PRODUCTION AND OPERATIONS MANAGEMENT Ch. 16: Project Management POM - J. Galván

Strategic Importance of Project Management Bechtel Kuwait Project: 8,000 workers 1,000 construction professionals 100 medical personnel 2 helicopter evacuation teams 6 full-service dining halls 27,000 meals per day 40 bed field hospital POM - J. Galván 8

Strategic Importance of Project Management - continued Microsoft Windows 98 Project: hundreds of programmers millions of lines of code millions of dollars cost Ford Redesign of Mustang Project: 450 member project team Cost $700-million 25% faster and 30% cheaper than comparable project at Ford POM - J. Galván 9

Project Characteristics Single unit Many related activities Difficult production planning and inventory control General purpose equipment High labor skills POM - J. Galván 10

An Example Building construction _ _ 11 © 1995 Corel Corp. POM - J. Galván 11

An Example Research project POM - J. Galván 12

An Example Sheer to waist pantyhose New product introduction New! Improved! 19 · Nude Sandalfoot Medium to Tall (B) No nonsense Sheer to waist pantyhose © 1995 Corel Corp. POM - J. Galván 13

What is a project? A project is unique/nonrepetitive. A project has a specific beginning, goal, purpose, and end. Thus a project is also temporary. Projects must be given specific resources. Projects usually cross functional lines and are organized as a matrix. Projects are for use by others: the usufructuary and the user. Projects generate systemic conflict. Projects are “open veins” from which the entity loses blood and where infection enter. POM - J. Galván

Formal definition A project is usually a one-time activity With a well-defined set of desired end results. It can be divided into subtasks that must be accomplished in order to achieve the project goals. The project is complex enough that the subtasks require careful coordination and control in terms of timing, precedence, cost, and performance. The project itself must often be coordinated with other projects being carried out by the same parent organization. POM - J. Galván

Management of Large Projects Planning - goal setting, project definition, team organization Scheduling - relating people, money, and supplies to specific activities and activities to one and other Controlling - monitoring resources, costs, quality, and budgets; revising plans and shifting resources to meet time and cost demands POM - J. Galván 14

Project Planning, Scheduling, and Controlling 1. Setting goals 2. Defining the project 3. Tying needs into timed project activities 4. Organizing the team Project Scheduling 1. Tying resources to specific 2. Relating activities to each other 3. Updating and revising on a regular basis Time/cost estimates Budgets Engineering diagrams Cash flow charts Material availability details CPM/PERT Gantt charts Milestone charts Cash flow schedules Project Controlling 1. Monitoring resources, costs, quality, and budgets 2. Revising and changing plans 3. Shifting resources to meet demands Reports budgets delayed activities slack activities Before Project During Project POM - J. Galván 16

Project Planning Establishing objectives Defining project Creating work breakdown structure Determining resources Forming organization © 1995 Corel Corp. POM - J. Galván 17

Project planning process Overview – a short summary of objectives and scope Objectives – a more detailed statement of the general goals General approach – managerial and technical approaches to the work Contractual aspects – contractual reporting and requirements Schedules – schedules and all milestone events Resources – budget and cost monitoring and control procedures Personnel – expected personnel requirements and their skills Evaluation methods – procedure for monitoring and evaluating Potential problems – preparation for problems POM - J. Galván

Project Organization Often temporary structure Uses specialists from entire company Headed by project manager Coordinates activities Monitors schedule & costs Permanent structure called ‘matrix organization’ Acct. Eng. Mkt. Mgr. POM - J. Galván 19

A Sample Project Organization President Finance Human Factors Engineering Quality Control Production Technician Test Engineer Propulsion Physiologist Project Manager Psychologist Structural Inspection Project 1 Project 2 Sales POM - J. Galván 20

J Matrix Organization Mkt Oper Eng Fin Project 1 Project 2 Project 3 POM - J. Galván 22

The Role of the Project Manager Project Plan and Schedule Revisions and Updates Project Manager Project Team Information regarding times, costs, problems, delays Performance Reports Feedback Loop Resources Top Management POM - J. Galván 23

Work Breakdown Structure Project Major tasks in the project Subtasks in the major tasks Activities POM - J. Galván 24

Project Scheduling Sequencing activities Identifying precedence relationships Determining activity times & costs Estimating material & worker requirements Determining critical activities PERT Test J J Build M Design F M Month A J Activity POM - J. Galván 25

Project Scheduling Techniques Gantt chart Critical Path Method (CPM) Program Evaluation & Review Technique (PERT) POM - J. Galván 27

Gantt Chart J F M A Time Period Activity Design Build Test 28 POM - J. Galván 28

Project Control Reports Detailed cost breakdowns for each task Total program labor curves Cost distribution tables Functional cost and hour summaries Raw materials and expenditure forecasts Variance reports Time analysis reports Work status reports POM - J. Galván 29

PERT and CPM Network techniques Developed in 1950’s CPM by DuPont for chemical plants PERT by U.S. Navy for Polaris missile Consider precedence relationships and interdependencies Each uses a different estimate of activity times POM - J. Galván 30

Questions Which May Be Addressed by PERT & CPM Is the project on schedule, ahead of schedule, or behind schedule? Is the project over or under cost budget? Are there enough resources available to finish the project on time? If the project must be finished in less than the scheduled amount of time, what is the way to accomplish this at least cost? POM - J. Galván 31

The Six Steps Common to PERT & CPM Define the project and all of its significant activities or tasks Develop relationships among the activities. (Decide which activities must precede and which must follow others.) Draw the network connecting all of the activities Assign time and cost estimates to each activity Compute the longest time path through the network. This is called the critical path Use the network to help plan, schedule, monitor, and control the project POM - J. Galván 32

2 1 Network Terms Project: Obtain a college degree (B.S.) 4 Years Activity (Arrow) Register Receive diploma Project: Obtain a college degree (B.S.) Event (Node) Attend class, study etc. 1 POM - J. Galván 33

Activity Relationships 1 A B A & B can occur concurrently 2 3 POM - J. Galván 34

Activity Relationships 1 4 2 3 A B C A must be done before C & D can begin D POM - J. Galván 35

Activity Relationships 1 4 2 3 A B E C B & C must be done before E can begin D POM - J. Galván 36

Dummy Activities Activities are defined often by beginning & ending events Example: Activity 2-3 Every activity must have unique pair of beginning & ending events Otherwise, computer programs get confused Dummy activities maintain precedence Consume no time or resources POM - J. Galván 37

Dummy Activity Example 1 4 3 1-2 2-3 Incorrect 2 5 3-4 2-4 4-5 3-4: Dummy activity Correct POM - J. Galván 38

·¸¹ PERT Activity Times 3 time estimates Follow beta distribution Optimistic times (a) Most-likely time (m) Pessimistic time (b) Follow beta distribution Expected time: t = (a + 4m + b)/6 Variance of times: v = (b - a)2/6 ·¸¹ POM - J. Galván 39

Critical Path Analysis Provides activity information Earliest (ES) & latest (LS) start Earliest (EF) & latest (LF) finish Slack (S): Allowable delay Identifies critical path Longest path in network Shortest time project can be completed Any delay on activities delays project Activities have 0 slack POM - J. Galván 40

Earliest Start and Finish Steps Begin at starting event & work forward ES = 0 for starting activities ES is earliest start EF = ES + Activity time EF is earliest finish ES = Maximum EF of all predecessors for non-starting activities POM - J. Galván 41

Latest Start and Finish Steps Begin at ending event & work backward LF = Maximum EF for ending activities LF is latest finish; EF is earliest finish LS = LF - Activity time LS is latest start LF = Minimum LS of all successors for non-ending activities POM - J. Galván 42

Critical Path in Network 1 4 2 3 Pour foundation & frame 3 wk. 4 wk. 2 wk. 6 wk. Do interior work Landscape Roof Buy shrubs etc. Critical path is longest path: 12 weeks. POM - J. Galván 43

Gantt Chart Earliest Start and Finish 1-2 Fdn & frame 1-3 Buy shrubs 2-3 Roof 2-4 Interior work 3-4 Landscape 4 5 6 7 8 9 1 2 3 Activity Build House Project POM - J. Galván 44

Gantt Chart Latest Start and Finish 1-2 Fdn & frame 1-3 Buy shrubs 2-3 Roof 2-4 Interior work 3-4 Landscape 4 5 6 7 8 9 1 2 3 Activity Build House Project POM - J. Galván 45

Project Times Expected project time (T) Project variance (V) Sum of critical path activity times, t Project variance (V) Sum of critical path activity variances, v Used to obtain probability of project completion! POM - J. Galván 46

An example St. Adolf’s Hospital setup POM - J. Galván

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. B Select site and do site survey. C Select equipment. D Prepare final construction plans and layout. E Bring utilities to the site. F Interview applicants and fill positions in nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. H Construct the hospital. I Develop an information system. J Install the equipment. K Train nurses and support staff. The first step is to create the list of activities and the required predecessors. POM - J. Galván 10

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop an information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J POM - J. Galván Example 4.1 11

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Then a network can be drawn. In fact, this step is not strictly necessary for management purposes and large projects are very difficult to represent in this fashion. But it is helpful to visualize this small project in this way. This series builds Figure 4.2. This slide advances automatically. This entire sequence can be automated by selecting automatic advance for each slide and setting the desired delay. POM - J. Galván 12

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D E POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D E F POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D E F G POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D E F G H POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D E F G H I POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D E F G H I J POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network Start A B C D E F G H I J K POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J AON Network I A F K Start C G Finish B D H J E Figure 4.2 POM - J. Galván 24

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time On the network (AON) we can show the completion times for each activity. This slide advances automatically. POM - J. Galván 33

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish We start with the completed project as shown in Figure 4.4. J 4 Figure 4.4 POM - J. Galván 39

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish We can then trace all the possible paths through the project. This sequence is not shown in the text but can be a useful learning tool for students. J 4 POM - J. Galván 39

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish J 4 POM - J. Galván 39

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish J 4 POM - J. Galván 39

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish J 4 POM - J. Galván 39

St. Adolf’s Hospital Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish J 4 POM - J. Galván 39

St. Adolf’s Hospital Path Expected Time (wks) Immediate A-F-K 28 A-I-K 33 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43 Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish The path with the longest time, B-D-H-J-K, is the critical path. J 4 POM - J. Galván 39

St. Adolf’s Hospital Path Expected Time (wks) Immediate A-F-K 28 A-I-K 33 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43 Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time I 15 F 10 C D E 24 A 12 B 9 K 6 G 35 H 40 Start Finish This slide advances automatically. J 4 POM - J. Galván 39

St. Adolf’s Hospital Path Expected Time (wks) Immediate A-F-K 28 A-I-K 33 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43 Immediate Activity Description Predecessor(s) A Select administrative and medical staff. — B Select site and do site survey. — C Select equipment. A D Prepare final construction plans and layout. B E Bring utilities to the site. B F Interview applicants and fill positions in nursing, support staff, maintenance, and security. A G Purchase and take delivery of equipment. C H Construct the hospital. D I Develop and information system. A J Install the equipment. E,G,H K Train nurses and support staff. F,I,J Completion Time Finish Start K 6 I 15 F 10 C D E 24 G 35 H 40 J 4 A 12 B 9 This slide advances automatically. POM - J. Galván 39

St. Adolf’s Hospital Figure 4.5 This is Figure 4.5 from the Chapter which presents the same information as in the previous slide. This Figure is adapted from Microsoft Project output. Figure 4.5 POM - J. Galván 39

St. Adolf’s Hospital The next series of slides presents Example 4.2. The series builds in steps to the conclusion of the Example showing the development of key equations along the way. This slide advances automatically. POM - J. Galván 44

St. Adolf’s Hospital Earliest Start and Earliest Finish Times I 15 A 12 F 10 K 6 C 10 G 35 Start Finish We can calculate the earliest possible starting times and earliest possible finishing times for each activity. B 9 D 10 H 40 J 4 Earliest Start and Earliest Finish Times E 24 POM - J. Galván 45

St. Adolf’s Hospital Earliest Start and Earliest Finish Times 15 Earliest start time A 12 F 10 K 6 C 10 G 35 Start Finish B 9 D 10 H 40 J 4 Earliest Start and Earliest Finish Times E 24 POM - J. Galván 46

St. Adolf’s Hospital Earliest Start and Earliest Finish Times 15 Earliest finish time Earliest start time A 12 F 10 K 6 0 12 C 10 G 35 Start Finish B 9 D 10 H 40 J 4 Earliest Start and Earliest Finish Times E 24 POM - J. Galván 47

St. Adolf’s Hospital Earliest Start and Earliest Finish Times I 15 A 12 F 10 K 6 0 12 C 10 G 35 Start Finish B 9 D 10 H 40 J 4 0 9 Earliest Start and Earliest Finish Times E 24 POM - J. Galván 48

St. Adolf’s Hospital Earliest Start and Earliest Finish Times I 15 A 12 F 10 K 6 0 12 C 10 G 35 Start Finish The calculations must proceed through the network after earlier activities are calculated. For example, activity D can not start until activity B is complete. B 9 D 10 H 40 J 4 0 9 9 19 Earliest Start and Earliest Finish Times E 24 9 33 POM - J. Galván 49

St. Adolf’s Hospital Earliest Start and Earliest Finish Times I 15 A 12 27 A 12 F 10 K 6 0 12 12 22 C 10 G 35 12 22 Start Finish B 9 D 10 H 40 J 4 0 9 9 19 Earliest Start and Earliest Finish Times E 24 9 33 POM - J. Galván 50

St. Adolf’s Hospital Earliest Start and Earliest Finish Times I 15 A 12 27 A 12 F 10 K 6 0 12 12 22 C 10 G 35 12 22 Start Finish B 9 D 10 H 40 J 4 0 9 9 19 19 59 Earliest Start and Earliest Finish Times E 24 9 33 POM - J. Galván 51

St. Adolf’s Hospital Earliest Start and Earliest Finish Times I 15 A 12 27 A 12 F 10 K 6 0 12 12 22 C 10 G 35 12 22 22 57 Start Finish B 9 D 10 H 40 J 4 0 9 9 19 19 59 Earliest Start and Earliest Finish Times E 24 9 33 POM - J. Galván 52

St. Adolf’s Hospital Earliest Start and Earliest Finish Times I 15 A 12 27 A 12 F 10 K 6 0 12 12 22 C 10 G 35 12 22 22 57 Start Finish B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 Earliest Start and Earliest Finish Times E 24 9 33 Example 4.2 POM - J. Galván 53

St. Adolf’s Hospital Earliest Start and Earliest Finish Times Earliest start time Earliest finish time A 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 Critical path Start In this way ES and EF times can be completed for the entire network. Earliest Start and Earliest Finish Times POM - J. Galván 54

St. Adolf’s Hospital Latest Start and Latest Finish Times A 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 Start Finish In much the same fashion, late start and late finish times can be calculated working backward through the network. This is Example 4.3 in the text. This slide advances automatically. Latest Start and Latest Finish Times POM - J. Galván 55

St. Adolf’s Hospital Latest Start and Latest Finish Times Latest 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 Latest finish time Start Finish Latest Start and Latest Finish Times POM - J. Galván 56

St. Adolf’s Hospital Latest Start and Latest Finish Times Latest start 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 Latest start time finish Start Finish Latest Start and Latest Finish Times POM - J. Galván 57

St. Adolf’s Hospital Latest Start and Latest Finish Times A 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 48 63 53 63 Start Finish Latest Start and Latest Finish Times POM - J. Galván 58

St. Adolf’s Hospital Latest Start and Latest Finish Times A 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 48 63 53 63 24 59 35 59 Start Finish Latest Start and Latest Finish Times POM - J. Galván 59

St. Adolf’s Hospital Latest Start and Latest Finish Times A 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 48 63 53 63 14 24 24 59 35 59 Start Finish Latest Start and Latest Finish Times POM - J. Galván 60

St. Adolf’s Hospital Latest Start and Latest Finish Times 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 48 63 2 14 53 63 14 24 24 59 35 59 Earliest start time Earliest finish time Latest start time Latest finish time Critical path Finish Start Latest Start and Latest Finish Times POM - J. Galván 61

St. Adolf’s Hospital Gantt charts Figure 4.8 is a screen shot from Project showing a Gantt chart for Example 4.3. This slide advances automatically. POM - J. Galván 61

St. Adolf’s Hospital Gantt Charts Figure 4.8 is a screen shot from Project showing a Gantt chart for Example 4.3. POM - J. Galván 61

St. Adolf’s Hospital Activity Slack Analysis A 12 K 6 C 10 G 35 J 4 H 40 B 9 D E 24 0 12 I 15 F 12 27 12 22 63 69 22 57 59 63 19 59 9 33 0 9 9 19 48 63 2 14 53 63 14 24 24 59 35 59 Start Finish Having these sets of times it is possible to analyze slack for the network. This starts the presentation of Example 4.4. The series first shows the manual development of activity slack and then presents the screen shot of the Project output, Figure 4.9. This slide advances automatically. Activity Slack Analysis POM - J. Galván 62

St. Adolf’s Hospital Activity Slack Analysis Activity Slack I 15 A 12 12 27 48 63 A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity Slack Analysis E 24 9 33 35 59 POM - J. Galván 68

St. Adolf’s Hospital Activity Slack Analysis Activity Slack 15 12 27 48 63 Slack = LS – ES or Slack = LF – EF A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity Slack Analysis E 24 9 33 35 59 POM - J. Galván 68

St. Adolf’s Hospital Activity Slack Analysis Activity Slack 15 12 27 48 63 SlackK = 63 – 63 or SlackK = 69 – 69 A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 Using either the ES/LS or EF/LF pairs results in the same analysis. B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity Slack Analysis E 24 9 33 35 59 POM - J. Galván 68

St. Adolf’s Hospital Activity Slack Analysis Activity Slack SlackK = 0 15 12 27 48 63 SlackK = 0 or A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity Slack Analysis E 24 9 33 35 59 POM - J. Galván 68

St. Adolf’s Hospital Activity Slack Analysis I 15 A 12 F 10 K 6 C 10 G 12 27 48 63 A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 This slide advances automatically. B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity Slack Analysis E 24 9 33 35 59 POM - J. Galván 68

St. Adolf’s Hospital Activity Slack Analysis Node Duration ES LS Slack 15 12 27 48 63 A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 Completing the analysis for the entire network, these are the results. B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity Slack Analysis E 24 9 33 35 59 POM - J. Galván 68

St. Adolf’s Hospital Activity Slack Analysis Node Duration ES LS Slack B 9 0 0 0 C 10 12 14 2 D 10 9 9 0 E 24 9 35 26 F 10 12 53 41 G 35 22 24 2 H 40 19 19 0 I 15 12 48 36 J 4 59 59 0 K 6 63 63 0 I 15 12 27 48 63 A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 Activity Slack Analysis E 24 9 33 35 59 POM - J. Galván 68

St. Adolf’s Hospital Critical Path Node Duration ES LS Slack B 9 0 0 0 C 10 12 14 2 D 10 9 9 0 E 24 9 35 26 F 10 12 53 41 G 35 22 24 2 H 40 19 19 0 I 15 12 48 36 J 4 59 59 0 K 6 63 63 0 I 15 12 27 48 63 F 10 K 6 12 22 63 69 53 63 63 69 C 10 G 35 12 22 22 57 Finish 14 24 24 59 The critical path will be the path with zero slack. B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 E 24 Critical Path 9 33 35 59 POM - J. Galván 69

St. Adolf’s Hospital Critical Path I 15 A 12 F 10 K 6 C 10 G 35 Start 12 27 48 63 A 12 F 10 K 6 0 12 12 22 63 69 2 14 53 63 63 69 C 10 G 35 12 22 22 57 Start Finish 14 24 24 59 B 9 D 10 H 40 J 4 0 9 9 19 19 59 59 63 0 9 9 19 19 59 59 63 E 24 Critical Path 9 33 35 59 POM - J. Galván 69

St. Adolf’s Hospital This slide advances automatically. POM - J. Galván 69

St. Adolf’s Hospital Activity Slack POM - J. Galván 69

St. Adolf’s Hospital The next series of slides presents Figure 4.10. The series builds in steps to the final Figure. This slide advances automatically. POM - J. Galván 89

St. Adolf’s Hospital Cost-Time Relationships in Cost Analysis 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) | | | | | | 5 6 7 8 9 10 11 Time (weeks) This slide advances automatically. POM - J. Galván 93

St. Adolf’s Hospital Cost-Time Relationships in Cost Analysis 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) Crash cost (CC) Normal cost (NC) | | | | | | 5 6 7 8 9 10 11 Time (weeks) (Crash time) (Normal time) POM - J. Galván 93

St. Adolf’s Hospital Cost-Time Relationships in Cost Analysis 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) Crash cost (CC) Linear cost assumption Normal cost (NC) | | | | | | 5 6 7 8 9 10 11 Time (weeks) (Crash time) (Normal time) POM - J. Galván 93

St. Adolf’s Hospital Cost-Time Relationships in Cost Analysis 8000 — 7000 — 6000 — 5000 — 4000 — 3000 — 0 — Direct cost (dollars) 5200 Crash cost (CC) Linear cost assumption Normal cost (NC) Estimated costs for a 2-week reduction, from 10 weeks to 8 weeks | | | | | | 5 6 7 8 9 10 11 Time (weeks) (Crash time) (Normal time) POM - J. Galván 93

St. Adolf’s Hospital The next series of slides presents Table 4.1. This slide advances automatically. POM - J. Galván 94

St. Adolf’s Hospital Maximum Normal Normal Crash Crash Time Cost of Time Cost Time Cost Reduction Crashing per Activity (NT) (NC) (CT) (CC) (wk) Week A 12 $ 12,000 11 $ 13,000 1 $ 1,000 B 9 50,000 7 64,000 2 7,000 C 10 4,000 5 7,000 5 600 D 10 16,000 8 20,000 2 2,000 E 24 120,000 14 200,000 10 8,000 F 10 10,000 6 16,000 4 1,500 G 35 500,000 25 530,000 10 3,000 H 40 1,200,000 35 1,260,000 5 12,000 I 15 40,000 10 52,500 5 2,500 J 4 10,000 1 13,000 2 1,000 K 6 30,000 5 34,000 1 4,000 Totals $1,992,000 $2,209,000 This slide presents Table 4.1 with all the necessary cost data. POM - J. Galván 94

St. Adolf’s Hospital The next series of slides presents Example 4.5. The series builds in steps to the conclusion of the Example showing the development of key equations along the way. This slide advances automatically. POM - J. Galván 94

St. Adolf’s Hospital Minimum-Cost Schedule Total cost = $2,624,000 A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This is the basic data for the Example. POM - J. Galván 95

St. Adolf’s Hospital Minimum-Cost Schedule Total cost = $2,624,000 A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 These three paths are discarded as they can never become critical paths. POM - J. Galván 96

St. Adolf’s Hospital Minimum-Cost Schedule Total cost = $2,624,000 A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Activity J is the cheapest to crash so we start there. Critical Path B-D-H-J-K: 69 weeks Crash Activity J by 3 weeks @ $1,000/week POM - J. Galván 97

St. Adolf’s Hospital Minimum-Cost Schedule Total cost = $2,624,000 A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This slide advances automatically. Critical Path B-D-H-J-K: 69 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) – 3($1,000) = $81,000 POM - J. Galván 98

St. Adolf’s Hospital Minimum-Cost Schedule Total cost = $2,624,000 A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Path B-D-H-J-K: 66 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) – 3($1,000) = $81,000 $2,624,000 – $81,000 = $2,543,000 POM - J. Galván 99

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,543,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This reduces the total cost of the project by $81,000. Critical Path B-D-H-J-K: 66 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) – 3($1,000) = $81,000 $2,624,000 – $81,000 = $2,543,000 POM - J. Galván 100

St. Adolf’s Hospital Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,543,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Path B-D-H-J-K: 69 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) – 3($1,000) = $81,000 $2,624,000 – $81,000 = $2,543,000 Finish Start A 12 B 9 C 10 D E 24 F G 35 H 40 I 15 J 1 K 6 This slide advances automatically. POM - J. Galván 101

St. Adolf’s Hospital Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,543,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Path B-D-H-J-K: 69 weeks Crash Activity J by 3 weeks @ $1,000/week 3($28,000) – 3($1,000) = $81,000 $2,624,000 – $81,000 = $2,543,000 Finish Start A 12 B 9 C 10 D E 24 F G 35 H 40 I 15 J 1 K 6 The critical path remains unchanged. POM - J. Galván 101

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,543,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 The next activity to crash is Activity D. Critical Path B-D-H-J-K: 66 weeks Crash Activity D by 2 weeks @ $2,000/week POM - J. Galván 103

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,543,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This slide advances automatically. Critical Path B-D-H-J-K: 66 weeks Crash Activity D by 2 weeks @ $2,000/week $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 104

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This results in a further savings of $32,000. Critical Path B-D-H-J-K: 64 weeks Crash Activity D by 2 weeks @ $2,000/week $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 105

St. Adolf’s Hospital Minimum Cost Schedule Finish Start A 12 B 9 C 10 D E 24 F G 35 H 40 I 15 J 1 K 6 Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This slide advances automatically. Critical Path B-D-H-J-K: 69 weeks Crash Activity D by 2 weeks @ $2,000/week $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 106

St. Adolf’s Hospital Minimum Cost Schedule 15 Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks A 12 F 10 K 6 Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 C 10 G 35 Start Finish B 9 D 8 H 40 J 1 Critical Path B-D-H-J-K: 69 weeks Crash Activity D by 2 weeks @ $2,000/week E 24 $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 106

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Activity K is the next one to crash. Critical Paths B-D-H-J-K and A-C-G-J-K: 64 weeks Crash Activity K by 1 week @ $4,000/week POM - J. Galván 109

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This slide advances automatically. Critical Paths B-D-H-J-K and A-C-G-J-K: 64 weeks Crash Activity K by 1 week @ $4,000/week $8,000 – $4,000 = $4,000 $2,511,000 – $4,000 = $2,507,000 POM - J. Galván 110

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,507,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This results in a further savings of $4,000. Critical Paths B-D-H-J-K and A-C-G-J-K: 63 weeks Crash Activity K by 1 week @ $4,000/week $8,000 – $4,000 = $4,000 $2,511,000 – $4,000 = $2,507,000 POM - J. Galván 111

St. Adolf’s Hospital Minimum Cost Schedule 15 Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks A 12 F 10 K 6 Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 C 10 G 35 Start Finish B 9 D 8 H 40 J 1 This slide advances automatically. Critical Path B-D-H-J-K: 69 weeks Crash Activity D by 2 weeks @ $2,000/week E 24 $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 106

St. Adolf’s Hospital Minimum Cost Schedule 15 Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks A 12 F 10 K 5 Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 C 10 G 35 Start Finish B 9 D 8 H 40 J 1 Critical Path B-D-H-J-K: 69 weeks Crash Activity D by 2 weeks @ $2,000/week E 24 $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 106

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,507,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Critical Paths B-D-H-J-K and A-C-G-J-K: 63 weeks Crash Activities B and C by 2 weeks @ $7,000/week and $600/week POM - J. Galván 114

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,507,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 This slide advances automatically. Critical Paths B-D-H-J-K and A-C-G-J-K: 63 weeks Crash Activities B and C by 2 weeks @ $7,000/week and $600/week 2($8,000) – 2($7,600) = $800 $2,507,000 – $800 = $2,506,200 POM - J. Galván 115

St. Adolf’s Hospital Minimum-Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks Total cost = $2,624,000 $2,506,200 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 Crashing Activities B and C results in a savings of $800. Both must be crashed as they occur at the same time in the network. Critical Paths B-D-H-J-K and A-C-G-J-K: 61 weeks Crash Activities B and C by 2 weeks @ $7,000/week and $600/week 2($8,000) – 2($7,600) = $800 $2,507,000 – $800 = $2,506,200 POM - J. Galván 116

St. Adolf’s Hospital Minimum Cost Schedule 15 Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks A 12 F 10 K 5 Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 C 10 G 35 Start Finish B 9 D 8 H 40 J 1 This slide advances automatically. Critical Path B-D-H-J-K: 69 weeks Crash Activity D by 2 weeks @ $2,000/week E 24 $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 106

St. Adolf’s Hospital Minimum Cost Schedule 15 Minimum Cost Schedule A-I-K: 33 weeks B-D-H-J-K: 69 weeks A-F-K: 28 weeks B-E-J-K: 43 weeks A-C-G-J-K: 67 weeks A 12 F 10 K 5 Total cost = $2,624,000 $2,511,000 Indirect costs = $8,000/week Penalty cost = $20,000/week after week 65 C 8 G 35 Start Finish B 7 D 8 H 40 J 1 Critical Path B-D-H-J-K: 69 weeks Crash Activity D by 2 weeks @ $2,000/week E 24 $28,000 + $8,000 – 2($2,000) = $32,000 $2,543,000 – $32,000 = $2,511,000 POM - J. Galván 106

St. Adolf’s Hospital Probabilistic Time Estimates A F I C G Finish D E J K Start The next series of slides presents Example 4.6. The series builds in steps to the conclusion of the Example showing the development of key equations along the way. This slide advances automatically. POM - J. Galván 74

St. Adolf’s Hospital Probabilistic Time Estimates Activity B Most G Finish D E H B J K Start Activity B Most Optimistic Likely Pessimistic (a) (m) (b) 7 8 15 Often referred to as the PERT technique, the use of probabilistic time estimates allows for additional analysis of the project network. POM - J. Galván 75

St. Adolf’s Hospital te = = 9 weeks Probabilistic Time Estimates G Finish D E H B J K Start Activity B Most Optimistic Likely Pessimistic (a) (m) (b) 7 8 15 te = = 9 weeks 7 + 4(8) + 15 6 POM - J. Galván 76

( ) St. Adolf’s Hospital te = = 9 weeks 2 = = 1.78 Probabilistic Time Estimates A F I C G Finish D E H B J K Start Activity B Most Optimistic Likely Pessimistic (a) (m) (b) 7 8 15 te = = 9 weeks 7 + 4(8) + 15 6 2 = = 1.78 ( ) 15 - 7 6 2 POM - J. Galván 77

St. Adolf’s Hospital Time Estimates (wk) Activity Statistics Optimistic Likely Pessimistic Expected Variance Activity (a) (m) (b) Time (te ) (2 ) Time Estimates (wk) Activity Statistics We can develop these estimates for the entire network. This slide advances automatically. POM - J. Galván 78

St. Adolf’s Hospital Time Estimates (wk) Activity Statistics Optimistic Likely Pessimistic Expected Variance Activity (a) (m) (b) Time (te ) (2 ) Time Estimates (wk) Activity Statistics A 11 12 13 12 0.11 B 7 8 15 9 1.78 C 5 10 15 10 2.78 D 8 9 16 10 1.78 E 14 25 30 24 7.11 F 6 9 18 10 4.00 G 25 36 41 35 7.11 H 35 40 45 40 2.78 I 10 13 28 15 9.00 J 1 2 15 4 5.44 K 5 6 7 6 0.11 This table shows all the expected task times and variances for use in the probabilistic calculations. POM - J. Galván 79

St. Adolf’s Hospital Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days The next series of slides presents Example 4.7. POM - J. Galván 80

St. Adolf’s Hospital T –TE 2 =  (variances of activities) 2 Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days 2 =  (variances of activities) z = T –TE 2 The objective is to find the probability of completing the project in 72 weeks. POM - J. Galván 81

St. Adolf’s Hospital T – TE 2 =  (variances of activities) 2 Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days 2 =  (variances of activities) z = T – TE 2 2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 POM - J. Galván 82

St. Adolf’s Hospital T – TE 2 =  (variances of activities) 2 Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days 2 =  (variances of activities) z = T – TE 2 This slide advances automatically. 2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z = 72 – 69 11.89 POM - J. Galván 83

St. Adolf’s Hospital T – TE 2 =  (variances of activities) 2 Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days 2 =  (variances of activities) z = T – TE 2 2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z = = 0.87 72 – 69 11.89 POM - J. Galván 84

St. Adolf’s Hospital T – TE 2 =  (variances of activities) 2 Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days 2 =  (variances of activities) z = T – TE 2 2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z = = 0.87 72 – 69 11.89 From Appendix 2 Pz = .8078  .81 POM - J. Galván 85

St. Adolf’s Hospital T - TE 2 =  (variances of activities) 2 Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days Normal distribution: Mean = 69 weeks;  = 3.45 weeks Length of critical path 2 =  (variances of activities) z = T - TE 2 Probability of meeting the schedule is 0.8078 Probability of exceeding 72 weeks is 0.1922 Here Figure 18.9 is overlaid to illustrate the current analysis. 2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89 z = = 0.87 72 - 69 11.89 69 72 Project duration (weeks) Figure 4.12 POM - J. Galván 86

St. Adolf’s Hospital T – TE 2 =  (variances of activities) 2 Probabilities Path = A - C - G - J - K T = 72 days TE = 67 days 2 =  (variances of activities) z = T – TE 2 2 = 0.11 + 2.78 + 7.11 + 5.44 + 0.11 = 15.55 z = = 1.27 72 – 67 15.55 From Appendix 2 Pz = .8980  .90 POM - J. Galván 87

St. Adolf’s Hospital A F I C G Finish D E H B J K Start This series of slides present Table 4.2 from the text showing the slack calculations after Activities A and B have been completed with longer than expected times. POM - J. Galván 87

St. Adolf’s Hospital Activity Duration Earliest Start Latest Start Slack C 10 16 14 –2 G 35 26 24 –2 J 4 61 59 –2 K 6 65 63 –2 D 10 10 9 –1 H 40 20 19 –1 E 24 10 35 25 I 15 16 48 32 F 10 16 53 37 This slide presents Table 4.2 from the text showing the slack calculations after Activities A and B have been completed. The longer completion times have results in negative slack for some tasks. POM - J. Galván 87

Project Life Cycle The next series of slides presents Figure 4.13. This slide advances automatically. POM - J. Galván 70

Project Life Cycle Resource requirements Start Finish Time This slide adds the coordinate system. This slide advances automatically. POM - J. Galván 70

Definition and organization Project Life Cycle Definition and organization Planning Execution Close out Start Finish Resource requirements Time This is the complete Figure 4.13. Figure 4.13 POM - J. Galván 70