standard tools for scheduling. Related ... for projects in which the work content (of the project) can be divided into several subprojects ... The proposed tool.
International Journal of Project Management Vol. 15, No. 1, pp. 15-19, 1997 Copyright © 1996 Elsevier Science Ltd and IPMA Printed in Great Britain. All rights reserved 0263-7863/96 $17.00 + 0.00
Pergamon
S0263-7863(96)00017-8
Project segmentation--a tool for project management Avraham Shtub Department of Industrial Engineering, Tel-Aviv University, Ramat Aviv 69978, Israel
Since the late 1950s network-based techniques are commonly used for project management. The critical path method (CPM) and programme evaluation and review technique (PERT) are standard tools for scheduling. Related techniques such as PERT-COST are used for budgeting and control. In this paper, a new tool for project management is suggested. This tool is designed for projects in which the work content (of the project) can be divided into several subprojects or segments so that the same set of activities is performed on each segment. The proposed tool is the basis of a project scheduling model and a project control model designed to support project management in cases where CPM and PERT are not suitable. Copyright © 1996 Elsevier Science Ltd and IPMA. Keywords: Project planning, project control, project scheduling
Project planning and project control are key issues in project management. A variety of models are used for project planning and control, including the critical path method (CPM), program evaluation and review technique (PERT) and PERT-COST I-3. Since its introduction in the late 1950s network-based project management techniques have been used for managing numerous projects of a very large variety, ranging from high tech projects (using GERT) to production and construction projects of different sizes. Excellent books on network models for project management 4'5 were published and used by researchers, students and practitioners throughout the world. The basic assumptions of CPM and PERT have been criticized in the past 6'7. For example Chase and Aquilano s present the following discussion on these assumptions: • Assumption: Project activities can be identified as entities;
that is, there is a clear beginning and ending point for each activity. Criticism: Projects, especially complex ones, change in content over time, and therefore a network constructed in the planning phase may be highly inaccurate later. Also, the very fact that activities are specified and a network formalized tends to limit the flexibility that is required to handle changing situations as the project progresses. • Assumption: Project activity-sequence relationships can be specified and arranged in a directed network. Criticism: Sequence relationships cannot always be specified beforehand. In some projects, in fact, the ordering of certain activities is conditional on previous activities. (PERT and CPM, in their basic form, have no
provision for dealing with this problem, although some other techniques have been proposed that present the project manager with several contingency paths, given different outcomes from each activity.) • Assumption: Project control should focus on the critical path. Criticism: It is not necessarily true that the longest path obtained from summing activity expected duration values will ultimately determine the project completion time. What often happens as the project progresses is that some activity not on the critical path becomes delayed to such a degree that it extends the entire project. For this reason it has been suggested that a critical activity concept should replace the critical path concept as the focus of managerial control. Under this approach, attention would centre on those activities that have a high potential variation and lie on a near-critical path. A near-critical path is one that does not share any activities with the critical path and, though it has slack, it could become critical if one or a few activities along it become delayed. Obviously, the more parallelism in a network, the more likely that one or more near-critical paths will exist. Conversely, the more a network approximates a single series of activities, the less likely it is to have near-critical paths. • Assumption: The activity times in PERT follow the beta distribution, with the variance of the project assumed to be equal to the sum of the variances along the critical path. Criticism: The beta distribution was selected for a variety of good reasons. Nevertheless, each component of the statistical treatment in PERT has been brought into question. First, the formulae are in reality a modification 15
Project segmentation: A Shtub
of the beta distribution mean and variance, which, when compared to the basic formulae, could be expected to lead to absolute errors of the order of 10% for the mean and 5 % for the individual variances. Second, given that the activity-time distributions have the properties of unimodality, continuity and finite positive endpoints, other distributions with the same properties would yield different means and variances. Third, obtaining three 'valid' time estimates to put into the PERX formulae presents operational problems, it is often difficult to arrive at one activity-time estimate, let alone three. The popularity of network-based project management techniques and the large number of software packages which are based on these techniques indicates, however, that for many types of projects network models are useful and the above assumptions are valid. Furthermore, the volume of research in this area indicates that these assumptions are acceptable by many researches as well. 9-~ There are projects, however, in which some of these assumptions are questionable and the implementation of network-based techniques is either impossible, or it may lead to errors in the analysis. The example of road construction projects may serve to illustrate this point. In a road construction project certain activities are performed in a predetermined sequence. Each part of the road requires some or all of these activities. The cost and duration of each activity can be estimated only if a specific part of the road is considered. Although the technological order in which the activities should be performed is known a priori, it is difficult or even impossible to represent it by the standard precedence relations commonly used in network analysis-finish to start (FS), start to start (SS) and finish to finish (FF). This is due to the fact that most activities can start on parts of the road before their corresponding predecessors have been completed on all 'preceding parts' of the road. In the above example, the project consists of repetitive elements (road segments). The effort required to complete each element depends on the size of the element (length of the road segment in the example) which is a decision variable. Two questions associated with the example are not addressed by PERT/CPM analysis: 1. Into how many segments should the project be divided and 2. What is the 'right size' of each segment. Similar questions are treated in the literature by the process of breaking down the work content of the project into manageable work packages and creating the work breakdown structure (WBS). The WBS is a 'product-oriented family tree composed of hardware, services, software and data which result from project engineering efforts '2. Unlike most of the work packages of a typical WBS, in the proposed project segmentation approach, the project is divided into segments that are similar to each other. All the segments require a similar set of activities and the number of segments, as well as the size of each segment are decision variables. Thus, by using segmentation, the project is divided into several repetitive subprojects. The management of repetitive projects is supported by the line of balance (LOB) approach. This approach, developed by the US Navy z, is based on a comparison between the number of identical projects that have completed certain milestones at a given point of time and the number of projects scheduled to complete these milestones by that time. 16
Thus, the proposed project segmentation approach is a special adaptation of the WBS concept for the case where a project can be divided into several repetitive subprojects, and the number of such projects is a decision variable. In the following section, the project segmentation idea is presented as a model, along with its assumptions and notation. Next, models for project planning and control are suggested and discussed and an example is used to demonstrate the proposed approach. A summary and conclusions are presented in the last section. Although road construction projects triggered the development of the project segmentation model, other examples can be thought of, including the construction of apartment buildings, where each apartment or each floor is a project segment, and writing a book, where each chapter is a segment. In these examples, (as before) each segment of the project requires a similar set of activities. The project segmentation approach can be used in conjunction with CPM or PERT analysis or as a stand-alone tool. By using the proposed models for project planning and control, management of such projects can be made easier and more efficient.
Project segmentation: assumptions and notation In the following section we present models for the planning and control of projects using project segmentation. All the models are based on the following assumptions: 1. The project can be divided into similar segments (e.g. road segments or chapters in a book). 2. Project activities are known a priori, all segments require a similar set of activities. 3. The technological order in which the activities should be performed on each segment is predefined, and is the same for all segments. 4. The duration and cost of performing each activity on each segment of the project can be estimated a priori, and it is a function of the segment size. 5. The actual duration and cost of performing each activity on each segment of the project can be measured. Notation n index set of project segments. m index set of project activities.
iJ jeJ
i = 1 ...... j = 1 ......
te O
t = 1 . . . . . . T index set of time periods. Planned duration of activity j on segment i. Planned cost per period of activity j on segment i. Actual duration of activity j on segment i. Actual cost per period of activity j on segment i. Planned start time of activity j on segment i. Actual start time of activity j on segment i. Planned finish time of activity j on segment i. Actual finish time of activity j on segment i.
PDij PCij ADij AC~ PSij ASi~ PF~j AFij
Using the above notation and assumptions, it is possible to plan the cost and schedule of a project divided into segments and to compare it to its actual cost and schedule. Furthermore, the size of each segment is a decision variable, controlled by management and it corresponds to the desired accuracy in planning and controlling the project.
Project segmentation: A Shtub
Models for planning and control of projects using project segmentation
Table 1 Data for example project Activity
Predecessors
1 2 3 4 5
None None 1 2 3,4
Activity duration in segment i [weeks]
Total activity duration [weeks]
Project planning
Project planning models can be categorized into two types: optimization models and evaluation models. An optimization model is designed to produce a project plan which is optimal (or at least relatively good) with respect to a given objective function and satisfies a set of constraints. CPM, for example, tries to minimize the project duration subject to precedence relations among activities, and it can be represented in terms of a linear function and a set of linear constraints (a linear programme) 2. An evaluation model is designed to analyse a given solution to the problem by calculating the value of an objective function and checking if any constraints are violated. Most spreadsheet applications, for example, are based on evaluation models as no optimum seeking mechanism such as the simplex algorithm for linear programming is used. The following model is an evaluation model. Its primary input parameters are the estimated values of P D u and PS u , for all ij combinations. The model output includes: 1. Planned finish time of each activity on each segment. P F u = PS u + PD u
if PRuk = 1
3 3 4 2 1
i=3 4 2 3 2 3
10 7 11 6 7
Table 2 Results of the planning model for the example project using segmentation Segment 1
Activity (j =)
Segment 2
Segment 3
PS u
PF~
PS2j
PF2j
PS3j
PF3j
1
0
3
0
3
0
4
2 3 4 5
0 3 2 7
2 7 4 10
0 3 3 7
3 7 5 8
0 4 2 7
2 7 4 10
Table 3 Results of the planning model for the example project without segmentation Activity
Duration
Planned start
Planned finish
(2)
1 2 3 4 5
10 7 11 6 7
0 0 10 7 21
10 7 21 13 28
Precedence relations are introduced into the model as follows: define PRuk as a control variable for precedence relations, PRuk = 1 if activity (,] + k) has a precedence relationship with activity j on project segment i. Thus PSu+ k >~PFu
i=2
3 2 4 2 3
(1)
2. PD--project duration P D = PFnm - PSl l
i=1
(3)
Because most spreadsheets can handle dates, the evaluation can be performed with respect to a predefined calendar. Furthermore, by using the graphical capabilities of the spreadsheet, a Gantt chart can be generated. The project planner has the flexibility of determining the number of project segments and the length of the project segments. The shorter the segments the higher the scheduling flexibility and the complexity of planning. This flexibility, along with the model capability to evaluate the schedule associated with a given project plan, are key features of the proposed model. To demonstrate the proposed evaluation model, consider a project that consists of five activities (j = 1,2,3,4,5). The project is divided into three segments (i = 1,2,3). Activity durations and the precedence relations among the activities are summarized in Table 1. Applying Equations (1), (2) and (3) to the example's data, we get the results summarized in Table 2 (all units are weeks). The results in Table 2 indicate that the project segmentation approach, dividing the project into three segments, results in a project duration of 10 days. If segmentation is not used, the schedule for the project is as summarized in Table 3. Thus, the length of the project is reduced due to segmentation from 28 days into 10 days. A review of project planning practices in a major constructing company revealed that project segmentation is
widely used in practice, although no formal model exists to support it. The proposed model is designed to support the evaluation of alternative segmentation decisions considered by the project manager and to present the schedule resulting from the segmentation decisions made. Project control
The output of the planning phase is a feasible, acceptable project plan, along with the resulting schedule. This plan, once adopted for implementation is the baseline against which performances are measured to establish a project control system t2'13. To monitor progress in repetitive projects, a technique called the line of balance (LOB) was developed by the US Navy 2. LOB is based on a set of milestones that are common to all the repetitive projects in a programme. A delivery schedule is constructed and the date by which each milestone on each project has to be finished according to the delivery schedule is calculated. A variance (or difference) between the number of projects that completed each milestone, and the number scheduled to complete that milestone is calculated and serves as a basis for control. The deviation of actual progress from the original plan is the basis of the proposed control system for project segmentation. Unlike a statistical variance, this deviation (which is also called a variance) is a simple difference between the actual value of a parameter and its planned value f o r a particular time period. Three parameters are used in the analysis and the corresponding variances are calculated. The three variances are defined as follows: 17
Project segmentation: A Shtub Start variance:
Table 5
SVo, = 6 [ A S o - t] - 6 [ PS~j - t] for all ij and A S o
