CHAPTER 4 PROJECT SCHEDULING

Transcription

1 HPTR PROJT SHULING In chapter, the O and ON networks were presented, also the time and cost of individual activities based were calculated. Yet, however, we do not know how long is the total project duration. lso, we need to evaluate the early and late times at which activities start and finish. In addition, since real-life projects involve hundreds of activities, it is important to identify the group of critical activities so that special care is taken to make sure they are not delayed. ll these statements are the basic objectives of the scheduling process, which adds a time dimension to the planning process. In other words, we can briefly state that: Scheduling = Planning + Time. Scheduling is the determination of the timing of the activities comprising the project to enable managers to execute the project in a timely manner. The project scheduling id sued for: - Knowing the activities timing and the project completion time. - Having resources available on site in the correct time. - Making correction actions if schedule shows that the plan will result in late completion. - ssessing the value of penalties on project late completion. - etermining the project cash flow. - valuating the effect of change orders on the project completion time. - etermining the value pf project delay and the responsible parties. onstruction Management 7 r. mad lbeltagi

2 . The ritical Path Method The most widely used scheduling technique is the critical path method (PM) for scheduling. This method calculates the minimum completion time for a project along with the possible start and finish times for the project activities. Many texts and managers regard critical path scheduling as the only usable and practical scheduling procedure. omputer programs and algorithms for critical path scheduling are widely available and can efficiently handle projects with thousands of activities. The critical path itself represents the set or sequence of activities which will take the longest time to complete. The duration of the critical path is the sum of the activities' durations along the path. Thus, the critical path can be defined as the longest possible path through the "network" of project activities. The duration of the critical path represents the minimum time required to complete a project. ny delays along the critical path would imply that additional time would be required to complete the project. There may be more than one critical path among all the project activities, so completion of the entire project could be delayed by delaying activities along any one of the critical paths. For example, a project consisting of two activities performed in parallel that each requires three days would have each activity critical for a completion in three days. Formally, critical path scheduling assumes that a project has been divided into activities of fixed duration and well defined predecessor relationships. predecessor relationship implies that one activity must come before another in the schedule. The PM is a systematic scheduling method for a project network and involves four main steps: - forward path to determine activities early-start times; - backward path to determine activities late-finish times; - Float calculations; and - Identifying critical activities. onstruction Management 7 r. mad lbeltagi

3 . alculations for the ritical Path Method The inputs to network scheduling of any project are simply the O or the ON networks with the individual activity duration defined. The network scheduling process for O and ON networks, however, is different. To demonstrate these two techniques, let s consider a simple -activity project, with activity at the start, followed by three parallel activities,, and ; which are then succeeded by activity. The O or the ON networks of this example are presented in Figure.. etailed analysis of theses O or the ON networks are presented in the following subsections. It is noted that the example at hand involves only simple finish-to-start relationships among activities. () d () () () () d i ctivity (duration) j 7 (a - O) () () () () ctivity (uration) (b - ON) () Figure.: Network example.. ctivity-on-rrow Networks alculations The objective of arrow network analysis is to compute for each event in the network its early and late timings. These times are defined as: - arly event time (T) is the earliest time at which an event can occur, considering the duration of preceding activities. onstruction Management 7 r. mad lbeltagi

4 - Late event time (LT) is the latest time at which an event can occur if the project is to be completed on schedule. Forward Path The forward path determines the early-start times of activities. The forward path proceeds from the most left node in the network (node Figure.) and moves to the right, putting the calculations inside the shaded boxes to the left. ach node in the network, in fact, is a point at which some activities end (head arrows coming into the node), as shown in Figure.. That node is also a point at which some activities start (tail arrows of successor activities). ertainly, all successor activities can start only after the latest predecessor is finished. Therefore, for the forward path to determine the early-start (S) time of an activity, we have to look at the head arrows coming into the start node of the activity. We then have to set the activity S time as the latest finish time of all predecessors. () d () () () () d 7 Figure.: Preparation for the forward path Predecessor Successor Predecessor no. Predecessor Successor Figure.: node in an O network onstruction Management 77 r. mad lbeltagi

5 In this example, the forward path calculations are as follows: - Start at node, the first node of the project, and assign it an early-start time of zero. Here, all activity times use an end-of-day notation. Therefore, the S of activity is zero means that activity starts at end of day zero, or the beginning of day in the project. - Then, move to node. This node receives one head arrow, and as such, it has one predecessor, activity. Since the predecessor started on time zero and has days duration, then, it ends early at time (arly-finish (F) = arly-start (S) + d). ccordingly, the S time of all successor activities to node (activities,, and ) is time. This value is therefore, put in the shaded box on top of node, as shown in Figure.. += Project S+d=F start= += d += d= d += +=7 or 7 += += Figure.: Forward path calculations in O networks - Now, move forward to successor nodes, 7, and. However, since node is linked to nodes and by dummy activities, we begin with nodes and 7. Node receives one head arrow from its predecessor activity, we evaluate the F time of as (S () + d ()). Successor activities to node, therefore, can have an S time of. Similarly, the S time at node 7 is calculated as time. - Moving to node, the F times of its predecessors (d,, and d) are time, 7, and, respectively. ccordingly, the S time of successor activities is the largest onstruction Management 78 r. mad lbeltagi

6 value. Notice that only the largest F value of predecessor activities is used to calculate the S of successor activities and all other values not used. s such, only S values can be directly read from the calculations in Figure.. F values, on the other hand can be calculated as F = S + d. - The last node () receives one head arrow, activity which has an S value of. The F time of activity, therefore = + = time. Since node is the last node, the F of this node becomes the end of the project, reaching total project duration of days. Generally, for any activity x connecting between nodes i and j as shown in Figure., the calculations as follows: Ti LTi ` i x dx Tj LTj j Figure.: ctivity times Tj = Ti + dx (.) In case of more than one arrow terminating at node j, then consider the largest value. ccordingly, Sx = Ti (.) Fx = Sx +dx (.) ackward Path The backward path determines the late-finish (LF) times of activities by proceeding backward from the end node to the starting node of the O network. We put the LF values in the right side boxes adjacent to the nodes, as shown in Figure.. For the example at hand, we do the following: onstruction Management 7 r. mad lbeltagi

7 -= -=, -=, or -= -= d d -= LF-d=LS 7 -= Figure.: ackward path calculations in O networks - Start from the last node of the network (node ) and we transfer the early-finish value from the left box to be the late-finish (LF) value at the right side box. - Then, move backward to node which has only one tail arrow of activity. With the LF time of being time, its LS time becomes LS = LF - d = = time. t node, therefore, time becomes the LF time of the predecessor activities of this node. - Moving backward to predecessor nodes, and 7. Node has one tail arrow of the dummy activity d, and as such, the LF time value to be used at node becomes. Similarly, the LF time value of node 7 becomes. - Moving to node, we evaluate the LS time of its successor activities,, and as,, and, respectively. The LF time at node, therefore, becomes the smallest value. With other LS values not used, the values in the calculation boxes, as such, directly show the LF times of activities. LS times can be calculated as LS = LF d. - Now, proceed to the first node in the network (node ). It connects to one tail arrow of activity. The LS time of, therefore, is LS = LF d = =, a necessary check to ensure the correctness of the calculation. onstruction Management 8 r. mad lbeltagi

8 Having Figure. again in mind and to generalize the calculations, for any activity x connecting between nodes i and j, the calculations as follows: LTi = LTj - dx (.) In case of more than one arrow leaving node i, then consider the smallest value. ccordingly, LFx = LTj (.) LSx = LFx -dx (.) Float alculations Once forward path and backward path calculations are complete, it is possible to analyze the activity times. First, let's tabulate the information we have as shown in Table.. One important aspect is Total-Float (TF) calculations, which determine the flexibility of an activity to be delayed. Notice in Table. that some activities such as activity has S time = LS time, and its F time = LF time, indicating no slack time for the activity. Other activities such as can start early at time and late at time, indicating a -day of total float. Float calculations can be illustrated as shown in Figure.7 for any activity. Table.: PM results ctivity uration arly Start (S) Late Finish (LF) Late Start (LS) arly Finish (F) Total Float (TF) ritical ctivity Yes No 7 No Yes Yes Figure.7 shows two ways of scheduling each activity using its activity times. One way is to schedule it as early as possible (using its S time). The other way is as late as onstruction Management 8 r. mad lbeltagi

9 possible (using its LS time). The activity float can, therefore, be represented by the following relationships: Total Float (TF) = LF F (.7) = LS S (.8) i Name duration = d j T LT T LT S = Ti Tj LF = LTj a) ctivity is early S F=S+d Total Float d LF b) ctivity is late S Total Float LS=LF-d d d Free Float (FF) Total time available for the activity = LF - S LF Figure.7: Float calculations lso, with the S and LF times directly read from the boxes used in forward and backward path calculations, the total float can also be calculated as; TF = LF S d. Using these relationships, activities total floats are calculated as shown in Table.. nother type of float often used in network analysis is the Free Float, which can be calculated as: Free Float (FF) = Tj Ti d (.) or FF = smallest S (of succeeding activities) F (of current activity) (.) The free float defines the amount of time that an activity can be delayed without affecting any succeeding activity. With free float available for an activity, a project manager onstruction Management 8 r. mad lbeltagi

10 knows that the float can be used without changes the status of any non-critical activity to become critical. Identifying the ritical ctivities ctivities with zero total floats mean that they have to be constructed right at their schedule times, without delays. These activities are considered to be critical. They deserve the special attention of the project manager because any delay in critical activities causes a delay in the project duration. One interesting observation in the results of PM analysis is that critical activities form a continuous path of the critical activities that spans from the beginning to the end of the network. In our example, activities,, and (excluding dummy activities) are critical and the critical path is indicated by bold lines on Figure.. Notice that among the paths in this example (--; --; and --e), the critical path is the longest one, an important characteristic of the critical path. In real-life projects with many activities, it is possible that more than one critical path are formed. y definition, the length of these critical paths is the same... Precedence iagram Method (PM) Precedence iagram Method (PM) is the PM scheduling method used for ON networks and it follows the same four steps of the PM for O method. Forward Path Forward path can proceed from one activity to the other; the process is as follow (Figure.8): - t activity. It is the first activity in the network. We give it an early-start (S) of in the left top box. dding the activity duration, we determine the F time of the activity and we put it in the top right box. onstruction Management 8 r. mad lbeltagi

11 () () 7 (), 7, or () arly start alry Finish Name (duration) Late start Late finish () Figure.8: Forward Path in PM nalysis - Then, move forward to the succeeding activities,, and. These three activities have only as a predecessor with time as its F. s such, all the three activities can start as early as time (S = ). ach activity, accordingly, has its own F time based on its duration. - Moving forward to activity. This activity has predecessors ( head arrows) of activities,, and with their largest F time being. The S of activity, thus, with becomes time. dding its duration, the F becomes time. To generalize the calculations consider Figure., of two activities i and j with relationship finish to start and overlap between them. Overlaps will have a positive sign, while lags will have a negative sign. The forward path calculations are as follows: Si Fi i (di) LSi LFi overlap ij Sj Fj j (dj) LSj LFj Figure.: ctivities times in PM nalysis Sj = Fi - overlap ij (.) In case of more than one activity precedes activity j then consider the maximum. Then, apply quation. to calculate the early finish times. onstruction Management 8 r. mad lbeltagi

12 ackward Path Once the forward path is finished, the backward path can start, moving from the last activity to the first, putting the calculations in the bottom two boxes of each activity, as shown in Figure.. The process is as follows: () (),, or arly start arly Finish Name (duration) Late start Late finish 7 () () () Figure.: ackward path in PM analysis - Start at the last activity and we transfer the early-finish value to become the activity's late-finish (LF) time. Then, subtracting the activity's own duration, the latestart (LS) time is calculated as time and put in the bottom left box of the activity. - Moving backward to activities,, and all have one successor (activity ) with LS time of. The LF of all these activities becomes time. ach activity then has its own LS time, as shown in Figure.. - Moving to activity. The activity is linked to tail arrows (i.e., has successors) of activities,, and. The LF of activity, thus, is the smallest of its successors' LS times, or time. ctivity then has LS equals zero. onsidering Figure. again, the backward path calculations are as follows: LFi = LSj + overlap ij (.) onstruction Management 8 r. mad lbeltagi

13 In case of more than one activity succeeds activity j then consider the minimum. Then, apply quation. to calculate the late start times. Notice that by the end of the backward path, all activity times can be read directly from the boxes of information on the activity, without additional calculations. This also, makes it simple to calculate the total float of each activity using the same relationships used in the O analysis. Identifying ritical ctivities ritical activities can also be easily determined as the ones having zero float times, activities,, and. The critical path is then shown in bold as Figure.. The PM analysis, as explained, is a straight forward process in which each activity is considered as an entity that stores its own information.. Time-Scaled iagrams Time-scaled diagrams are used extensively in the construction industry. Such diagrams enable one to determine immediately which activities are scheduled to proceed at any point in time and to monitor field progress. lso, it can be used to determine resources need. The time scale used in time-scaled diagrams can be either the calendar dates or the working periods (ordinary dates), or using both at the same time. The activities are represented as arrows that drawn to scale to reflect the activity duration it represents. The horizontal dashed lines represent total float for groups of activities and free float for the immediate activity to the left of the dashed line. The precedence of an activity is the immediate activities before it or that linked to it through vertical dashed lines. The name and the duration of an activity are written above and below the arrow representing it respectively (Figure.). The S, F, and FF times of the activities can be easily read directly from the diagram. The TF for an activity is the smallest sum of succeeding FF on all paths. ccordingly, the LS and LF times can be easily calculated as follows: onstruction Management 8 r. mad lbeltagi

14 LSi = Si + TFi (.) LFi = LSi + i (.) The critical path can be easily determined as the continuous lines from the beginning to the end of the network with any dashed lines. The main advantage of this diagram is its simple representation and it can be sued directly for determining resources need. However, its disadvantage is that it needs a great effort to be modified or updated. lso, it cannot be used to represent overlapping activities. Figure. shows the time-scaled diagram for the same -activities project solved previously using O and ON networks. 7 8 Figure.: Time-scaled diagram The TF for activity equals the smallest of the sum of the floats along all paths from the end of activity to the end of the project. The float on path =, path = and path =, then the TF of activity =. The calculations are shown in Table.. Table. Time-scaled diagram calculations ctivity S F FF TF LF=F+TF LS=LF-d 7 onstruction Management 87 r. mad lbeltagi

15 . Schedule Presentation fter the O and ON calculations are made, it is important to present their results in a format that is clear and understandable to all the parties involved in the project. The simplest form is the ar chart or Gantt chart, named after the person who first used it. bar chart is a time versus activity chart in which activities are plotted using their early or late times, as shown in Figures. a and b. arly bar chart is drawn using the S times of activities, while the late bar chart is drawn using the LS times. a) ctivity d= S = d= TF= S= d= TF= S= d= S= S= d= 7 8 Time ctivity b) d= LF= TF= d= TF= d= d= LF= LF= LF= d= LF= 7 8 Time Figure.: a) arly bar chat b) Late bar chart The bar chart representation, in fact, shows various details. Float times of activities, critical activities can be shown in a different color, or bold borders, as shown in Figure.. The bar chart can also be used for accumulating total daily resources and / or costs, as shown at the bottom part of Figure.. In this figure, the numbers on each activity represent the number of labors needed. onstruction Management 88 r. mad lbeltagi

16 ctivity 7 8 Time Profile of the labor resource demand Total labors Figure.: Using bar chart to accumulate resources One additional benefit of the bar chart is its use on site to plot and compare the actual progress in the various activities to their scheduled times. n example is shown on Figure., showing actual bars plotted at the bottom of the original bars of the schedule.. riticisms to Network Techniques The PM and PM analyses for network scheduling provide very important information that can be used to bring the project to success. oth methods, however, share some drawbacks that require special attention from the project manager. These drawbacks are: - ssume all required resources are available: The PM calculations do not incorporate resources into their formulation. lso, as they deal with activity durations only, it can result in large resource fluctuations. ealing with limited resources and resource leveling, therefore, has to be done separately after the analysis; onstruction Management 8 r. mad lbeltagi

17 - Ignore project deadline: The formulations of PM and PM methods do not incorporate a deadline duration to constrain project duration; - Ignore project costs: Since PM and PM methods deal mainly with activities durations, they do not deal with any aspects related to minimize project cost; - Use deterministic durations: The basic assumption in PM and PM formulations is that activity durations are deterministic. In reality, however, activity durations take certain probability distribution that reflect the effect of project conditions on resource productivity and the level of uncertainty involved in the project.. Solved xamples.. xample For the project data in Table., answer the following questions: a) raw an O network of the project? b) Perform forward path and backward path calculations? c) What is the effect of delaying activity by days? Table.: ata for xample ctivity F G uration Immediate predecessor -,, F onstruction Management r. mad lbeltagi

18 Solution a, b) or or or 8 G F ritical or c) Total float of activity = LF S d = 8 =. Then delaying activity by day more than its total float will cause a net delay in the whole project by day to become 7 days... xample Perform PM calculations for the small project below and determine activity times. urations are shown on the activities. I () () () G () () J (7) L () () () H () F () K () onstruction Management r. mad lbeltagi

19 Solution 7 I () () or () () 7 () () 7 7 G () 7 or 7 H () 7 or 8 or 7 J (7) 7 or or L () S F Name (duration) LS LF F () 8 K () ritical path.. xample For the activities listed in the table below, draw the time-scaled diagram and mark the critical path. etermine the completion time for the project. Tabulate activities times and floats. ctivity uration Predecessor F G H I J ,, F, G - G, I onstruction Management r. mad lbeltagi

20 Solution H 8 F G 8 I J 7 7 ctivity S F TF FF LS LF F G H I J xample Perform PM calculations for the small on network shown here. Pay special attention to the different relationships and the lag times shown on them. SS= () () () () () FF= onstruction Management r. mad lbeltagi

21 Solution () S Name (duration) LS SS= or or (-+) F LF += () 7 7 () 7 () -=, 7 or (+-) 7 () 7 FF=.7 xercises. The free float is defined as: a. The amount of time an activity can be delayed without affecting the following activity. b. The amount of time an activity can be delayed without affecting total project duration.. Total float equals: a. Late finish minus early finish c. Late start minus early start b. Late finish minus (early start + duration) d. ll of the above. State True (T) or False (F): a. The critical activities can be determined easily when using the bar chart. b. The network must have definite points of beginning and end. c. The network must be continuous from start to end. d. There s no dummy activities in the arrow networks, e. forward pass is used to determine late start and late finish times. onstruction Management r. mad lbeltagi

22 f. The time for completing a project is equal to the sum of the individual activity times.. For the Following project data, answer the following questions: ctivity uration (days) Predecessor F G --,, F a. raw an O network and perform forward and backward pass calculations? b. raw an ON network and perform forward and backward pass calculations? c. raw a time-scaled diagram of the project? d. Tabulate activities S, F, LS, LF, TF, and FF. e. What is the effect of delaying activity by days?. For the following O network, determine the following: a. alculate S, LF, & TF for all activities. Identify critical ones. b. raw an early ar hart for the project. c. What is the effect of delaying activity H by two days on the total project duration? () 7 7 onstruction Management r. mad lbeltagi

23 . Perform PM calculations for the project below and determine activity times. urations are shown on the activities I () () () G () () J (7) L () () () H () F () K () 7. gas station is proposed to be built on an already developed site. It will consist essentially of a sales outlet and an office block. The sales outlet comprises of cash office and gas pumps. The manager s office building, which also houses public washrooms and an air compressor, is called the office block. djacent to pumps will be a concrete pit that will house the gas tanks. The entire area, excluding the office and pumps site, is covered with a concrete slab, and there is a low perimeter wall in the rear. The utility company has undertaken to install an electric meter on the site and connect it to the mains. Gasoline pumps must be obtained from the manufacturers, and after being installed, they are to be connected to the gasoline tanks and the power supply. efore use the local authority to ensure safety and compliance with regulations must inspect them. Gasoline tanks are housed in concrete pits and covered by concrete slabs. efore they are covered, however, the tanks and the associated pipe work have to be inspected by the local authority. The sales outlet base is excavated first, the pipe work and tanks second, the office block third, and the onstruction Management r. mad lbeltagi

24 trench for underground services last. fter the excavation for the tanks and pipe work is completed, work can proceed on the construction of the perimeter wall and air points. No ctivity escription uration F G H I J K L M N O P Q R S T U V W X Y Z FF xcavate for sales outlet onstruct sales outlet base onstruct cash office Obtain pumps Install pumps onnect pumps Inspector approves pumps installation Paint & furnish office & washrooms onnect office & toilet lighting xcavate for office block onstruct office block uild office & washrooms + services Install electric meter onnect main cable to meter Install area lighting Mobilize site Set out and level site xcavate & lay underground services xcavate for pipes and tanks onstruct concrete pit Obtain pipes and tanks Install pipes and tanks Obtain compressor Install compressor onnect power to compressor Inspection of compressor ackfill and cover tanks Pour concrete slab onstruct perimeter wall + air points onnect air points emobilize and clean site Inspection of pipes and tanks onstruction Management 7 r. mad lbeltagi

25 ompressed air for inflated tires will be supplied by an electrically driven compressor, which must be inspected by a competent person before the compressor is put into use. The air lines to the free air points are installed with the general underground services, and the points themselves are mounted on the perimeter wall. The air pints can be hooked up after the concrete slab has been poured. Mobilization to start work comprises, among other preparations, the moving of a trailer to the site to store tools, furnishings, and any weather prone parts and to serve as the site office. Similarly, when work at the site is completed, the trailer will be removed, and all scaffolding and construction equipment taken away. This is known as demobilization and clean up of site. You are required to determine the project duration, critical path(s), and tabulate activity times (S, F, LS, LF, TF, and FF). 8. For the following list of activities, draw a time-scaled diagram and mark the critical path. etermine activities S, F, LS, LF, FF, and TF. ctivity uration (days) Predecessor F G H I J K L M --,, F,, G, H I J K, L onstruction Management 8 r. mad lbeltagi

26 . For the following PM, perform the forward pass and backward pass calculations. etermine the project duration and critical path. Tabulate the S, F, LS, LF, TF, and FF information for each activity. 7 FF7 SS, FF 8 SS FF F SS8 G SF 8 SS8 J FS H FF I 8 onstruction Management r. mad lbeltagi