Chapter 4 Project Scheduling
CHAPTER 4PROJECT SCHEDULINGIn chapter 3, the AOA and AON networks were presented, also the time and cost ofindividual activities based were calculated. Yet, however, we do not know how long isthe total project duration. Also, we need to evaluate the early and late times at whichactivities start and finish. In addition, since real-life projects involve hundreds ofactivities, it is important to identify the group of critical activities so that special care istaken to make sure they are not delayed. All these statements are the basic objectives ofthe scheduling process, which adds a time dimension to the planning process. In otherwords, we can briefly state that: Scheduling Planning Time.Scheduling is the determination of the timing of the activities comprising the project toenable managers to execute the project in a timely manner. The project scheduling idsued 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 latecompletion.-Assessing the value of penalties on project late completion.-Determining the project cash flow.-Evaluating the effect of change orders on the project completion time.-Determining the value pf project delay and the responsible parties.Construction Management74Dr. Emad Elbeltagi
4.1The Critical Path MethodThe most widely used scheduling technique is the critical path method (CPM) forscheduling. This method calculates the minimum completion time for a project alongwith the possible start and finish times for the project activities. Many texts and managersregard critical path scheduling as the only usable and practical scheduling procedure.Computer programs and algorithms for critical path scheduling are widely available andcan efficiently handle projects with thousands of activities.The critical path itself represents the set or sequence of activities which will take thelongest 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 possiblepath through the "network" of project activities. The duration of the critical pathrepresents the minimum time required to complete a project. Any delays along the criticalpath 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 completionof the entire project could be delayed by delaying activities along any one of the criticalpaths. For example, a project consisting of two activities performed in parallel that eachrequires 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 activitiesof fixed duration and well defined predecessor relationships. A predecessor relationshipimplies that one activity must come before another in the schedule.The CPM is a systematic scheduling method for a project network and involves four mainsteps:-A forward path to determine activities early-start times;-A backward path to determine activities late-finish times;-Float calculations; and-Identifying critical activities.Construction Management75Dr. Emad Elbeltagi
4.2Calculations for the Critical Path MethodThe inputs to network scheduling of any project are simply the AOA or the AONnetworks with the individual activity duration defined. The network scheduling processfor AOA and AON networks, however, is different. To demonstrate these two techniques,let’s consider a simple 5-activity project, with activity A at the start, followed by threeparallel activities B, C, and D; which are then succeeded by activity E. The AOA or theAON networks of this example are presented in Figure 4.1. Detailed analysis of thesesAOA or the AON networks are presented in the following subsections. It is noted that theexample at hand involves only simple finish-to-start relationships among activities.5B (3)A (3)1d1C (4)3D (6)iActivity (duration)9E (5)11d27j(a - AOA)B(3)A(3)Activity(Duration)C(4)D(6)E(5)(b - AON)Figure 4.1: Network example4.2.1 Activity-On-Arrow Networks CalculationsThe objective of arrow network analysis is to compute for each event in the network itsearly and late timings. These times are defined as:-Early event time (ET) is the earliest time at which an event can occur, consideringthe duration of preceding activities.Construction Management76Dr. Emad Elbeltagi
-Late event time (LT) is the latest time at which an event can occur if the project isto be completed on schedule.Forward PathThe forward path determines the early-start times of activities. The forward path proceedsfrom the most left node in the network (node 1 – Figure 4.2) and moves to the right,putting the calculations inside the shaded boxes to the left.Each node in the network, in fact, is a point at which some activities end (head arrowscoming into the node), as shown in Figure 4.3. That node is also a point at which someactivities start (tail arrows of successor activities). Certainly, all successor activities canstart only after the latest predecessor is finished. Therefore, for the forward path todetermine the early-start (ES) time of an activity, we have to look at the head arrowscoming into the start node of the activity. We then have to set the activity ES time as thelatest finish time of all predecessors.5B (3)1A (3)d1C (4)3D (6)E (5)911d27Figure 4.2: Preparation for the forward pathPredecessor 1Successor 1Predecessor 2no.Predecessor 3Successor 2Figure 4.3: A node in an AOA networkConstruction Management77Dr. Emad Elbeltagi
In this example, the forward path calculations are as follows:-Start at node 1, 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 ES of activity A iszero means that activity starts at end of day zero, or the beginning of day 1 in theproject.-Then, move to node 3. This node receives one head arrow, and as such, it has onepredecessor, activity A. Since the predecessor started on time zero and has 3 daysduration, then, it ends early at time 3 (Early-Finish (EF) Early-Start (ES) d).Accordingly, the ES time of all successor activities to node 3 (activities B, C, and D)is time 3. This value is therefore, put in the shaded box on top of node 3, as shown inFigure 4.4.63 3 6ES d EF0 3 3Projectstart 0031Ad 35B3d1C43D614E9d279959 5 14116 0 63 4 7 or9 0 93 6 9Figure 4.4: Forward path calculations in AOA networks-Now, move forward to successor nodes 5, 7, and 9. However, since node 9 is linkedto nodes 5 and 9 by dummy activities, we begin with nodes 5 and 7. Node 5 receivesone head arrow from its predecessor activity B, we evaluate the EF time of B as 6 (ES(3) d (3)). Successor activities to node 5, therefore, can have an ES time of 6.Similarly, the ES time at node 7 is calculated as time 9.-Moving to node 9, the EF times of its 3 predecessors (d1, C, and d2) are time 6, 7,and 9, respectively. Accordingly, the ES time of successor activities is the largestConstruction Management78Dr. Emad Elbeltagi
value 9. Notice that only the largest EF value of predecessor activities is used tocalculate the ES of successor activities and all other values not used. As such, onlyES values can be directly read from the calculations in Figure 4.4. EF values, on theother hand can be calculated as EF ES d.-The last node (11) receives one head arrow, activity E which has an ES value of 9.The EF time of activity E, therefore 9 5 time 14. Since node 11 is the last node,the EF of this node becomes the end of the project, reaching total project duration of14 days.Generally, for any activity x connecting between nodes i and j as shown in Figure 4.5, thecalculations as follows:ETj LTjETi LTi ixdxjFigure 4.5: Activity timesETj ETi dx(4.1)In case of more than one arrow terminating at node j, then consider the largest value.Accordingly,ESx ETi(4.2)EFx ESx dx(4.3)Backward PathThe backward path determines the late-finish (LF) times of activities by proceedingbackward from the end node to the starting node of the AOA network. We put the LFvalues in the right side boxes adjacent to the nodes, as shown in Figure 4.6. For theexample at hand, we do the following:Construction Management79Dr. Emad Elbeltagi
69-3 6,9-4 5, or9-6 33-3 0030A31399-0 95B3d1C4314 14E9Dd29951114-5 9LF-d LS67999-0 9Figure 4.6: Backward path calculations in AOA networks-Start from the last node of the network (node 11) and we transfer the early-finishvalue from the left box to be the late-finish (LF) value at the right side box.-Then, move backward to node 9 which has only one tail arrow of activity E. With theLF time of E being time 14, its LS time becomes LS LF - d 14 – 5 time 9. Atnode 9, therefore, time 9 becomes the LF time of the predecessor activities of thisnode.-Moving backward to predecessor nodes 5, and 7. Node 5 has one tail arrow of thedummy activity d1, and as such, the LF time value to be used at node 5 becomes 9.Similarly, the LF time value of node 7 becomes 9.-Moving to node 3, we evaluate the LS time of its 3 successor activities B, C, and D as6, 5, and 3, respectively. The LF time at node 3, therefore, becomes the smallest value3. With other LS values not used, the values in the calculation boxes, as such, directlyshow the LF times of activities. LS times can be calculated as LS LF – d.-Now, proceed to the first node in the network (node 1). It connects to one tail arrowof activity A. The LS time of A, therefore, is LS LF – d 3 – 3 0, a necessarycheck to ensure the correctness of the calculation.Construction Management80Dr. Emad Elbeltagi
Having Figure 4.5 again in mind and to generalize the calculations, for any activity xconnecting between nodes i and j, the calculations as follows:LTi LTj - dx(4.4)In case of more than one arrow leaving node i, then consider the smallest value.Accordingly, LFx LTj(4.5)LSx LFx -dx(4.6)Float CalculationsOnce forward path and backward path calculations are complete, it is possible to analyzethe activity times. First, let's tabulate the information we have as shown in Table 4.1. Oneimportant aspect is Total-Float (TF) calculations, which determine the flexibility of anactivity to be delayed. Notice in Table 4.1 that some activities such as activity A has EStime LS time, and its EF time LF time, indicating no slack time for the activity. Otheractivities such as B can start early at time 3 and late at time 6, indicating a 3-day of totalfloat. Float calculations can be illustrated as shown in Figure 4.7 for any activity.Table 4.1: CPM resultsActivity DurationEarly Start(ES)Late Finish(LF)Late Start(LS)Early Finish(EF)Total 2NoD639390YesE59149140YesFigure 4.7 shows two ways of scheduling each activity using its activity times. One wayis to schedule it as early as possible (using its ES time). The other way is as late asConstruction Management81Dr. Emad Elbeltagi
possible (using its LS time). The activity float can, therefore, be represented by thefollowing relationships:Total Float (TF) LF – EF(4.7) LS – ES(4.8)Nameduration dijET LTET LTES ETia) Activity is earlyb) Activity is lateETjESEF ES dLF LTjTotal FloatdLFESTotal FloatLS LF-dddLFFree Float (FF)Total time available for the activity LF - ESFigure 4.7: Float calculationsAlso, with the ES and LF times directly read from the boxes used in forward andbackward path calculations, the total float can also be calculated as; TF LF – ES – d.Using these relationships, activities total floats are calculated as shown in Table 4.1.Another type of float often used in network analysis is the Free Float, which can becalculated as:Free Float (FF) ETj – ETi – d(4.9)or FF smallest ES (of succeeding activities) – EF (of current activity)(4.10)The free float defines the amount of time that an activity can be delayed without affectingany succeeding activity. With free float available for an activity, a project managerConstruction Management82Dr. Emad Elbeltagi
knows that the float can be used without changes the status of any non-critical activity tobecome critical.Identifying the Critical ActivitiesActivities with zero total floats mean that they have to be constructed right at theirschedule times, without delays. These activities are considered to be critical. Theydeserve the special attention of the project manager because any delay in criticalactivities causes a delay in the project duration.One interesting observation in the results of CPM analysis is that critical activities form acontinuous path of the critical activities that spans from the beginning to the end of thenetwork. In our example, activities A, D, and E (excluding dummy activities) are criticaland the critical path is indicated by bold lines on Figure 4.6. Notice that among the 3paths in this example (A-B-E; A-C-E; and A-D-e), the critical path is the longest one, animportant characteristic of the critical path. In real-life projects with many activities, it ispossible that more than one critical path are formed. By definition, the length of thesecritical paths is the same.4.2.2 Precedence Diagram Method (PDM)Precedence Diagram Method (PDM) is the CPM scheduling method used for AONnetworks and it follows the same four steps of the CPM for AOA method.Forward PathForward path can proceed from one activity to the other; the process is as follow (Figure4.8):-At activity A. It is the first activity in the network. We give it an early-start (ES) of 0in the left top box. Adding the activity duration, we determine the EF time of theactivity and we put it in the top right box.Construction Management83Dr. Emad Elbeltagi
36B (3)6, 7, or 903A (3)914E (5)39D (6)Early start Ealry FinishName (duration)Late start37C (4)Late finishFigure 4.8: Forward Path in PDM Analysis-Then, move forward to the succeeding activities B, C, and D. These three activitieshave only A as a predecessor with time 3 as its EF. As such, all the three activitiescan start as early as time 3 (ES 3). Each activity, accordingly, has its own EF timebased on its duration.-Moving forward to activity E. This activity has 3 predecessors (3 head arrows) ofactivities B, C, and D with their largest EF time being 9. The ES of activity E, thus,with becomes time 9. Adding its duration, the EF becomes time 14.To generalize the calculations consider Figure 4.9, of two activities i and j withrelationship 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:ESi EFii (di)LSi LFioverlapijESj EFjj (dj)LSj LFjFigure 4.9: Activities times in PDM AnalysisESj EFi - overlapij(4.11)In case of more than one activity precedes activity j then consider the maximum. Then,apply Equation 4.3 to calculate the early finish times.Construction Management84Dr. Emad Elbeltagi
Backward PathOnce the forward path is finished, the backward path can start, moving from the lastactivity to the first, putting the calculations in the bottom two boxes of each activity, asshown in Figure 4.10. The process is as follows:36B (3)6903A (3)0337C (4)59914E (5)9146, 5, or 339D (6)39Early start Early FinishName (duration)Late startLate finishFigure 4.10: Backward path in PDM analysis-Start at the last activity E and we transfer the early-finish value to become theactivity's late-finish (LF) time. Then, subtracting the activity's own duration, the latestart (LS) time is calculated as time 9 and put in the bottom left box of the activity.-Moving backward to activities B, C, and D all have one successor (activity E) withLS time of 9. The LF of all these activities becomes time 9. Each activity then has itsown LS time, as shown in Figure 4.10.-Moving to activity A. The activity is linked to 3 tail arrows (i.e., has 3 successors) ofactivities B, C, and D. The LF of activity A, thus, is the smallest of its successors' LStimes, or time 3. Activity A then has LS equals zero.Considering Figure 3.9 again, the backward path calculations are as follows:(4.12)LFi LSj overlapijConstruction Management85Dr. Emad Elbeltagi
In case of more than one activity succeeds activity j then consider the minimum. Then,apply Equation 4.6 to calculate the late start times.Notice that by the end of the backward path, all activity times can be read directly fromthe boxes of information on the activity, without additional calculations. This also, makesit simple to calculate the total float of each activity using the same relationships used inthe AOA analysis.Identifying Critical ActivitiesCritical activities can also be easily determined as the ones having zero float times,activities A, D, and E. The critical path is then shown in bold as Figure 4.10. The PDManalysis, as explained, is a straight forward process in which each activity is consideredas an entity that stores its own information.4.3Time-Scaled DiagramsTime-scaled diagrams are used extensively in the construction industry. Such diagramsenable one to determine immediately which activities are scheduled to proceed at anypoint in time and to monitor field progress. Also, it can be used to determine resourcesneed. The time scale used in time-scaled diagrams can be either the calendar dates or theworking periods (ordinary dates), or using both at the same time.The activities are represented as arrows that drawn to scale to reflect the activity durationit represents. The horizontal dashed lines represent total float for groups of activities andfree float for the immediate activity to the left of the dashed line. The precedence of anactivity is the immediate activities before it or that linked to it through vertical dashedlines. The name and the duration of an activity are written above and below the arrowrepresenting it respectively (Figure 4.11). The ES, EF, and FF times of the activities canbe easily read directly from the diagram. The TF for an activity is the smallest sum ofsucceeding FF on all paths. Accordingly, the LS and LF times can be easily calculated asfollows:Construction Management86Dr. Emad Elbeltagi
LSi ESi TFi(4.13)LFi LSi Di(3.14)The critical path can be easily determined as the continuous lines from the beginning tothe end of the network with any dashed lines. The main advantage of this diagram is itssimple 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. Also,it cannot be used to represent overlapping activities. Figure 4.11 shows the time-scaleddiagram for the same 5-activities project solved previously using AOA and AONnetworks.1234567891011121314BACDFigure 4.11: Time-scaled diagramThe TF for activity A equals the smallest of the sum of the floats along all paths from theend of activity A to the end of the project. The float on path ABE 3, path ACE 2 andpath ADE 0, then the TF of activity A 0. The calculations are shown in Table 3.2.Table 4.2 Time-scaled diagram calculationsActivityESEFFFTFLF EF TFLS ion Management87Dr. Emad Elbeltagi
4.4Schedule PresentationAfter the AOA and AON calculations are made, it is important to present their results in aformat that is clear and understandable to all the parties involved in the project. Thesimplest form is the Bar chart or Gantt chart, named after the person who first used it. Abar chart is a time versus activity chart in which activities are plotted using their early orlate times, as shown in Figures 4.12 a and b. Early bar chart is drawn using the ES timesof activities, while the late bar chart is drawn using the LS times.ActivityAa)d 3ES 0d 3BES 3CES 3DES 3TF 3d 4TF 2d 6d 5ES 9E012345678910 1112 1314 TimeActivityd 3ALF 3TF 3Bb)d 3LF 9TF 2Cd 4LF 9d 6DLF 9d 5ELF 140123456Figure 4.12: a) Early bar chat789101112 1314 Timeb) Late bar chartThe 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 Figure4.12. The bar chart can also be used for accumulating total daily resources and / or costs,as shown at the bottom part of Figure 4.13. In this figure, the numbers on each activityrepresent the number of labors needed.Construction Management88Dr. Emad Elbeltagi
ActivityA0122234567893310111213 14Time2BCD222111133331E111166Profile of the laborresource demand54433221222666433111111Total laborsFigure 4.13: Using bar chart to accumulate resourcesOne additional benefit of the bar chart is its use on site to plot and compare the actualprogress in the various activities to their scheduled times. An example is shown on Figure4.13, showing actual bars plotted at the bottom of the original bars of the schedule.4.5Criticisms to Network TechniquesThe CPM and PDM analyses for network scheduling provide very important informationthat can be used to bring the project to success. Both methods, however, share somedrawbacks that require special attention from the project manager. These drawbacks are:-Assume all required resources are available: The CPM calculations do not incorporateresources into their formulation. Also, as they deal with activity durations only, it canresult in large resource fluctuations. Dealing with limited resources and resourceleveling, therefore, has to be done separately after the analysis;Construction Management89Dr. Emad Elbeltagi
-Ignore project deadline: The formulations of CPM and PDM methods do notincorporate a deadline duration to constrain project duration;-Ignore project costs: Since CPM and PDM methods deal mainly with activitiesdurations, they do not deal with any aspects related to minimize project cost;-Use deterministic durations: The basic assumption in CPM and PDM formulations isthat activity durations are deterministic. In reality, however, activity durations takecertain probability distribution that reflect the effect of project conditions on resourceproductivity and the level of uncertainty involved in the project.4.6Solved Examples4.6.1 Example 1For the project data in Table 4.3, answer the following questions:a) Draw an AOA network of the project?b) Perform forward path and backward path calculations?c) What is the effect of delaying activity D by 3 days?Table 4.3: Data for Example 2AABBC, DE, FConstruction Management90Dr. Emad Elbeltagi
Solutiona, b)8012A28 or1032 or80814 orE 1214 14B266D 12C3G26F 349 or5Critical516 16911c) Total float of activity D LF – ES – d 11 – 8 – 1 2.Then delaying activity D by 1 day more than its total float will cause a net delay inthe whole project by 1 day to become 17 days.4.6.2 Example 2Perform PDM calculations for the small project below and determine activity times.Durations are shown on the )Construction ManagementL(2)K(4)91Dr. Emad Elbeltagi
Solution79I (2)12155B (4)1066D (1)557G (1)6679 or9 or1412 or717A (1)01414J (7)17141416L (2)14161 or 6122C (1)6445H (1)910E (2)7797 or 8ESEF5 or 4248F (2)10Name (duration)LSLF59K (4)1014Critical path4.6.3 Example 3For the activities listed in the table below, draw the time-scaled diagram and mark thecritical path. Determine the completion time for the project. Tabulate activities times 5AF2B, EG8C, FH5D, GI17-J10G, IConstruction Management92Dr. Emad Elbeltagi
Solution1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 416G1624001624H2429552934I01777724J24340024344.6.4 Example 4Perform PDM calculations for the small AoN network shown here. Pay special attentionto the different relationships and the lag times shown on them.SS 2A(3)B(3)C(4)E(5)D(6)Construction ManagementFF 293Dr. Emad Elbeltagi
Solution0 2 225B (3)SS 2475, 7 or(9 2-5)033A (3)034 or3 or(4-2 3)ESEF34.779D (6)410712E (5)7123Name (duration)LS7C (4)FF 212-2 10LFExercises1. The free float is defined as:a. The amount of time an activity can be delayed without affecting the followingactivity.b. The amount of time an activity can be delayed without affecting total projectduration.2. Total float equals:a. Late finish minus early finishc. Late start minus early startb. Late finish minus (early start duration)d. All of the above3. 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. A forward pass is used to determine late start and late finish times.Construction Management94Dr. Emad Elbeltagi
f. The time for completing a project is equal to the sum of the individual activitytimes.4. For the Following project data, answer the following questions:ActivityDuration (days)PredecessorA2--B6AC3AD1BE6BF3C, DG2E, Fa. Draw an AOA network and perform forward and backward pass calculations?b. Draw an AON network and perform forward and backward pass calculations?c. Draw a time-scaled diagram of the project?d. Tabulate activities ES, EF, LS, LF, TF, and FF.e. What is the effect of delaying activity D by 3 days?5. For the following AOA network, determine the following:a. Calculate ES, LF, & TF for all activities. Identify critical ones.b. Draw an early Bar Chart for the project.c. What is the effect of delaying activity “H” by two days on the total projectduration?3159E (10)1517137Construction Management1195Dr. Emad Elbeltagi
6. Perform PDM calculations for the project below and determine activity times.Durations are shown on the F(2)K(4)7. A gas station is proposed to be built on an already developed site. It will consistessentially of a sales outlet and an office block. The sales outlet comprises of cashoffice and gas pumps. The manager’s office building, which also houses publicwashrooms and an air compressor, is called the office block. Adjacent to pumpswill be a concrete pit that will house the gas tanks.The entire area, excluding the office and pumps site, is covered with a concreteslab, and there is a low perimeter wall in the rear. The utility company hasundertaken to install an electric meter on the site and connect it to the mains.Gasoline pumps must be obtained from the manufacturers, and after beinginstalled, they are to be connected to the gasoline tanks and the power supply.Before use the local authority to ensure safety and compliance with regulationsmust inspect them. Gasoline tanks are housed in concrete pits and covered byconcrete slabs. Before they are covered, however, the tanks and the associatedpipe work have to be inspected by the local authority. The sales outlet base isexcavated first, the pipe work and tanks second, the office block third, and theConstruction Management96Dr. Emad Elbeltagi
trench for underground services last. After the excavation for the tanks and pipework is completed, work can proceed on the construction of the perimeter walland air ivity DescriptionExcavate for sales outletConstruct sales outlet baseConstruct cash officeObtain pumpsInstall pumpsConnect pumpsInspector approves pumps installationPaint & furnish office & washroomsConnect office & toilet lightingExcavate for office blockConstruct office blockBuild office & washrooms servicesInstall electric meterConnect main cable to meterInstall area lightingMobilize siteSet out and level siteExcavate & lay underground servicesExcavate for pipes and tanksConstruct concrete pitObtain pipes and tanksInstall pipes and tanksObtain compressorInstall compressorConnect power to compressorInspection of compressorBackfill and cover tanksPour concrete slabConstruct perimeter wall air pointsConnect air pointsDemobilize and clean siteInspection of pipes and tanksConstruction 122112Dr. Emad Elbeltagi
Compressed air for inflated tires will be supplied by an electrically drivencompressor, which must be inspected by a competent person before thecompressor is put into use. The air lines to the “free air” points are installed withthe general underground services, and the points themselves are mounted on theperimeter wall. The air pints can be hooked up after the concrete slab has beenpoured. Mobilization to start work comprises, among other preparations, themoving of a trailer to the site to store tools, furnishings, and any weather proneparts 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 takenaway. This is known as “demobilization and clean up of site.You are required to determine the project duration, critical path(s), and tabulateactivity times (ES, EF, LS, LF, TF, and FF).8. For the following list of activities, draw a time-scaled diagram and mark thecritical path. Determine activities ES, EF, LS, LF, FF, and TF.ActivityConstruction ManagementDuration (days)PredecessorA4--B10AC2AD6CE15B, DF4B, DG3FH2B, DI1E, G, HJ3IK2EL1JM2K, L98Dr. Emad Elbeltagi
9. For the following PDM, perform the forward pass and backward passcalculations. Determine the project duration and critical path. Tabulate the ES,EF, LS, LF, TF, and FF information for each activity.E7A10SS3, n ManagementJ099FF3I8Dr. Emad Elbeltagi
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:
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
Production scheduling methods can be further classified as static scheduling and dynamic scheduling. Static operation scheduling is performed during the compilation of the application. Once an acceptable scheduling solution is found, it is deployed as part of the application image. In dynamic scheduling, a dedicated system component makes
application to the occurrences of the observed scheduling problems. Keywords: scheduling; class-scheduling; collaborative scheduling; web-based scheduling . 1. Introduction . Academic institutions and universities often find difficulties in scheduling classes [1]. This difficult task is devoted with hefty amount of time, human, and material .
scheduling, focusing on scheduling problems that increased in complexity based on the number of activities to be scheduled and the number of planning constraints. Nine non-expert planners were recruited to complete scheduling tasks using Playbook, a scheduling software. The results of this pilot study show that scheduling
Apr 10, 2014 · Operating System Concepts! 6.1! Silberschatz, Galvin and Gagne 2002 Chapter 5: CPU Scheduling! Basic Concepts! Scheduling Criteria ! Scheduling Algorithms! Multiple-Processor Scheduling! Real-Time Scheduling! Algorithm Evaluation!
cepté la motion du 18 février 2003 (03.3007 - Recherche sur l’être humain. Création d’une base constitutionnelle), la chargeant de préparer une disposition constitutionnelle concernant la re- cherche sur l’être humain. Pour sa part, la mise en chantier de la loi fédérale relative à la recher-che sur l’être humain a démarré en décembre 2003. La nouvelle disposition .
