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Chapter 8 - Project Management1 Chapter 8 - Project Management Chapter Topics The Elements of Project Management The Project Network Probabilistic Activity Times Project Crashing and Time-Cost Trade-Off Formulating the CPM/PERT Network as a Linear Programming Model

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Chapter 8 - Project Management2 Project Management Overview Uses networks for project analysis. Networks show how projects are organized and are used to determine time duration for completion. Network techniques used are - CPM (Critical Path Method) - PERT (Project Evaluation and Review Technique) Developed during late 1950s.

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Chapter 8 - Project Management3 The Elements of Project Management Management is generally perceived as concerned with planning, organizing, and control of an ongoing process or activity. Project Management is concerned with control of an activity for a relatively short period of time after which management effort ends Primary elements of Project Management to be discussed: - Project team - Project planning - Project control.

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Chapter 8 - Project Management4 The Elements of Project Management The Project team Project team typically consists of a group of individuals from various areas in an organization and often includes outside consultants. Members of engineering staff often assigned to project work. Most important member of project team is the project manager. Project manager is often under great pressure because of uncertainty inherent in project activities and possibility of failure. Project manager must be able to coordinate various skills of team members into a single focused effort.

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Chapter 8 - Project Management5 Project Planning: PERT/CPM PERT –Program Evaluation and Review Technique –Developed by U.S. Navy for Polaris missile project –Developed to handle uncertain activity times CPM –Critical Path Method –Developed by Du Pont & Remington Rand –Developed for industrial projects for which activity times generally were known Todays project management software packages have combined the best features of both approaches.

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Chapter 8 - Project Management6 PERT and CPM have been used to plan, schedule, and control a wide variety of projects: –R&D of new products and processes –Construction of buildings and highways –Maintenance of large and complex equipment –Design and installation of new systems PERT/CPM

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Chapter 8 - Project Management7 Project managers rely on PERT/CPM to help them answer questions such as: –What is the total time to complete the project? –What are the scheduled start and finish dates for each specific activity? –Which activities are critical and must be completed exactly as scheduled to keep the project on schedule? –How long can noncritical activities be delayed before they cause an increase in the project completion time? PERT/CPM

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Chapter 8 - Project Management8 PERT Network: Activity-on-Node Approach A PERT network can be constructed to model the precedence of the activities. The arcs of the network represent the precedence relationships of the activities. The nodes (rectangles) of the network represent activities. –You will need to add a Start and a Finish nodes.

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Chapter 8 - Project Management9 Activity time estimates usually can not be made with certainty. In the three-time estimate approach, the time to complete an activity is assumed to follow a Beta distribution. An activity is mean completion time is: t i = (a i + 4m i + b i )/6 An activitys completion time variance is: 2 i = ((b i -a i )/6) 2 –a i = activitity is optimistic completion time estimate –b i = activitity is pessimistic completion time estimate –m i = activitity is most likely completion time estimate PERT Network: Activity-on-Node Approach

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Chapter 8 - Project Management10 In the three-time estimate approach, the critical path is determined as if the mean times for the activities were fixed times. The expected project time is the sum of the expected times of the critical path activities. The project variance is the sum of the variances of the critical path activities. The expected project time is assumed to be normally distributed (based on central limit theorem). PERT Network: Activity-on-Node Approach

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Chapter 8 - Project Management11 Step 1: Make a forward pass through the network as follows: For each of these activities, i, compute: –Earliest Start (ES) Time = the maximum of all earliest finish times for all its immediate predecessors. (For node START, this is 0.) ES i = Maximum (EF j ) for all immediate proceeding activities j. –Earliest Finish (EF) Time = (Earliest Start Time) + (Time to complete activity i). EF i = ES i + t i The project completion time is the of the Earliest Finish Times at the FINISH node. –This will also be used as Latest Finish Time at FINISH node in the next step. PERT Analysis Algorithm

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Chapter 8 - Project Management12 Step 2: Make a backwards pass through the network as follows: Move sequentially backwards from the last node, FINISH to its immediate predecessors, etc. At a given node, j, consider all activities immediately following it and compute: –Latest Finish (LF) Time = the minimum of the latest start times for all activities that immediately follow j. (For node FINISH, this is the project completion time.) LF j = Minimum (LS i ) for all immediate following activities i. –Latest Start (LS) Time = (Latest Finish Time) - (Time to complete activity j). LS j = LF j - t j PERT Analysis Algorithm

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Chapter 8 - Project Management13 Step 3: Calculate the slack time for each activity by: Slack = (Latest Start) - (Earliest Start) or = (Latest Finish) - (Earliest Finish). A critical path is a path of activities, from node START to FINISH, with 0 slack times. – Shared slack is slack available for a sequence of activities. PERT Analysis Algorithm

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Chapter 8 - Project Management14 Example: Riverwalk Associates Riverwalk Associates is in the business of building elaborate parade floats. Its crew has a new float to build and want to use PERT/CPM to help them manage the project. The table on the next slide shows the activities that comprise the project. Each activitys estimated completion time (in weeks) and immediate predecessors are listed as well. The project manager wants to know the total time to complete the project, which activities are critical, and the earliest and latest start and finish dates for each activity.

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Chapter 8 - Project Management15 Project activity initial information: Immed. Optimistic Most Likely Pessimistic Activity (i) Predec. Time (weeks) Time (wk.) Time (wk.) A 4 6 8 B 1 4.5 5 C A 3 3 3 D A 4 5 6 E A 0.5 1 1.5 F B,C 3 4 5 G B,C 1 1.5 5 H E,F 5 6 7 I E,F 2 5 8 J D,H 2.5 2.75 4.5 K G,I 3 5 7 Example: Riverwalk Associates

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Chapter 8 - Project Management16 Activity Expected Time and Variances t i = (a i + 4m i + b i )/6 2 i = ((b i -a i )/6) 2 Activity (i) Expected Time Variance (week 2 ) A 6 4/9 B 4 4/9 C 3 0 D 5 1/9 E 1 1/36 F 4 1/9 G 2 4/9 H 6 1/9 I 5 1 J 3 1/9 K 5 4/9 Example: Riverwalk Associates

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Chapter 8 - Project Management17 PERT Activity Node Representation A 6 ES EF LS LF Earliest StartEarliest Finish Expected Duration of the activity Latest StartLatest Finish Example: Riverwalk Associates

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Chapter 8 - Project Management18 PERT Network Representation A 6 C 3 B 4 E 1 D 5 F 4 G 2 J 3 H 6 I 5 K 5 FINISH START 0 Example: Riverwalk Associates

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Chapter 8 - Project Management19 Earliest/Latest Times Activity ES EF LS LF Slack A 0 6 0 6 0 *critical B 0 4 5 9 5 C 6 9 6 9 0 * D 6 11 15 20 9 E 6 7 12 13 6 F 9 13 9 13 0 * G 9 11 16 18 7 H 13 19 14 20 1 I 13 18 13 18 0 * J 19 22 20 23 1 K 18 23 18 23 0 * The estimated project completion time is t0 = 23 (weeks) at FINISH. Example: Riverwalk Associates

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Chapter 8 - Project Management20 Define variables for each activity in the following manner: ES_i = Earliest Start time for activity i EF_i = Earliest Finish time for activity i LS_i = Latest Start time for activity i LF_i = Latest Finish time for activity i where i=A, B…K; and FINISH = the earliest and also latest completion time of the project. Riverwalk Associates – Linear Programming Form

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Chapter 8 - Project Management21 Minimize ES_A + EF_A + ES_B + EF_B + … + EF_K + FINISH S.t. EF_A - ES_A >= 6 (= OK) EF_B - ES_B >= 4 EF_C - ES_C >= 3 EF_D - ES_D >= 5 EF_E - ES_E >= 1 EF_F - ES_F >= 4 EF_G - ES_G >= 2 EF_H - ES_H >= 6 EF_I - ES_I >= 5 EF_J - ES_J >= 3 EF_K - ES_K >= 5 (= OK) ES_C - EF_A >= 0 (Not = ) ES_D - EF_A >= 0 ES_E - EF_A >= 0 Riverwalk Associates – LP Model 1 for Earliest Times ES_F - EF_B >= 0 ES_G - EF_B >= 0 ES_F - EF_C >= 0 ES_G - EF_C >= 0 ES_J - EF_D >= 0 ES_J - EF_H >= 0 ES_H - EF_E >= 0 ES_H - EF_F >= 0 ES_I - EF_E >= 0 ES_I - EF_F >= 0 ES_K - EF_G >= 0 ES_K - EF_I >= 0 FINISH - EF_J >= 0 FINISH - EF_K >= 0

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Chapter 8 - Project Management22 Maximize LS_A + LF_A + LS_B + LF_B + … + LF_K S.t. LF_A - LS_A >= 6 (= OK) LF_B - LS_B >= 4 LF_C - LS_C >= 3 LF_D - LS_D >= 5 LF_E - LS_E >= 1 LF_F - LS_F >= 4 LF_G - LS_G >= 2 LF_H - LS_H >= 6 LF_I - LS_I >= 5 LF_J - LS_J >= 3 LF_K - LS_K >= 5 (= OK) LS_C - LF_A >= 0 (Not just =) LS_D - LF_A >= 0 LS_E - LF_A >= 0 Riverwalk Associates – LP Model 2 for Latest Times LS_F - LF_B >= 0 LS_G - LF_B >= 0 LS_F - LF_C >= 0 LS_G - LF_C >= 0 LS_J - LF_D >= 0 LS_J - LF_H >= 0 LS_H - LF_E >= 0 LS_H - LF_F >= 0 LS_I - LF_E >= 0 LS_I - LF_F >= 0 LS_K - LF_G >= 0 LS_K - LF_I >= 0 FINISH - LF_J >= 0 FINISH - LF_K >= 0 FINISH = 23 (from the optimal results of Model 1) – this is the main diff.)

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Chapter 8 - Project Management23 Probability the project will be completed within t1=24 weeks project time variance 2 = 2 A + 2 C + 2 F + 2 I + 2 K = 4/9 + 0 + 1/9 + 1 + 4/9 = 2 (weeks-squared) project time standard deviation = 1.414 (weeks). z1 = (24 - 23)/ = (24-23)weeks/1.414weeks =.71 From the Standard Normal Distribution table: P(z < z1=.71) =.5 +.2611 =.7611 More precisely, P(t < t1) = P(t-t0 < t1-t0) = P[(t-t0)/ < (t1-t0)/ ] = P(z < z1=.71) =.7611 if we define z= (t-t0)/ and z1 = (t1-t0)/. Example: Riverwalk Associates

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Chapter 8 - Project Management24 Probability Analysis of the Project: Example 2 Question: If the mean project completion time is X 0 = 25, what is the probability that the project will be completed within X 1 =30 weeks? 2 = 6.9, = 2.63. Z 1 = (X 1 - X 0 )/ = (30 -25)/2.63 = 1.90 Z 1 value of 1.90 corresponds to probability of.4713 in Table A.1, appendix A. Probability of completing project in 30 weeks or less : (.5000 +.4713) =.9713. More precisely, P(x < X 1 ) = P(x- X 0 < X 1 - X 0 ) = P[(x- X 0 )/ < (X 1 - X 0 )/ ] = P(z < Z 1 =1.90) =.9713 if we define z= (x - X 0 )/ (new variable) and Z 1 = (X 1 - X 0 )/ (constant). Figure 8.14 Probability the network will be completed in 30 weeks or less

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Chapter 8 - Project Management25 Question: If the mean project completion time is X 0 = 25, what is the probability that the project will be completed within X 1 =22 weeks? Z 1 = (22 - 25)/2.63 = -1.14 Where Z 1 value of 1.14 (ignore negative) corresponds to probability of 0.3729 in Table A.1, appendix A. Probability that customer will be retained is.1271 Figure 8.15 Probability the network will be completed in 22 weeks or less Probability Analysis of the Project: Example 3

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Chapter 8 - Project Management26 Probability Analysis of the Project Network CPM/PERT Analysis with QM for Windows Exhibit 8.1

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Chapter 8 - Project Management27 Project Crashing and Time-Cost Trade-Off: Definition Project duration can be reduced by assigning more resources to project activities. Doing this however increases project cost. Decision is based on analysis of trade-off between time and cost. Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time. Crashing achieved by devoting more resources to crashed activities.

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Chapter 8 - Project Management28 Crashing Activity Times In the Critical Path Method (CPM) approach to project scheduling, it is assumed that the normal time to complete an activity, t j, which can be met at a normal cost, c j, can be crashed to a reduced time, t j, under maximum crashing for an increased cost, c j. It is assumed that its cost per unit reduction, K j, is linear and can be calculated by: K j = ( c j ' - c j )/( t j - t j '). E.g.: in the example on the right, K j = total crash cost/total crash time = $2000/5 = $400/wk

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Chapter 8 - Project Management29 Normal Crash Normal Crash Activity Time Cost Time Cost Activity Time Cost Time Cost A) Study Feasibility 6 $ 80,000 5 $100,000 B) Purchase Building 4 100,000 4 100,000 C) Hire Project Leader 3 50,000 2 100,000 D) Select Advertising Staff 5 150,000 2 300,000 E) Purchase Materials 1 180,000 1 180,000 F) Hire Manufacturing Staff 4 300,000 1 480,000 G) Manufacture Prototype 2 100,000 2 100,000 H) Produce First 50 Units 6 450,000 5 800,000 I) Advertising Product 5 350,000 1 650,000 I) Advertising Product 5 350,000 1 650,000 J) Assessing User Feedback 3 300,000 3 300,000 J) Assessing User Feedback 3 300,000 3 300,000 K) Distributing Product 5 550,000 5 550,000 K) Distributing Product 5 550,000 5 550,000 n Normal Costs and Crash Costs Crashing Example for Riverwalk Associates

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Chapter 8 - Project Management30 Crashing: The completion time for this project using normal times is 23 weeks. Which activities should be crashed, and by how many weeks, in order for the project to be completed in a Target of 20 weeks? Let: Y i = the amount of time activity i is crashed. Then borrow from the LP formulation for the Earliest Times, we have the following… Crashing Example for Riverwalk Associates

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Chapter 8 - Project Management31 Min 20 Y A + 50 Y C + 50 Y D + 60 Y F + 350 Y H + 75 Y I S.t. EF_A - ES_A >= 6 - Y A EF_B - ES_B >= 4 EF_C - ES_C >= 3 - Y C EF_D - ES_D >= 5 - Y D EF_E - ES_E >= 1 EF_F - ES_F >= 4 - Y F EF_G - ES_G >= 2 EF_H - ES_H >= 6 - Y H EF_I - ES_I >= 5 - Y I EF_J - ES_J >= 3 EF_K - ES_K >= 5 ES_C - EF_A >= 0 (Not = ) ES_D - EF_A >= 0 ES_E - EF_A >= 0 Riverwalk Associates – LP Model for Crashing ES_F - EF_B >= 0 ES_G - EF_B >= 0 ES_F - EF_C >= 0 ES_G - EF_C >= 0 ES_J - EF_D >= 0 ES_J - EF_H >= 0 ES_H - EF_E >= 0 ES_H - EF_F >= 0 ES_I - EF_E >= 0 ES_I - EF_F >= 0 ES_K - EF_G >= 0 ES_K - EF_I >= 0 FINISH - EF_J >= 0 FINISH - EF_K >= 0 FINISH <= 20 (Target) Y A <=1 Y C <=1 Y D <=3 Y F <=3 Y H <=1 Y I <=4

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Chapter 8 - Project Management32 Project Crashing and Time-Cost Trade-Off Project Crashing with QM for Windows Exhibit 8.2

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Chapter 8 - Project Management33 Project Crashing and Time-Cost Trade-Off General Relationship of Time and Cost Project crashing costs and indirect costs have an inverse relationship. Crashing costs are highest when the project is shortened. Indirect costs increase as the project duration increases. Optimal project time is at minimum point on the total cost curve. Figure 8.20 The time–cost trade-off

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