Project Scheduling Start A A Elimam Finish Project

Project Scheduling Start A. A. Elimam Finish

Project Scheduling Need to plan and control large/time consuming projects

Projects Characteristics n Projects are unique n Time Estimation Difficulty n Control • Decomposition into smaller tasks • Responsibility of a task given to a specific individual

Project Management: Stages 1. 2. 3. Define: Describe goal or Final outcome of Project Plan: Identify tasks / resources / time Execute / Control: Time-cost Trade-off

Activity The smallest unit of work effort consuming both time and resources that the project manager can schedule and control.

Precedence Relationship A sequencing constraint between interrelated activities by which one activity cannot start until a preceeding activity has been completed.

Schedule A plan that sets priorities, determines start and finish times, and allocates resources to accomplish the activities.

Examples 1. Constructing a building or amusement park 2. Constructing a road, dam, or oil pipeline 3. Renovating a blighted urban area 4. Developing a prototype for a new airplane 5. Installing a large computer system 6. Introducing a new product 7. Organizing a state fair

Measuring Success of a project Conformance Time Budget

Basic Questions 1. 2. 3. Project completion time? Critical activities? Activities that can be delayed? How Long? 4. Starting / ending time of each activity? 5. Range of $’s spent on project? 6. Time-cost trade-off

Project Management Basic Steps i. Describe project ii. Draw a network diagram iii. Provide time estimates iv. Analyze network v. Develop project plan vi. Update project plan

i. Describe project n n Activities / precedence end points

ii. Draw a network diagram n AOA: Arcs: Activities Nodes: Event n AON: Nodes: Activities Arcs: Sequence

AOA and AON relationships Event 1 Activity A 3 Event 2 Event C Event A Activity 4 Activity C B B (a) AOA approach: Event 4 cannot (b) AON approach: Activity C take place until activities A, B and cannot take place until C have been completed. activities A and B completed. Implies time and resource consumption Software

Activity Relationships Activity Relationship AOA AON

Activity Relationships Activity Relationship S precedes T, which precedes U. AOA 1 S 2 T AON 3 U 4 S T U

Activity Relationships Activity Relationship S and T must be completed before U can be started. AOA 1 2 S S T AON 3 U 4 U T

Activity Relationships Activity Relationship T and U cannot begin until S has been completed. AOA 1 S AON T 2 3 T S U 4 U

Activity Relationships Activity Relationship U and V cannot begin until both S and T have been completed. AOA 1 S T 2 U 3 AON 4 S U 5 T V V

Activity Relationships Activity Relationship U cannot begin until both S and T have been completed; V cannot begin until T has been completed. AOA 1 2 S T 3 4 U Dummy V AON 5 S U 6 T V

Activity Relationships Activity Relationship T and U cannot begin until S has been completed; V cannot begin until both T and U have been completed. AOA 1 S 2 T Dummy AON 4 V 5 S T U 3 U V

iii. Provide Time Estimates n Deterministic CPM Critical Path Method or n Probabilistic PERT Program Evaluation and Review Technique then CPM

iv. Analyze Network n Identify critical path (CP) and activities on it n Estimate probability of completing project on time n Explore time-cost trade-off

v. Develop project plan n Schedule each activity (particularly on CP) n Monitor actual planned.

vi. Update project plan n Adjust schedule on the basis of actuals

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

St. Adolf’s Hospital I 12 27 48 1563 0 A 12 12 F 12 Start 63 63 12 22 53 1063 C 22 22 10 0 Latest Start and Latest Finish Times B 9 9 9 D 19 10 9 E 33 24 K 69 6 69 G 57 Finish 35 19 H 59 40 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 A 12 12 F 12 Start C 22 10 0 Latest Start and Latest Finish Times B 9 9 63 63 12 22 53 1063 9 D 19 10 9 E 33 35 2459 K 69 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 A 12 12 F C 12 22 14 1024 Start 0 Latest Start and Latest Finish Times B 9 9 63 63 12 22 53 1063 D 9 19 9 1019 9 E 33 35 2459 K 69 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 2 A 12 1214 F C 12 22 14 1024 Start 0 0 Latest Start and Latest Finish Times B 9 9 9 63 63 12 22 53 1063 D 9 19 9 1019 9 E 33 35 2459 K 69 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 2 A 12 1214 F C 12 22 14 1024 Start 0 0 Activity Slack Analysis B 9 9 9 63 63 12 22 53 1063 D 9 19 9 1019 9 E 33 35 2459 K 69 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 2 A 12 1214 F C 0 0 Activity Slack Analysis B 9 9 9 63 63 12 22 53 1063 12 22 14 1024 Start LS - ES = S D 9 19 9 1019 9 E 33 35 2459 K 69 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 2 A 12 1214 F C 0 0 Activity Slack Analysis B 9 9 9 63 63 12 22 53 1063 12 22 14 1024 Start LS - ES = S 63 - 63 = 0 D 9 19 9 1019 9 E 33 35 2459 K 69 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 2 A 12 1214 F C 0 0 Activity Slack Analysis B 9 9 9 63 63 12 22 53 1063 12 22 14 1024 Start LF - EF = S 69 - 69 = 0 D 9 19 9 1019 9 E 33 35 2459 K 69 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 2 A 12 F 22 12 K 69 63 1214 53 1063 63 C 12 22 14 1024 Start 0 0 Activity Slack Analysis B 9 9 9 D 9 19 9 1019 9 E 33 35 2459 0 6 69 G 22 57 24 3559 H 19 59 19 4059 Finish 59 59 J 63 4 63

St. Adolf’s Hospital I 12 27 48 1563 0 2 A 12 F 22 12 K 69 63 1214 53 1063 63 C 0 0 Activity Slack Analysis B 9 9 9 0 D 19 9 9 1019 9 E 33 35 2459 6 69 G 12 22 14 1024 Start 0 22 57 24 3559 0 H 59 19 19 4059 Finish 0 J 63 59 59 4 63 0

St. Adolf’s Hospital I 12 27 48 1563 36 A 12 F 22 12 41 1214 53 1063 2 0 2 C 22 12 Start 0 0 Activity Slack Analysis 63 2 9 9 0 D 19 9 9 1019 9 E 33 35 2459 G 57 22 0 6 69 2 Finish 24 3559 14 1024 B 9 K 69 63 0 H 59 19 19 4059 26 0 J 63 59 59 4 63 0

St. Adolf’s Hospital I 12 27 48 1563 36 A 12 F 22 12 41 1214 53 1063 2 0 2 C 22 12 Start 0 0 Critical Path 63 2 9 9 0 D 19 9 9 1019 9 E 33 35 2459 G 57 22 0 6 69 2 Finish 24 3559 14 1024 B 9 K 69 63 0 H 59 19 19 4059 26 0 J 63 59 59 4 63 0

Probabilistic Time Estimates

Probability Probabilistic Time Estimates Time

Probability Probabilistic Time Estimates a m b Mean Time

Probability Probabilistic Time Estimates 3 s a Time 3 s m Mean b

St. Adolf’s Hospital Probabilistic Time Estimates I A Start B F K C G D H E Finish J

St. Adolf’s Hospital Probabilistic Time Estimates I A Activity B Most Optimistic Likely Pessimistic (a) (m) (b) 7 8 15 Start B F K C G D H E Finish J

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

St. Adolf’s Hospital Probabilistic Time Estimates I A Activity B Most Optimistic Likely Pessimistic (a) (m) (b) 7 8 15 te = 7 + 4(8) + 15 = 9 weeks 6 2 = ( ) 2 15 - 7 = 1. 78 6 Start B F K C G D H E Finish J

I A St. Adolf’s Hospital Time Estimates (wk) Optimistic Activity (a) Likely (m) Pessimistic (b) Start B F C G D H E Activity Statistics Expected Variance Time (te ) ( 2 ) K Finish J

I A St. Adolf’s Hospital Time Estimates (wk) Optimistic Activity (a) A B C D E F G H I J K 11 7 5 8 14 6 25 35 10 1 5 Likely (m) Pessimistic (b) 12 8 10 9 25 9 36 40 13 2 6 13 15 15 16 30 18 41 45 28 15 7 Start B F C G D H E Activity Statistics Expected Variance Time (te ) ( 2 ) 12 9 10 10 24 10 35 40 15 4 6 0. 11 1. 78 2. 78 1. 78 7. 11 4. 00 7. 11 2. 78 9. 00 5. 44 0. 11 K Finish J

I A St. Adolf’s Hospital Probabilities Critical Path = B - D - H - J - K T = 72 days TE = 69 days Start B F K C G D H E Finish J

I A St. Adolf’s Hospital Start B Critical Path = B - D - H - J - K 2 TE = 69 days = (variances of activities) T - TE z= 2 K C G D H E Probabilities T = 72 days F Finish J

I A St. Adolf’s Hospital Start B Critical Path = B - D - H - J - K 2 TE = 69 days = (variances of activities) T - TE z= 2 2 = 1. 78 + 2. 78 + 5. 44 + 0. 11 = 11. 89 K C G D H E Probabilities T = 72 days F Finish J

I A St. Adolf’s Hospital Start B Critical Path = B - D - H - J - K 2 TE = 69 days = (variances of activities) T - TE z= 2 2 = 1. 78 + 2. 78 + 5. 44 + 0. 11 = 11. 89 z= 72 - 69 11. 89 K C G D H E Probabilities T = 72 days F Finish J

I A St. Adolf’s Hospital Start B Critical Path = B - D - H - J - K 2 TE = 69 days = (variances of activities) T - TE z= 2 2 = 1. 78 + 2. 78 + 5. 44 + 0. 11 = 11. 89 z= 72 - 69 = 0. 87 11. 89 K C G D H E Probabilities T = 72 days F Finish J

I A St. Adolf’s Hospital Start B Critical Path = B - D - H - J - K 2 TE = 69 days = (variances of activities) T - TE z= 2 2 = 1. 78 + 2. 78 + 5. 44 + 0. 11 = 11. 89 z= 72 - 69 = 0. 87 11. 89 From Appendix 2 Pz =. 8078 . 81 K C G D H E Probabilities T = 72 days F Finish J

I A St. Adolf’s Hospital Start B Length of critical path Probability of meeting the schedule is 0. 8078 Probability of exceeding 72 weeks is 0. 1922 72 Project duration (weeks) K C G D H E Normal distribution: Mean = 69 weeks; = 3. 45 weeks 69 F Finish J

I A St. Adolf’s Hospital Start B Path = A - C - G - J - K 2 TE = 67 days = (variances of activities) T - TE z= 2 2 = 0. 11 + 2. 78 + 7. 11 + 5. 44 + 0. 11 = 15. 55 z= 72 - 67 = 1. 27 15. 55 From Appendix 2 Pz =. 8980 . 90 K C G D H E Probabilities T = 72 days F Finish J

I A St. Adolf’s Hospital Start B F K C G D H E Normal distribution for path B-D-H-J-K: Mean = 69 weeks; = 3. 45 weeks Normal distribution for path A-C-G-J-K: Mean = 67 weeks; = 3. 94 weeks Probability path A -C-G-J-K is more than 69 weeks Probability path BD-H-J-K is less than 67 weeks 67 69 Project duration (weeks) Finish J

I A St. Adolf’s Hospital Start B Direct cost (dollars) 7000 — 6000 — 5000 — 4000 — 3000 — | 5 | 6 | 7 8 | 9 | 10 | 11 K C G D H E 8000 — 0— F Finish J

I A St. Adolf’s Hospital Start B Direct cost (dollars) Crash cost (CC) 7000 — 6000 — 5000 — 4000 — Normal cost (NC) 0— | 5 | 6 (Crash time) | 7 8 | 9 | 10 | 11 (Normal time) Time (weeks) K C G D H E 8000 — 3000 — F Finish J

I A St. Adolf’s Hospital Start B Direct cost (dollars) Crash cost (CC) Linear cost assumption 6000 — 5000 — 4000 — Normal cost (NC) 3000 — 0— | 5 | 6 (Crash time) | 7 8 | 9 | 10 | 11 (Normal time) Time (weeks) K C G D H E 8000 — 7000 — F Finish J

I A St. Adolf’s Hospital Start B F C G D H E 8000 — Direct cost (dollars) Crash cost (CC) 7000 — Linear cost assumption 6000 — 5200 5000 — Estimated costs for a 2 -week reduction, from 10 weeks to 8 weeks 4000 — Normal cost (NC) 3000 — 0— | 5 | 6 (Crash time) | 7 8 | 9 | 10 | 11 (Normal time) Time (weeks) K Finish J

I A St. Adolf’s Hospital Start B 33 weeks 28 weeks 67 weeks B-D-H-J-K: B-E-J-K: 69 weeks 43 weeks Total cost = $2, 624, 000 Indirect costs = $8, 000/week Penalty cost = $20, 000/week after week 65 K C G D H E Minimum Cost Schedule A-I-K: A-F-K: A-C-G-J-K: F Finish J

I A St. Adolf’s Hospital Start B 33 weeks 28 weeks 67 weeks B-D-H-J-K: B-E-J-K: 69 weeks 43 weeks Total cost = $2, 624, 000 Indirect costs = $8, 000/week Penalty cost = $20, 000/week after week 65 K C G D H E Minimum Cost Schedule A-I-K: A-F-K: A-C-G-J-K: F Finish J

I A St. Adolf’s Hospital Start B 33 weeks 28 weeks 67 weeks B-D-H-J-K: B-E-J-K: 69 weeks 43 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: 69 weeks Crash Activity J by 3 weeks @ $1, 000/week K C G D H E Minimum Cost Schedule A-I-K: A-F-K: A-C-G-J-K: F Finish J

I A St. Adolf’s Hospital Start B 33 weeks 28 weeks 67 weeks B-D-H-J-K: B-E-J-K: 69 weeks 43 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: 69 weeks Crash Activity J by 3 weeks @ $1, 000/week 3($28, 000) - 3($1, 000) = $81, 000 K C G D H E Minimum Cost Schedule A-I-K: A-F-K: A-C-G-J-K: F Finish J

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

I A St. Adolf’s Hospital Start B 33 weeks 28 weeks 67 weeks B-D-H-J-K: B-E-J-K: 69 weeks 43 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: 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 K C G D H E Minimum Cost Schedule A-I-K: A-F-K: A-C-G-J-K: F Finish J

I A St. Adolf’s Hospital 36 Start I 27 B 12 48 1563 2 0 2 F A 12 12 22 53 10 63 12 14 C 12 22 14 10 24 Start 0 0 B 9 9 9 0 D 19 9 9 10 19 9 E 33 35 2459 63 63 K 69 G D H Finish J 6 69 2 G 0 Finish H 59 19 J 63 59 19 40 59 59 4 63 26 C 0 22 57 24 35 59 0 K E 41 2 F 0

Precedence for Playground activities Code Activity Name A Planning Find location, determine resource requirements 20 None Purchasing Requisition lumber and sand 60 Planning (A) Excavation Dig and grade 100 Planning (A) Sawing Saw lumber into appropriate sizes 30 Purchasing (B) Placement Position lumber in correct locations 20 Sawing, excavation (D, C) Assembly Nail lumber together` 10 Placement (E) Infill Put sand in and under equipment 20 Assembly (F) Outfill Put dirt around equipment 10 Assembly( F) Decoration Landscape, paint 30 Infill, outfill (G, H) B C D E F G H I Description (days) Time Immediate Predecessors

Playground Project B Purchasing D Sawing A Planning E Placement C Excavation G Infill I Decoration F Assembly H Outfill

Playground Project A Planning ES=0 EF=20 B Purchasing D Sawing ES=20 EF=80 ES=80 EF=110 C Excavation Two pass approach E Placement ES=120 EF=140 F Assembly ES=140 EF=150 ES=20 EF=120 G Infill ES=150 EF=170 H Outfill ES=150 EF=160 Forward Pass I Decoration ES=170 EF=200

Playground Project B Purchasing A Planning ES=0 EF=20 LS=0 ES=20 EF=80 LF=90 LS=30 D Sawing ES=80 EF=110 E LF=120 LS=90 Placement C Excavation ES=20 EF=120 LS=20 Two pass approach ES=120 EF=140 LS=120 F Assembly ES=140 EF=150 LS=140 Backward Pass G Infill ES=150 EF=170 LS=150 H Outfill ES=150 EF=160 LF=170 LS=160 I Decoration ES=170 EF=200 LS=170

Playground Project B Purchasing A Planning ES=0 EF=20 LS=0 SA=0 ES=20 EF=80 LF=90 LS=30 SB=10 D Sawing ES=80 EF=110 E LF=120 LS=90 Placement SD=10 C Excavation ES=20 EF=120 LS=20 SC=0 Two pass approach ES=120 EF=140 LS=120 SE=0 F Assembly ES=140 EF=150 LS=140 SF=0 G Infill ES=150 EF=170 LS=150 SG=0 H Outfill ES=150 EF=160 LF=170 LS=160 SH=10 I Decoration ES=170 EF=200 LS=170 SI=0

Playground Project B Purchasing A Planning ES=0 EF=20 LS=0 SA=0 ES=20 EF=80 LF=90 LS=30 SB=10 D Sawing ES=80 EF=110 E LF=120 LS=90 Placement SD=10 C Excavation ES=20 EF=120 LS=20 SC=0 Critical Path ES=120 EF=140 LS=120 SE=0 F Assembly ES=140 EF=150 LS=140 SF=0 G Infill ES=150 EF=170 LS=150 SG=0 H Outfill ES=150 EF=160 LF=170 LS=160 SH=10 I Decoration ES=170 EF=200 LS=170 SI=0

Total direct activity cost ($) Cost-time relationships analysis Cost to crash per week = CC - NC NT - CT Linear cost assumption CC CT Crash time, cost 8, 000 7, 000 6, 000 Estimated costs for a 2 -week reduction 5, 000 4, 000 3, 000 Normal time, cost NC NT Hypothetical actual cost curve 5 6 7 8 9 10 11 Activity time duration (weeks)

Limitations of PERT / CPM n n n project activities must be clearly defined, independent, and stable in their relationships precedence relationships must be specified and networked together time activities in PERT are assumed to follow the beta probability distribution this may be difficult to verify time estimates tend to be subjective, and are subject to fudging by managers there is inherent danger in too much emphasis being placed on the critical path

Resource Limitations 2 B Workers required per day Activity time in days 5 Start 5 6 3 A D E 1 3 3 4 C 2 Finish

Resource Limitations Gantt Charts Day Activity A B C D E Resource Requirements 1 2 3 4 5 6 7 8 9 10 11 12