are lessons learned from the literature review in this study and the author’s experience.

The scheduler, however, can manipulate diverse float values by using artificial lead/lags, unprecedentedly long activity durations, preferential logic relationships and other constraints. Furthermore, some informal schedule development approaches, for example, using multiple calendars [36], lead to unreasonable and un-predictable float values. When managing float in a construction project, the project manager/scheduler needs to decipher all assumptions and options of schedule developments; otherwise, he/she might manage the project based on unrealistic/unreasonable float values.

As concluded by a previous study, a professional project scheduler should have discipline (scheduling knowledge), experience and honesty; otherwise, he/she ends up with a schedule that is at best useless and at worst deceptive [37]. Disclosing flawless float values based on a generally recognized scheduling practice for all project stakeholders and sharing potential risks and benefits from float management improve the possibility of project success.

Using PMSs to plan and control project schedules is a must for the project manager and scheduler. According to available PMSs, when advanced logical relationships (i.e., start-to-start, finish-to-finish and start-to-finish relationships) and multiple calendars are used, the scheduler should display suitable float types (i.e., start and finish floats) as well as early and late bar charts for identifying key managerial activities, driving relationships and complicated float values to manage project schedules. Otherwise, hidden floats (the float value is hidden and does not appear in TF or FF) might appear in a partially critical activity, i.e., only the activity’s start or finish time is critical. For example, an activity has a five-day finish TF but a zero-day start TF when the start-to-start and finish-to-finish logical relationships are used concurrently. This makes PMSs determining the activity critical. However, this study identifies the activity having five-day hidden float.

Furthermore, float values would be changed while a project is in-progress. Regularly updating project schedules and monitoring the variations of floats for coming activities can easily identify possible schedule delays. Some PMSs have provided “remaining float” for monitoring float values. Notably, different PMSs provide different processes or steps to update a project schedule. For example, the timing, i.e., start or end of a day, for updating the schedule is different for various PMSs. The scheduler should manage critical activities with the start and finish floats simultaneously; otherwise, managing a critical activity merely based on the criterion of critical/non-critical might lead to wrong decision making.

Positive floats reflect that the activity with these float values has a large completion buffer time. However, practical experience has shown that nearly independent work in a project is relatively rare; thus, a high free float value often identifies missing logical relationships. When the project manager and scheduler want to manage floats proactively, they should understand float definitions clearly because float values for the project and activity levels have different connotations.

For a project, if either its start date or finish date is determined for scheduling, the activity on the longest path will have zero TF. If the identified time period from start date to finish date is larger or less than the duration of the longest path, the activity on the longest path will have positive or negative TF. The longest path with positive TF means that the project has buffer time for executing the critical activities. On the contrary, the longest path with negative TF represents that the project does not have sufficient time for executing all activities on the longest path according to their scheduled dates.

For an activity, TF can be positive or negative. A positive TF for an activity indicates the amount of time within which the activity can be delayed without delaying the project finish date. A negative TF indicates the amount of time that must be saved so that the project finish date is not delayed. Negative float generally indicates that there is not enough time scheduled for the activity and is usually caused by constraint dates.

Maintaining positive floats for both the activity and project levels decreases the possibility of a project delay and increases the chance to complete the project on time or even ahead of the targeted completion date. Notably, when adopting PMSs for scheduling, a scheduler should use target dates for projects and activities carefully, particularly in the early stages of the planning process. The extensive use of target dates often has the effect of artificially distorting the patterns of float within a project, making analysis of the network more difficult.

Most scheduling textbooks illustrate that an activity can have individual TF, FF, INTF and INDF. However, advanced floats (the floats excluding TF and FF) are ignored in most available PMSs. This fact implies that advanced floats are useless. Thus, software users no longer have the possibility to use those advanced floats by using available PMSs. A previous study has concluded that different float types can be used in different management scenarios. For example, FF plays an important role for subcontractors, whose own delays could cause a ripple effect on subcontractors further downstream; INTF measures how much delay can be absorbed within the entire project by delaying subcontractors [13].

Generally, advanced floats are proposed and derived based on the ADM approach. Most available PMSs no longer support the ADM approach due to complicated logical relationships that cannot easily be simulated by the ADM approach. However, whether using complicated logical relationships can improve the possibility of easily or successfully managing a project is an interesting question. Some PMSs provide customized fields for storing user-defined values. If the project manager and scheduler have knowledge and the capability to define the required float values by using available PMSs, it is possible for them to manage their projects based on more informative indicators. Furthermore, simply using TF is an acceptable choice for managing most projects. However, if the project’s logical relationships among activities are complex, it is necessary to employ other float types. This implies customizing advanced floats in PMSs is consequently necessary.

There is no consensus on the ownership of project floats in the construction practice. Managing floats for simplicity or complexity appears to be in dilemma. If the floats ownership is not clearly described in a contract, the owner usually asks the contractor to arrange the floats for simplicity; however, the contractor always hides the floats for potential use, which makes managing floats complex because the reasonable floats belonging to the activities are difficult to identify.

Simplifying the use of floats should be a trend in PMSs although these systems provide comprehensive program options for the software user. The project stakeholders, particularly the owner and the contractor, should understand that completing a project on time or even ahead of the targeted dates should be a common project goal. Therefore, developing project schedules against a background of mutual trust and managing floats for simplicity would make project stakeholders focus on project execution and complete projects with mutual benefits.

The ownership of project floats had received much attention in the past [2, 5]. Based on the construction practice and CPM theory, all float ownership options can be common divided into three categories: the owner, the contractor and the project [38-40]. Notably, float ownership discussion focuses merely on TF, which must be regarded as “common property” among the activities in the longest chain [41]. If a delay appears to influence an activity with positive TF, a dispute about the right to consume the TF usually arises. The contractor considers TF as a time contingency to cope with unanticipated conditions; on the contrary, the owner considers it as his/her right to use the float. Using an approach to pre-allocate TF would be an alternative for solving expected disputes [38].

The use of float as a resource should be reserved for the party who loses or gains as a result of fluctuations in the project cost [2]. Floats should be used on the basis of fundamental fairness and equity [2]. Based on the acknowledged fact that TF is beneficial to both the owner and contractor, a previous study proposed an approach to manage TF as a commodity with explicit contract language, which provides the contractor with the right to administer TF and the obligation to disclose its value and trade it on demand [5]. How to develop a clear and acceptable approach for measuring float consumption and the related liability, particularly when concurrent delays occur, and how to adjust the already existing knowledge and treatment to be on a basis of fairness and equity would be a challenge for researchers and practice. However, for better schedule management, clarifying float ownership in advance is a fundamental of proactive strategies on mitigating challenging float-related problems.

In practice, an activity has one of the following criticality situations: (1) not critical; (2) critical-TF less than or equal to zero or a predefined value; (3) most critical-TF equal to the smallest value for the entire project; and (4) controlling critical-has float due to its own calendar but causes a successor to be critical [35]. It is clear that the so-called critical activity does not have a fixed float value when complex scheduling options are used. Therefore, a critical activity should be clearly defined with explicit scheduling specifications and contract language based on the project level. By using strong and clear scheduling specifications, the owner can help ensure that the contractor’s schedule realistically reflects the project requirements, the contractor’s approach to the work, and the status of the project [42]. Notably, most owners have no strong background knowledge to develop scheduling specifications.

To setup a transparent and manageable project schedule, many construction-related government agencies in the US, for example, the Departments of Transportation (DOTs) in the states of New Jersey, Virginia, and Texas, have developed different scheduling guidelines, checklists, specifications and best practices for the officer, the designer/engineer and the contractor to prepare to review and to update construction schedules [43-45]. It is quite frustrating that there are no clear specifications from the above-mentioned documents to define the relationship between float and critical activity. It could be an important research topic in the future.

For achieving better schedule management, to understand the relationship between float and critical activity in employed PMS and then to develop clear scheduling guideline would be another fundamental of proactive strategies on mitigating challenging float-related problems.

When the start-to-start and finish-to-finish logical relationships are used in developing project schedules, the pitfall of hidden float (the float value is hidden and does not appear in TF or FF in employed PMS) usually appears in developed schedules. Traditionally, when an activity is defined as critical, any delay in this critical activity will delay the project completion date. Compared to traditional critical activity (both start and finish time are critical), a partial-critical activity is defined as that either the starting time or finish time is critical for the activity. For example, if an activity only has a start-to-start relationship to its successor and is on a critical path, then only its start time is critical. In such a situation, the activity usually has a hidden float. Therefore, it is necessary to manage the hidden float when complex project schedule is developed.

Several PMSs exhibit the hidden float in the format of a finish float. To manage the liability of schedule delay correctly, suitable float controlling is required. Managing a critical activity merely based on the criterion of critical/non-critical will lead to wrong information for decision making if complex logical relationships exist. It is suggested that avoiding employing start-to-start and finish-to-finish relationships is a basic principle in developing project schedules; otherwise, the scheduler should manage the start and finish float independently while using start-to-start and finish-to-finish relationships. How to develop a clear specification for detecting and managing hidden floats is an essential issue when complex logical relationships are used. There is no doubt that managing hidden floats aggressively is another fundamental of proactive strategies on mitigating float-related problems.