Chapter 11: Engineering Project Management
Upcoming SlideShare
Loading in...5

Chapter 11: Engineering Project Management






Total Views
Views on SlideShare
Embed Views



1 Embed 1 1



Upload Details

Uploaded via as Microsoft Word

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
Post Comment
Edit your comment

Chapter 11: Engineering Project Management Chapter 11: Engineering Project Management Document Transcript

  • Chapter 11 Engineering Project Management In this chapter, we will discuss the techniques used in various stages of engineering project management. These include: project selection, project organization, project scheduling, project budgeting (life-cycle costing), and project control. 11.1. Project Selection (1) Introduction - Project selection is usually done in the first or second phase of the project management (conceptual design and advanced development). - Projects are from ideas. When a business decision is made, a project is born. However, new ideas would arrive continuously from various sources. Hence, it is necessary to screen these ideas and determine what to pursue. - Project selection concerns not only to decide on which project to carry out but also on which way pursue a project - Project selection can be very dynamic. New information and changed circumstances may call for rejecting or abandoning a previous decision. The available fund and labor skill may constrain the project selection. In general, the project selection process is complex consisting of many interrelated decisions. - In order to assist project selection, various methods have been developed, following is a description of several commonly used methods - Checklist and scoring method - Benefit-cost analysis method - Cost-effectiveness analysis method - Decision tree method (2) Checklists and scoring models - Let us start with an example. The following table is a checklist for a project selection Criteria Profitability Time to Developing Commercial market risk success Score 3 2 1 3 2 1 3 2 1 3 2 1 Total score Project A X X X X 10 Project B X X X X 6 Project C X X X X 8 - From the table, it is seen that a checklist contains a set of criteria, the scores, and the total score. In the above example, four criteria are used: profitability, time to market, developing risk, and commercial success, though other criteria may be more important to the other projects. - The scores are used to measure how well a project does with respect to each criterion. Words such as excellent, good and so on may be associated with the numerical values.
  • - The total score can be used to decide which project is more favor. Typically, a cutoff point or threshold is specified below which the project is abandoned. In the above example, if 7 is specified as the threshold, only project A and C would be pursued. - If the criteria are not equally important, we can use the weighting method to calculate the total score: T j = ∑ wi sij i where, j is used to index the projects, i is used to index the criteria, sij are the rating and wi are the weighting factors. In particular, the weighting factors can be determined by the following ways: - Uniform or equal weight: 1 wi = N where, N is the number of criteria - Rank sum weights: N − Ri + 1 wi = ∑ ( N − Ri + 1) i where, Ri is the rank position of criterion i (with 1 as the highest rank). - Rank reciprocal weights: 1 Ri wi = ∑1 Ri i - For instance, in the example above, if the importance of the criteria are ranked as follows: Profitability > Developing risk > Commercial success > Time to market. Then, using the reciprocal weights: w(Profitability) = 12/25, w(developing risk) = 6/25, w(commercial success) = 4/25, and w(time to market) = 3/25. You may calculate the scores for each project accordingly. - The checklist table can be represented by a graphic model:
  • Profitability Project C Project A Commercial Project B success Time to market Developing risk From the graph, it is seen that Project B is completely enclosed by Project A and hence, it will not be better Project A in any aspects. Therefore, there is no reason to pursue Project B. (3) Benefit-cost analysis - Many projects, for example the government projects, cannot be evaluated by means of the attractive rate of return (MARR). At this time, the Benefit-Cost (B/C) analysis is an important method for project selection. - Following are the formulas to calculate B/C: PW of benefits to user PW [ B ] B/C = = PW of total costs to supplier PW [CR + (O + M )] or: AW of benefits to user B B/C = = AW of total costs to supplier CR + (O + M ) where, B = annual worth of benefits to user CR = capital recovery cost (equivalent annual cost of initial investment) O = equivalent uniform annual operating cost M = equivalent uniform maintenance These two formulas should yield the same results. - To government projects, as they usually focus on the actual benefit, modified B/C formulas are more suitable and they are defined as follows: PW [ B − (O + M )] B/C = PW [CR ] or: B − (O + M ) B/C = CR
  • The modified formula may occasionally generate different results in comparison to the conventional formula. - An example. An individual investment opportunity is deemed to be worthwhile if its B/C ratio is greater than one. Consider the project of installing a new inventory control system with the following data: Initial cost $20,000 Project life 5 years Salvage value $4,000 Annual savings $10,000 O&M disbursements $4,400 MARR $15% By interpreting annual savings as benefit, the conventional and modified AW B/C ratios are computed as follows: CR = $20,000(A/P, 15, 5) - $4,000(A/F, 15, 5) = $5,373 B $10,000 Conventional B / C = = = 1.02 CR + (O + M ) $5,373 + $4,000 B − (O + M ) $10,000 − $4,400 Modified B / C = = = 1.04 CR $5,373 Since B/C is greater than one, the investment is worthwhile. However, it is noted in either case, the benefit and cost ratio is close to one and hence may be offset by many possibilities. Therefore, further investigation is necessary. - In summary, the benefit-cost analysis should follow the procedure below: S1: Identify the problem clearly S1: Explicitly define the set of objectives to be accomplished S2: Generate alternatives that satisfy the stated objectives S3: Identify clearly the constraints (e.g., technological, political, legal, social, financial) that exist with project environment. This step will help narrow the alternatives generated S4: Determine and list the benefits and costs associated with each alternative. Specify each in monetary terms. If this cannot be done for all factors, this fact should be stated clearly in the report S5: Calculate the B/C ratios and other indicators (e.g., present value, rate of return) for each alternative. S6: Prepare the report, comparing the results of the evaluation of each alternative examined. (4) Cost-effectiveness analysis - The objective of cost-effectiveness analysis is find what is the most effective way to use the money - The effectiveness can be measured by: - Availability - Dependability - Capability - Similar to cost-effectiveness analysis, the procedure of C/E analysis is as follows: S1: Define the desired goals
  • S2: Identify the mission requirements S3: Develop alternative systems 4. Establish system evaluation criteria S5: Determine capabilities of alternative systems S6: Analyze the merits of each S7: Perform sensitivity analysis S8: Document results and make recommendations (4) Decision trees - Decision tree is a graphical method of expressing, in chronological order, the alternative actions that are available to the decision maker and the outcomes determined by chance. - The following figure shows a decision tree. - Decision tree consists of two types of nodes: decision nodes and chance nodes. Each node may be followed by another node (decision node or chance node), or by a payoff (value). - A decision node is represented as a box and a chance node is represented as a cycle. - Each node (both decision node and chance node) has an expected monetary value (EMV) associated with it. - The branches from the decision tree represents the alternatives and the branches from the chance node represent the random events (Si) that may happen and the probability (Pi) associated with them. EMV P1 payoff S1 S2 P2 payoff EMV A1 2a S3 Chance P3 payoff 1 nodes Decision A2 payoff node 2b payoff EMV payoff - Constructing a tree:
  • - A tree is started on the left with one or more decision nodes. From these all possible alternatives are drawn branching. - Then a chance node or a decision node, associated with either subsequent events or decisions, is added. Each time a chance node is added, the appropriate states and their probability emanate rightward from it. - The above procedure is continue until all the possibilities are included. - Finding a solution: - Divide the tree into two segments: (1) chance nodes with all their emerging states of nature, and (2) decision nodes with all their alternatives. - For the chance nodes segments, - For the decision nodes segments - The process starts in the final payoffs and continues in the reverse order until reaching the beginning of the tree. - An example: Automation or not? - Question: should the company invest to automate the process? - Data: Automate: -$90K(0.5) + $40K(0.3) + $300K(0.2) = $27K Don’t automate: $0 - the decision tree: $27K Poor (0.5) -$90K $27K Fair (0.3) $40K 1 Excel. (0.2) a $300K automate 1 $0 Don’t automate From the decision tree, it is easy to see that automation has better payoff and hence should be carried out. - In summary, the procedure to conduct a decision tree analysis is as follows: S1: Identify the points of decision and alternatives available at each point S2: Identify the points of uncertainty and the type or range of possible outcomes at each point (layout of decision tree) S3: Estimate the values needed to conduct the analysis, especially the probabilities of different outcomes and the costs / returns for various outcomes and alternative actions
  • S4: Analyze the alternatives, starting with the most distant decision point(s) and working back, to choose the best initial decision. 11.2. Project Organization (1) Introduction - Project management deals with the one-time effort to achieve a specific goal within a given set of resources and budget constraints. - The fundamentals of project management involve the allocation of work to the participating units at the planning stage, and the continuous integration of work through the execution stage. Hence, the breakdown of work, the allocation of specific tasks to individuals and subcontractors, the management and control during execution, and finally, the integration of the parts into the pre-specified whole is the focus. - There are three types of structures involved in the project management: - The organizational structure of each unit participating in the project - The organizational structure of the project itself, and - The work breakdown structure (WBS), that is the way the work division and integration. - In this section, we will discuss these structures and their management. (2) The structures of organizational - Business organizations may be organized in various ways. In all cases, the objective of the organizational structure is to arrive at an orderly arrangement of the interdependent components of the business. - Business is usually decomposed into departments. The departmentalization is integral to the delegation process. It may be arranged in a number of ways, such as: - Functional organization* - Product / project oriented organization* - Customer organization - Territorial organization - Process organization - Functional organization and product / project oriented organization are the most commonly used organization methods and their structures are shown below:
  • President VP VP manu- VP engineering facturing marketing Electric Plant manager Sales Engineering Quality control Mechanical Engineering Illustration of functional organization President Engineering Manufacturing Marketing VP Project 1 VP Project 2 Engineering Engineering Manufacturing Manufacturing Marketing Marketing Illustration of project-oriented organization - Most companies use functional organization while projects are typically vertical. Hence, the so-called matrix organization is sometimes used.
  • President VP VP VP engineering manufacturing marketing PM1 VP projects PM2 PMn (3) The structures of projects - A project can be viewed as a small business within a large enterprise whose ultimate goal is to go out of business when all tasks are completed. However, the enterprise may have many projects flowing through it in various stages of completion. The challenge faced by the management is to juggle budgets, resources, and schedules to keep the projects flowing smoothly. - The selection of project structure depends on various factors such as: - Number of projects on hand and their relative importance (To handle just a few projects, functional organization is efficient. To handle a large number of projects, matrix organization may be desirable) - Level of uncertainty in projects (With high level of uncertainty, project oriented organization is desirable) - Type of technology used (When the project involve a number of complicated technologies, the project oriented organization is desirable) - Project complexity (High complexity projects should use project oriented organization while low complexity projects could use functional organization) - Duration of projects (Short projects do not justify a special organization) - Resources used by projects (When common resources are shared by two or more projects, matrix organizations should be used) - Overhead costs (Matrix organization may reduce the overhead cost) - Data requirements (If many projects have to share the same data, functional organization is desirable).
  • (4) Work breakdown structure - In order to build a building or a machine, we need a blueprint. In order to execute a project, we need the work breakdown structure (WBS) that defines the objectives, deliverables, and specifications for each task to be accomplished. - WBS is a schematic presentation of the disaggregation-integration process by which the project manager plans to execute the project. It is organized level by level. The lower level, the more detailed tasks. - In general, each task in the WBS should includes the following elements: (1) Objectives (a task without objectives is either unnecessary or cannot be done) (2) Deliverables (deliverables may include hardware, software, or a report of study) (3) Schedule (4) Budget (5) Performance measures (6) Responsibilities - An example: design and manufacture a new assembly line. A possible WBS is as follows: 1. New assembly line 1.1 Process design 1.1.1 Develop a list of assembly operations 1.1.2 Estimate assembly time for each operation 1.1.3 Assignment of operations to workstations 1.1.4 Design of equipment required at each station 1.2 Capacity planning 1.2.1 Forecast of future demand 1.2.2 Estimate of required assembly rates 1.2.3 Design of equipment required at each station 1.2.4 Estimate of labor requirements 1.3 Material handling 1.3.1 Design of line layout 1.3.2 Selection of material handling system 1.3.3 Integration design for the material handling system 1.4 Facility planning 1.4.1 Determination of space requirements 1.4.2 Analysis of energy requirements 1.4.3 Temperature and humidity analysis 1.4.4 Facility and integration design for the whole line 1.5 Purchasing 1.5.1 Equipment 1.5.2 Material handling system 1.5.3 Assembly machines 1.6 Development of training programs 1.6.1 For assembly line operators 1.6.2 For quality control personnel 1.6.3 For foremen and mangers 1.7 Actual training
  • 1.7.1 Assembly line operators 1.7.2 Quality control 1.7.3 Foremen and mangers 1.8 Installation and integration 1.8.1 Shipment of equipment and machines 1.8.2 Installations 1.8.3 Testing of components 1.8.4 Integration and testing of line 1.8.5 Operations 1.9 Management of projects 1.9.1 Design and planning 1.9.2 Implementation monitoring and control - WBS can be represented graphically as well. (7) Combining the organizational and work breakdown structures - The organizational structure (OS) and work breakdown structure (WBS) form the basis for project planning, management and control - Combining OS and WBS at detailed level is called work package. A work package is the smallest unit used by the project manager for planning and control the project. - The development of the OS and WBS relationship at different levels of the integration is the blueprint of the project. - The person responsible for a work package is responsible for the detailed scheduling, and resource planning of its constituent tasks. - For instant, develop a training program (1.6.2) and conduct actual training (1.7.2) are the jobs of the quality control department. The schedule, budget, resources and most importantly, the deliverables shall be clearly defined in the work package. 11.4. Project Scheduling (1) Introduction - Project scheduling deals with the planning of timetables and the establishment of dates during which various resources, such as equipment and personnel, will perform the tasks required to complete the project. - Schedules provide an essential communication and coordination link between the individuals and the organization, specific tasks to the whole project. They are working tools for project planning, evaluation, and control. - A proper schedule defines time, money and resources in time and shall answer the following questions: (1) If each of the activities goes according to plan, when will the project be completed? (2) Which tasks are most critical to ensure the timely completion of the project? (3) Which tasks can be delayed, if necessary, without delaying the project, and how much? (4) At what time should each activity begin and end?
  • (5) At any given time during the project, what is the range of dollars that should have been spent? (6) Is it worthwhile to incur extra costs to accelerate some of the activities? - There are a number of ways to represent a schedule, such as WBS. Also, there are a number of ways to deliver a schedule. In general, however, two types of schedules are often used: - Milestone list - Network techniques - The milestone list is relative simple and sketchy. It shows the important dates of the project is a simple chronological order. Following is an example of developing a computer peripherals: - Project kickoff - Requirement analysis complete - Preliminary design review - Critical design review - Prototype fabricated - Integration and testing completed - Quality assurance review - Start volume production - Marketing program defined - First shipment - Customer acceptance test complete While it is simple and easy to follow, this one-dimension view is often lack of details and correlation. In comparison, the network techniques are more effective. - This section will discuss several network techniques including - Gantt chart - PERT chart and CPM method - AOA network - AON network - However, let us first deal with the time estimation (2) Time estimation - Time estimation refers to estimate the time required for each and every task in the project. It is the basis of time scheduling. - In order to estimate the time, we shall first determine the tasks. In general, the tasks have been specified in WBS, however, it may be necessary to re-organize the WBS so that the tasks can be scheduled. The rules for dividing tasks are: - Each task shall take 2 – 0.5% of the total project time - Important tasks must be included - Large tasks may be subdivided - There are various methods for time estimation including - Stochastic method - Deterministic method
  • - The stochastic method is based on the statistics. Assuming that, based on the historical data, we have: a – optimistic time b – pessimistic time m – most likely time then, the expected time would be: 1 1  d =  2m + ( a + b)  3 2  This is illustrated in the following figure. The (histogram) probability distribution obtained from historical data a m m d And the variance is: b−a s= 6 - The deterministic method is based on simple cost-effective analysis. For example, if it takes 10 minutes to install an electric outlet, then installing 10 would take 100 minutes. Such a scheme is usually represented by a linear equation: y = ax + b where, y is the required time, a is the unit time, x represents the number of subtasks and b is the setup time. - The effect of learning. It is well know that learning takes time. Hence, it is necessary to include the effect of learning in the schedule. This is done by means of the learning time formula: T(n) = T(1)nβ where, T(n) is the time required in nth repetition, β is the learning coefficient. (3) Gantt chart - Gantt chart is the most widely used time management tool.
  • - The basic idea of Gantt is just to add a dimension to the time axis: the horizontal axis is the time while the added vertical axis is the activities. The time spend of an activity is represented by means of a bar in the graph. The correlation among the activities are shown by the start-to-end dates. - To describe the correlation among the activities of a project, we first develop a “start- to-end” table as the example shown below: Activity Immediate predecessors duration (weeks) A - 5 B - 3 C A 8 D A, B 7 E - 7 F C, E, D 4 G F 5 - The Gantt chart is shown in the following figure. The difference between two scheduled activities is called the slack of the activities. A B C D E F G 5 10 15 20 - From a Gantt chart, a schedule may have two ways to start: - Early start: all activities start as soon as possible, without violating the precedence relations - Late start: all activities start as late as possible, as long as the finish date is not compromised - In the above example, the Gantt chart uses early start. Note that the shaded boxes show the critical path of the project, which has no slack time. Any delay along the critical path will result in the delay of the project. - Using the same idea, one can generate the late start Gantt chart as well. - Gantt chart can accommodate additional information. These include:
  • - The interpretation of the activities - The work breakdown structure number (note that each activity corresponds to WBS task). - The original scheduled milestone (denoted by ∇) - The review date - The rescheduled milestone (denoted by ∆) - The completed milestone (denoted by ♦) - An example is shown below. No. Task/milestone WBS 5 10 15 20 25 A 1.1 B 1.2 C 1.3 D 1.4 E 1.5 F 1.6 G 1.7 - There are computer software systems that will help to generate the Gantt chart. (4) PERT chart and CPM method – the basic idea - The basic approach to all project scheduling is to form an actual or implied graph that graphically portrays the relationship between the tasks and milestones in the project. Gantt chart is one of them and PERT/CPM chart is the other, which is more powerful. - PERT stands for program evaluation and review technique. CPM stands for critical path method. Although they are different, nowadays, PERT/CPM are used together for scheduling. - PERT/CPM is based on a diagram that represents the entire project as a network of arrows and nodes, resulting the AOA (Activity On Arrows) and AON (Activity on Node) methods. We will discuss both methods. - To apply PERT/CPM, we must answer the following questions: - What are chief project activities? (the WBS) - What are sequencing requirement? (the start-to-end table) - Which activities can be conducted simultaneously? - What are the estimated requirements for each activity? - There are a number of advantages that make PERT/CPM the prime tool for scheduling (5) PERT/CPM method – AOA network - AOA networks, as its name indicated, are made of a number of arrows. Each arrow represents an activity. Note: - Each arrow has two events: a head and tail - Each event represents a point in time
  • - The head represents the beginning event of the activity - The tail represents the completing event of the activity - The direction of the arrow indicates the progress of the project (time) - The rules for constructing an AOA are as follows: - rule 1: each activity is represented by one Project direction and only arrow in the network - rule 2: no two activities can be identified by the same head and tail events (to do this, it i j may be necessary to add some dummy Beginning Completing events) state state - rule 3: to ensure the correct representation in the AOA diagram, the following questions must be answered as each activity is added to the network: (a) Which activities must be completed immediately before this activity can start? (b) Which activities must immediately follow this activity? (c) Which activities must occur concurrently with this activity? - An example: Develop an AOA network for the same data in the previous section. - Solution: - From the example, we know the correlation among the activities Activity Immediate predecessors duration (weeks) A - 5 B - 3 C A 8 D A, B 7 E - 7 F C, E, D 4 G F 5 - First, it is good to have a common starting point. So, we start at state 1. - Second, identify all activities that have no predecessors, which are A, B, E. They lead to states 2, 3, 4. C 2 5 A D1 B D2 D F 1 3 6 7 8 E 4
  • - After the completion of A, B, E, we can then start C and D. C leads to state 5. However, D cannot start until the completion of both A and B. Since there is no correlation between A and B, hence a dummy state, 6, is introduced. The activities to complete this states, D1 and D2, require zero time. From state 6, we can then have D, which leads to 7. - After the completion of C, D, and E, we can start F. At this point, it is interesting to know that there are no activities between 5 to 7 and between 4 to 7. Hence, these two states can be deleted. In addition, state 6 is a dummy state (both D1 and D2 require no time to complete). Hence, it can be merged to the state 3. The resulting diagram is shown below. - After the completion of F, G can start. - Finally, affiliate the required time to the activities, the AOA network is completed. 2 A, 5 C, 8 B, 3 D, 7 F, 4 G, 5 1 3 4 5 6 E, 7 - Based on the AOA network, we can find much useful information for scheduling as discussed below. - The event matrix shows the correlation among the activities Ending event 1 2 3 4 5 6 1 X X X 2 X X Starting event 3 X 4 X 5 X 6 - The sequences of the network:
  • Sequence number Events in the Activities in the Sum of activity sequence sequence times 1 1-2-4-5-6 A, C, F, G 22 2 1-2-3-4-5-6 A, (D), D, F, G 21 3 1-3-4-5-6 B, D, F, G 19 4 1-4-5-6 E, F, G 16 - Observations: - Among all the sequences, the one that takes most time is the critical path (Sequence 1 in the above example). A delay in the critical path will result in a delay of the project. - Activities not on the critical path have slack time and can be delayed to start in temporally bases. (In the above example, task C is not on the critical path, and hence can be delayed to start) - In general, there may be two types of slacks: - Free slack represents the time that an activity can be delayed without delaying the start of any succeeding activity and the end of the project. The activities whose end events are on the critical path have free slacks (In the above example, C has a free slack time 22 – 16 = 8). - Total slack is the time that the completion of an activity can be delayed without delaying the end of the project. The activities whose end events are not on the critical path have total slacks. The increase of the total slack time will effect the subsequent tasks (In the above example, B has a total slack time of 22 – 19 = 3. However, different to the free slack time, if B takes this period of time, D will be affected). - Important times in the schedule include the earliest and latest times each event can take place without causing a schedule overrun. This information is needed to calculate the critical path as well as balance the project load (work load and budget). - Early time: - Notation: the early time of a event i is denoted as ti, - Meaning: early time is the length of the longest sequence from the start node (event 1) to event i. (note that ti = 0 implies the corresponding activities have no precedence constraints and can begin as early as possible. - Calculation formula: to determine ti for event i, a forward pass is made through the network. Let Lij be the duration or length of activity (i, j), then: tj = maxi[ti + Lij] for all (i, j) activities defined. - for instance, in the above example, the early time of event 3 is determined be: t3 = max[t1 + L13, t2 + L23] = max[0+3, 0+5] = max[3, 5] = 5. - it is interesting to know that the last early time is the total project time. For instance, in the above example, the early time of event 6 is: t6 = max[t5 + L56] = 17 + 5 = 22. - Late time:
  • - Notation: the late time of a event i is denoted as Ti, - Meaning: late time is the length of the shortest path from the end of the project to the activity. - Calculation formula: to determine the late time, we start from the end of the project and make a backward pass through the network to the activity: Tj = minj[Ti - Lij] for all (i, j) activities defined. - For instance, in the above example, the late time for event 2 is: T2 = min[T3 – L23, T4 + L24] = max[6-0, 13-8] = max[6, 5] = 5. - In the above example, time early time and the late time are summarized below: Event (i) early time (ti) late time (Ti) 1 0 0 2 5 5 3 5 6 4 13 13 5 17 17 6 22 22 - We can also calculate the start and finish time of each activity: - ESij = ti, early start time is the earliest time activity (i, j) can start without violating any precedence relations - EFij = ESij – Lij, early finish time is the earliest time activity (i, j) can finish without violating any precedence relations - LFij = Tj, late finish time is the latest time activity (i, j) can start delaying the completion of the project. - LSij = LFij – Lij, late start time is the latest time activity (i, j) can start without delaying the completion of the project - Furthermore, we can calculate the slack times as well: - TSij = LSij – ESij = LFij - EFij, for activity (i, j), the total slack time is the difference between its late start and its early start times. It is also equal to the difference between its late finish time and early finish time. - FSij = tj – (ti – Lij), assuming that all activities are started as soon as possible, for activity (i, j), the free slack time is the difference between its early time of its end event j and the sum of the early time of its start even i plus its length. - For the example above, the following table summarizes these times: activity (i, j) Lij ESij EFij LFij LSij TSij FSij A 1, 2 5 0 5 5 0 0 0 B 1, 3 3 0 3 6 3 3 2 C 2, 4 8 5 13 13 5 0 0 D 3, 4 7 5 12 13 6 1 1 E 1, 4 7 0 7 13 6 6 6 F 4, 5 4 13 17 17 13 0 0 G 5, 6 5 17 22 22 17 0 0
  • D1 2, 3 0 5 5 6 6 1 0 - Although computer software systems have been developed to generate PERT / CPM and calculate the important times, it is a good practice to work on calculations by hand as it will help you to gain an insight look of the project. (6) PERT/CPM method – AON network - Similar to the AOA method but focus on the activity (each node represent a task together with its early start time and late start time) - It can be shown that the topology of AON and AOA are the same. - For the example above, the AON network is shown below. ES = 0 ES = 5 LS = 0 LS = 5 A C ES = 13 ES = 0 LS = 13 ES = 17 ES = 22 LS = 0 ES = 0 ES = 5 LS = 17 LS = 22 LS = 3 LS = 6 Start B D F G End ES = 0 LS = 6 E