Time-Cost Tradeoff by Examples
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This document describes the process of time-cost tradeoff analysis to minimize the total cost of a project. It involves shortening the duration of critical project activities by paying extra money according to each activity's crash rate or slope. The process begins with creating an activity-on-node network using normal activity durations. It then iteratively selects the cheapest critical activity to crash based on crash rates, updates the network, and identifies the next critical path to determine if further crashing is needed to shorten the project duration. The objective is to determine the combination of critical activities to crash that results in the minimum total project cost.
Time-Cost Tradeoff by Examples
- 1. Time-Cost Tradeoff by Examples INTRODUCTION 1 Chachrist Srisuwanrat ชาคริต ศรีสุวรรณรัตน์
- 2. 2 YouTube
- 3. What is Time-Cost Tradeoff ? • It is the Exchange between “Time” and “Money” Introduction to Time-Cost Tradeoff DirectCost Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost (Project Duration) (Cost) Pay Extra Money to shorten the project 3
- 4. What is Time-Cost Tradeoff ? • It is the Exchange between “Time” and “Money” What is its Objective? • Find Minimum Total Cost Introduction to Time-Cost Tradeoff DirectCost Total Cost Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost (Project Duration) (Cost) Pay Extra Money to shorten the project 4
- 5. What is Time-Cost Tradeoff ? • It is the Exchange between “Time” and “Money” What is its Objective? • Find Minimum Total Cost About Total Cost: • Total Cost = Direct + Indirect • Direct Cost: labor, materials, equipment, … • Indirect Cost : managers, safety, accountants, parking, … Introduction to Time-Cost Tradeoff DirectCost 450 600 750 900 1,050 Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost (Project Duration) (Cost) Total Cost IndirectCost150k/m Pay Extra Cost to shorten the project 5
- 6. Time-Cost Tradeoff by Examples Shorten Project by Shorten Critical Activities +Slope 6
- 7. How much? • Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month) Shorten “Project Duration” by Shorten “Critical Activity Duration” Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost Activity 5 – 7 months 700k – 500k = Cost Duration Normal Duration (ND) Normal Cost (NC) Crash Duration (CD) Crash Cost (NC) Extra cost/duration = +Slope 500 Direct Cost 7
- 8. How much? • Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month) Shorten “Project Duration” by Shorten “Critical Activity Duration” Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost = Cost Duration Normal Duration – Crash Duration Crash Cost – Normal Cost= ND - CD CC - NC= Activity 5 – 7 months 700k – 500k Normal Duration (ND) Normal Cost (NC) Crash Duration (CD) Crash Cost (NC) Extra cost/duration = +Slope 500 Direct Cost 8
- 9. How much? • Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month) Shorten “Project Duration” by Shorten “Critical Activity Duration” Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) Activity 5 7 700 500 ? ND - CD CC - NC 700 - 500 7 - 5 +100 k/m= =+Slope = Normal Duration – Crash Duration Crash Cost – Normal Cost== Cost Duration ND - CD CC - NC=Extra cost/duration = +Slope 500 Direct Cost Activity 5 – 7 months 700k – 500k Normal Duration (ND) Normal Cost (NC) Crash Duration (CD) Crash Cost (NC) 9
- 10. How much? • Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month) Shorten “Project Duration” by Shorten “Critical Activity Duration” 600 Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) Activity 5 7 700 500 +100 500 Direct Cost Normal Duration – Crash Duration Crash Cost – Normal Cost== Cost Duration Extra cost/duration = +Slope +100k/m ND - CD CC - NC 700 - 500 7 - 5 +100 k/m= =+Slope = ND - CD CC - NC= Activity 5 – 7 months 700k – 500k Normal Duration (ND) Normal Cost (NC) Crash Duration (CD) Crash Cost (NC) 10
- 11. +100k/m How much? • Different activities have different “Extra Cost”, extra money per shorten duration (day, week, or month) Shorten “Project Duration” by Shorten “Critical Activity Duration” Project Duration 76543 500k 600k 700k 800k 900k 1,000k 1,100k 1,200k 1,300k 1,400k 400k 1,500k 1,600k Cost Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) Activity 5 7 700 500 +100 600 700 +100 500 Direct Cost Normal Duration – Crash Duration Crash Cost – Normal Cost== Cost Duration DONE ! Extra cost/duration = +Slope ND - CD CC - NC 700 - 500 7 - 5 +100 k/m= =+Slope = ND - CD CC - NC= Activity 5 – 7 months 700k – 500k Normal Duration (ND) Normal Cost (NC) Crash Duration (CD) Crash Cost (NC) 11
- 12. Time-Cost Tradeoff by Examples The Process of Shortening Project 12
- 13. Process of Shortening Project P0: Use Normal Duration to create AON A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 13 = shorten Critical Activities by +Slope
- 14. Process of Shortening Project P0: Use Normal Duration to create AON A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 14 = shorten Critical Activities by +Slope
- 15. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 Step 1 Choices: A+100, C+75, D+150 15 = shorten Critical Activities by +Slope
- 16. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 Step 1 Choices: A+100, C+75, D+150 Choose: C+75 16 = shorten Critical Activities by +Slope
- 17. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75 17 = shorten Critical Activities by +Slope
- 18. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 18 = shorten Critical Activities by +Slope
- 19. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D150 19 = shorten Critical Activities by +Slope
- 20. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D150 Choose: A+100 20 = shorten Critical Activities by +Slope
- 21. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D+150 Choose: A+100, Project duration = 15--- 3 --- 3 --- 3 --- 7 --- 3 --- 7 --- 7 --- 15 21 = shorten Critical Activities by +Slope
- 22. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125 --- 3 --- 3 --- 3 --- 7 --- 3 --- 7 --- 7 --- 15 22 = shorten Critical Activities by +Slope
- 23. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 --- 3 --- 3 --- 3 --- 7 --- 3 --- 7 --- 7 --- 15 --- 3 --- 3 --- 6 --- 6 --- 14 6 --- 23 = shorten Critical Activities by +Slope
- 24. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150 --- 3 --- 3 --- 3 --- 7 --- 3 --- 7 --- 7 --- 15 --- 3 --- 3 --- 6 --- 6 --- 14 6 --- 24 = shorten Critical Activities by +Slope
- 25. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration = 13 --- 3 --- 3 --- 3 --- 7 --- 3 --- 7 --- 7 --- 15 --- 3 --- 3 --- 6 --- 6 --- 14--- 13 --- 7 6 --- 25 = shorten Critical Activities by +Slope
- 26. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 4 4 5 8 --- 4 --- 8 --- 8 --- 16 --- 3 --- 3 --- 3 --- 7 --- 3 --- 7 --- 7 --- 15 --- 3 --- 3 --- 6 --- 6 --- 14--- 13 --- 7 6 --- Step 5 Choice: B+50, D+150 Choose: D+150 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration = 13 26 = shorten Critical Activities by +Slope
- 27. Process of Shortening Project P0: Use Normal Duration to create AON P1: Consider spend Extra Money (+Slope) on critical activities P2: Choose the cheapest critical activity (minimum slope) P3: Update/check/confirm that the +Slope shortens the project P4: Update AON, Critical Activities, and Critical Paths A 3 – 4 m +100k/m 0 4 B 2 – 4 m +50 k/m 4 8 C 3 – 5 m +75 k/m 4 9 D 6 – 8 m + 150k/m 9 17 = shorten Critical Activities by +Slope 4 4 5 8 --- 4 --- 8 --- 8 --- 16 --- 3 --- 3 --- 3 --- 7 --- 3 --- 7 --- 7 --- 15 --- 3 --- 3 --- 6 --- 6 --- 14--- 13 --- 7 6 --- Step 5 Choice: B+50, D+150 Choose: D+150, Project duration= 12 12 --- --- 6 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: B+50 Anothercritical pathA-C-D still pushes the project. Choices: A+100, B&C+125, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration = 13 27
- 28. Time-Cost Tradeoff by Examples Minimum Total Cost 28
- 29. Total Cost = Direct Cost + Indirect Cost A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 29
- 30. Total Cost = Direct Cost + Indirect Cost Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 30
- 31. Total Cost = Direct Cost + Indirect Cost A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 125 x Duration Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 31
- 32. Total Cost = Direct Cost + Indirect Cost A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 125 x Duration Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 32
- 33. Total Cost = Direct Cost + Indirect Cost A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 125 x Duration Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 33
- 34. Total Cost = Direct Cost + Indirect Cost A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 125 x Duration Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 34
- 35. Total Cost = Direct Cost + Indirect Cost A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 125 x Duration Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 35
- 36. Total Cost = Direct Cost + Indirect Cost A 3 – 4 m +100k/m B 2 – 4 m +50 k/m C 3 – 5 m +75 k/m D 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m Min Total Cost 125 x Duration Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 36
- 37. Time-Cost Tradeoff by Examples S-Curve at Min Total Cost 37
- 38. Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 Step 4 Choice: B+50, D+150 Choose: D+150, Project duration= 13 Step 5 Choice: B+50, D+150 Choose: D+150, Project duration = 12 S-Curve at Min Total Cost A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m 38
- 39. A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m --- 4 -------- 375 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 39 S-Curve at Min Total Cost
- 40. A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m --- 4 --- 3 -------- 500 -------- 375 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 40 S-Curve at Min Total Cost
- 41. A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m --- 4 --- 3 --- 3 --- 3 -------- 500 -------- 375-------- 450 -------- 150 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 41 S-Curve at Min Total Cost
- 42. A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m --- 4 --- 3 --- 3 --- 3 -------- 500 -------- 375-------- 450 -------- 150 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 42 S-Curve at Min Total Cost
- 43. A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m --- 4 --- 3 --- 3 --- 3 -------- 500 -------- 375-------- 450 -------- 150 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 43 S-Curve at Min Total Cost
- 44. A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m --- 4 --- 3 --- 3 --- 3 -------- 500 -------- 375-------- 450 -------- 150 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 44 S-Curve at Min Total Cost
- 45. A 4 3 – 4 m +100k/m B 4 2 – 4 m +50 k/m C 5 3 – 5 m +75 k/m D 8 6 – 8 m + 150k/m 400k 100k 300k 300k Indirect cost= 125 k/m --- 4 --- 3 --- 3 --- 3 -------- 500 -------- 375-------- 450 -------- 150 Step 1 Choices: A+100, C+75, D+150 Choose: C+75, Project duration = 16 Step 2 Choices: A+100, B+50, C+75, D+150 Choose: A+100, Project duration = 15 Step 3 Choices: B&C+125, D+150 Choose: B&C+125, Project duration= 14 45 S-Curve at Min Total Cost
- 46. Time-Cost Tradeoff by Examples Example 1-A: Direct Cost A B C Activity Duration Cost Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 Indirect cost= 65 k/m46
- 47. Example 1-A A B C Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 47
- 48. Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 Example 1-A: Calculate +Slope A B C +70 k/m +80 k/m + 50 k/m +70 +80 +50 3 – 4 m 10 – 12 m 6 – 8 m 48
- 49. Example 1-A: Start with “Normal Duration” for all activities A B C +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 49
- 50. Example 1-A: Perform CPM A B C +70 k/m +80 k/m + 50 k/m 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 50
- 51. Example 1-A: Identify critical activities and critical path A B C +70 k/m +80 k/m + 50 k/m 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 51
- 52. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50 A B C +70 k/m +80 k/m + 50 k/m 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 52
- 53. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 53
- 54. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 54
- 55. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 --- 6 --- 22 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 55
- 56. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 --- 6 --- 22 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 56
- 57. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 --- 6 --- 22 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 --- 3 --- 3 --- 3 --- 15 --- 15 --- 21 57
- 58. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 --- 6 --- 22 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 --- 3 --- 3 --- 3 --- 15 --- 15 --- 21 58
- 59. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80, Project duration = 20 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 --- 6 --- 22 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 --- 3 --- 3 --- 3 --- 15 --- 15 --- 21 --- 11 --- 14 14 --- 20 --- 59
- 60. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80, Project duration = 20 Step 5 Choices: B+80 Choose: B+80 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 --- 6 --- 22 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 --- 3 --- 3 --- 3 --- 15 --- 15 --- 21 --- 11 --- 14 14 --- 20 --- 60
- 61. Example 1-A: Shortening Project = Shortening critical activities Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80, Project duration = 20 Step 5 Choices: B+80 Choose: B+80, Project duration = 19 A B C +70 k/m +80 k/m + 50 k/m --- 7 0 4 3 – 4 m 10 – 12 m 6 – 8 m 4 12 8 4 16 16 24--- 23 --- 6 --- 22 Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 --- 3 --- 3 --- 3 --- 15 --- 15 --- 21 --- 11 --- 14 14 --- 20 --- --- 10 --- 13 --- 13 --- 19 61
- 62. Time-Cost Tradeoff by Examples Example 1-B: Minimum Total Cost Indirect cost= 65 k/m62
- 63. Example 1-B: Minimum Total Cost 400k 300k 500k A B C +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 (Indirectcost = 65 k/m) Normal Direct Cost = 400 + 300 + 500 = 1,200 k 63
- 64. Example 1-B: Minimum Total Cost Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80, Project duration = 20 Step 5 Choices: B+80 Choose: B+80, Project duration = 19 400k 300k 500k A B C +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 (Indirectcost = 65 k/m) Normal Direct Cost = 400 + 300 + 500 = 1,200 k 64
- 65. Example 1-B: Minimum Total Cost 400k 300k 500k A B C +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 (Indirectcost = 65 k/m) Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80, Project duration = 20 Step 5 Choices: B+80 Choose: B+80, Project duration = 19 Normal Direct Cost = 400 + 300 + 500 = 1,200 k 65
- 66. Example 1-B: Minimum Total Cost 400k 300k 500k A B C +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 (Indirectcost = 65 k/m) Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80, Project duration = 20 Step 5 Choices: B+80 Choose: B+80, Project duration = 19 Normal Direct Cost = 400 + 300 + 500 = 1,200 k 66
- 67. Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 Step 3 Choices: A+70, B+80 Choose: A+70, Project duration= 21 Step 4 Choices: B+80 Choose: B+80, Project duration = 20 Step 5 Choices: B+80 Choose: B+80, Project duration = 19 Example 1-B: Minimum Total Cost 400k 300k 500k A B C +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m Activity Duration Cost +Slope Crash (CD) Normal(ND) Crash (CC) Normal(NC) A 3 4 470 400 B 10 12 460 300 C 6 8 600 500 +70 +80 +50 (Indirectcost = 65 k/m) Normal Direct Cost = 400 + 300 + 500 = 1,200 k 67
- 68. Example 1-B: Minimum Total Cost Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 400k 300k 500k A B C +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m Min Total Cost (Indirectcost = 65 k/m) 68
- 69. Time-Cost Tradeoff by Examples Example 1-C: S-Curve at Min Total Cost 69
- 70. Example 1-C: S-Curve Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 400k 300k 500k A 4 B 12 C 8 +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m (Indirectcost = 65 k/m) 70
- 71. Example 1-C: S-Curve 400k 300k 500k A 4 B 12 C 8 +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m -------- 550 --- 7 (Indirectcost = 65 k/m) Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 71
- 72. Example 1-C: S-Curve 400k 300k 500k A 4 B 12 C 8 +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m -------- 550-------- 600 --- 7--- 6 (Indirectcost = 65 k/m) Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 72
- 73. Example 1-C: S-Curve 400k 300k 500k A 4 B 12 C 8 +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m (Indirectcost = 65 k/m) -------- 550-------- 600 --- 7--- 6 Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 73
- 74. Example 1-C: S-Curve 400k 300k 500k A 4 B 12 C 8 +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m (Indirectcost = 65 k/m) -------- 550-------- 600 --- 7--- 6 Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 74
- 75. Example 1-C: S-Curve 400k 300k 500k A 4 B 12 C 8 +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m (Indirectcost = 65 k/m) -------- 550-------- 600 --- 7--- 6 Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 75
- 76. Example 1-C: S-Curve 400k 300k 500k A 4 B 12 C 8 +70 k/m +80 k/m + 50 k/m 3 – 4 m 10 – 12 m 6 – 8 m (Indirectcost = 65 k/m) -------- 550-------- 600 --- 7--- 6 Step 1 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 23 Step 2 Choices: A+70, B+80, C+50 Choose: C+50, Project duration= 22 76
- 77. Time-Cost Tradeoff by Examples Example 2-A: Direct Cost 77
- 78. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m Example 2-A 78
- 79. Example 2-A: Perform CPM B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 13 18 79
- 80. Example 2-A: Identify critical path and critical activities B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 13 18 80
- 81. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 13 18 81 Example 2-A: Direct Cost
- 82. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- 82
- 83. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- 83
- 84. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- 84
- 85. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- 85
- 86. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- 86
- 87. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 11 --- 5 --- 11 --- 15 --- 11 --- 87
- 88. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- 88
- 89. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- 89
- 90. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- 90
- 91. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- 91
- 92. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- 92
- 93. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- 93
- 94. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- 94
- 95. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 6 5 11 6 13 6 12 --- 6 13 18 --- 12 12 --- 17 --- --- 4 16 --- --- 5 5 --- 5 --- 11 --- 11 --- 15 --- 11 --- --- 1 --- 5 --- 10 --- 4 --- 4 --- 10 --- 4 --- 10 10 --- 14 --- 95
- 96. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 4 5 10 4 10 4 10 --- 6 10 14 --- 4 --- 1 --- 5 96
- 97. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 4 5 10 4 10 4 10 --- 6 10 14 --- 4 --- 1 --- 5 97
- 98. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 4 5 10 4 10 4 10 --- 6 10 14 --- 4 --- 1 --- 5--- 4 --- 5 --- 5 --- 9 --- 9 --- 9 9 --- 13 --- 98
- 99. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 14 Step 6 Choices: A+155, B&E&F+150 Choose B&E&F+150 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 4 5 10 4 10 4 10 --- 6 10 14 --- 4 --- 1 --- 5--- 4 --- 5 --- 5 --- 9 --- 9 --- 9 9 --- 13 --- 99
- 100. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 4 5 10 4 10 4 10 --- 6 10 14 --- 4 --- 1 --- 5--- 4 --- 5 --- 5 --- 9 --- 9 --- 9 9 --- 13 ------ 4 --- 8 --- 4 --- 1 --- 4 --- 4 --- 8 --- 8 8 --- 12 --- 100
- 101. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 4 5 10 4 10 4 10 --- 6 10 14 --- 4 --- 1 --- 5--- 4 --- 5 --- 5 --- 9 --- 9 --- 9 9 --- 13 --- --- 1 --- 4 --- 4 --- 8 --- 4 --- 8 --- 4 --- 8 8 --- 12 --- 101
- 102. Example 2-A: Direct Cost B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m --- 2 Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11 C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 0 3 3 5 3 4 5 10 4 10 4 10 --- 6 10 14 --- 4 --- 1 --- 5--- 4 --- 5 --- 5 --- 9 --- 9 --- 9 9 --- 13 --- --- 1 --- 4 --- 4 --- 8 --- 4 --- 8 --- 4 --- 8 8 --- 12 ---2 --- 2 --- 3 --- 2 --- 3 --- 3 --- 7 --- 3 --- 7 --- 3 --- 7 --- 7 --- 11 --- --- 2 102
- 103. Time-Cost Tradeoff by Examples Example 2-B: Minimum Total Cost 103
- 104. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m) B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 104
- 105. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m) B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Normal Direct Cost = 245 + 175 + 160 + 300 + 325 + 700 + 340 = 2,245 k 105
- 106. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m) B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11 Normal Direct Cost = 245 + 175 + 160 + 300 + 325 + 700 + 340 = 2,245 k 106
- 107. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11107
- 108. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11108
- 109. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11109
- 110. Example 2-B: Minimum Total Cost (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11 Min Total Cost 110
- 111. Time-Cost Tradeoff by Examples Example 2-C: S-Curve at Min Total Cost 111
- 112. Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11 Min Total Cost 112
- 113. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 Step 5 Choices: A+155, B&E&F+150, D&E&F+125 Choose D&E&F+125, Project duration = 13 Step 6 Choices: A+155, B&E&F+150, Choose B&E&F+150, Project duration = 12 Step 7 Choices: A+155 Choose A+155, Project duration = 11113
- 114. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 114
- 115. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 --- 4 --------- 400 115
- 116. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 --- 4 --------- 400 --- 2 --------- 230 116
- 117. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 --- 4 --------- 400 --- 2 --------- 230 --- 1 --------- 300 --- 5 --------- 350 117
- 118. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 --- 4 --------- 400 --- 2 --------- 230 --- 1 --------- 300 --- 5 --------- 350 0 3 3 5 5 10 3 4 4 10 4 10 10 14 118
- 119. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 --- 4 --------- 400 --- 2 --------- 230 --- 1 --------- 300 --- 5 --------- 350 0 3 3 5 5 10 3 4 4 10 4 10 10 14 119
- 120. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 --- 4 --------- 400 --- 2 --------- 230 --- 1 --------- 300 --- 5 --------- 350 0 3 3 5 5 10 3 4 4 10 4 10 10 14 120
- 121. B 2 +75 k/m A 3 +155 k/m 2 – 3 m 1 – 2 m D 6 +50 k/m 4 – 6 m C 3 +70 k/m 1 – 3 m F 6 +50 k/m 2 – 6 m E 7 +25 k/m 3 – 7 m G 5 +60 k/m 4 – 5 m 245k 175k 160k 300k 340k 325k 700k Example 2-C: S-Curve (Indirectcost = 120 k/m) Step 1 Choices: A+155, C+70, E+25, G+60 Choose: E+25, Project duration = 17 Step 2 Choices: A+155, C+70, E&F+75, G+60 Choose: G+60, Project duration= 16 Step 3 Choices: A+155, C+70, E&F+75 Choose: C+70, Project duration = 15 Step 4 Choices: A+155, B&C+145, D&C+120, B&E&F+150, D&E&F+125 Choose D&C+120, Project duration = 14 --- 6 --------- 350 --- 4 --------- 400 --- 2 --------- 230 --- 1 --------- 300 --- 5 --------- 350 0 3 3 5 5 10 3 4 4 10 4 10 10 14 121
- 122. Example 2-C: S-Curve 122 (Indirectcost = 120 k/m)
- 123. Time-Cost Tradeoff by Examples Example 2-D: Excel Solver 123
- 124. Time-Cost Tradeoff by Examples Example 2-D: Activate Excel Solver 124
- 125. Check if there is “Solver” button If not, go to File menu 125
- 126. Select “Options” 126
- 127. 127
- 128. Select “Add-ins”, and choose “Excel Add-ins”, then click “Go…” 1 2 3 128
- 129. Check “Solver Add-in” checkbox, and click “OK” button 4 5 129
- 131. The “Solver” 131
- 132. The “Solver” Actual Duration (AD)2. Variables AD >= CD AD <= ND AD must be “Integer”. Project Duration= … 3. Constraints 1. Objective: Minimize… Project Direct Cost 132
- 133. Time-Cost Tradeoff by Examples Example 2-D: Let’s Start 133
- 134. Create table, add initial data, and calculate +Slope if necessary +Slope = (Crash Cost – Normal Cost) (Normal Duration – Crash Duration) 134
- 135. Setup Columns for Actual Duration & Actual Cost +Slope = (Crash Cost – Normal Cost) (Normal Duration – Crash Duration) Actual Cost = Normal Cost +Slope x (Normal Duration – Actual Duration) Actual Duration could be any number between “Crash” and “Normal” durations. Variables in Solver 135
- 136. Add Formula for CPM: ESD and EFD +Slope = (Crash Cost – Normal Cost) (Normal Duration – Crash Duration) Actual Cost = Normal Cost +Slope x (Normal Duration – Actual Duration) Actual Duration could be any number between “Crash” and “Normal” durations. Variables in Solver 136
- 137. Find the Normal and Crash Durations of the Project Normal Duration of the Project = 18 Crash Duration of the Project = 11 Therefore, we will analyze the project between 11 to 18 months. 137
- 138. Create a table for Total Cost = Direct + Indirect 138
- 139. Activate Solver by going to “Data” menu -> Solver 139
- 140. Set Objective, Variables, and Constraints in Excel Solver 1. Objective: Minimize Actual Direct Cost 140
- 141. Set Objective, Variables, and Constraints in Excel Solver 2. Variables 1. Objective: Minimize Actual Direct Cost 141
- 142. Set Objective, Variables, and Constraints in Excel Solver 2. Variables 1. Objective: Minimize Actual Direct Cost 3. Constraints: Actual duration<= ND Actual duration must be “Integer” Actual duration >= CD Project duration= 18 142
- 143. Set Objective, Variables, and Constraints in Excel Solver 2. Variables 1. Objective: Minimize Actual Direct Cost 3. Constraints: Actual duration<= ND Actual duration must be “Integer” Actual duration >= CD Project duration= 18 143
- 144. Set Objective, Variables, and Constraints in Excel Solver 2. Variables 1. Objective: Minimize Actual Direct Cost 3. Constraints: Actual duration<= ND Actual duration must be “Integer” Actual duration >= CD Project duration= 18 144
- 145. Set Objective, Variables, and Constraints in Excel Solver 2. Variables 4. Click “Solve” button 1. Objective: Minimize Actual Direct Cost 3. Constraints: Actual duration<= ND Actual duration must be “Integer” Actual duration >= CD Project duration= 18 145
- 146. Manually type the Cost in the table after finish solving Click “OK” button And type in the number. 146
- 147. Change “Constraint of Project Duration” to the next one, 17 Constraints Actual duration<= ND Actual duration must be “Integer” Actual duration >= CD Project duration= 17 1. Select the constraint and click“Change” button 2. Click “Solve” button 147
- 148. 148
- 149. Keep Solving until reaching the Crash Duration of the Project 149
- 150. Finish Solving 150
- 151. Calculate Total Cost and indicate the Minimum Total Cost 151
- 152. Calculate Total Cost and indicate the Minimum Total Cost Minimum Total Cost With the shortest duration 152
- 153. Use Solver to determine activities’ duration & cost at Min Total Cost Minimum Total Cost With the shortest duration 153 2. Click “Solve” button 1. Change
- 154. Actual Duration & Cost at Minimum Total Cost Minimum Total Cost With the shortest duration 154
- 155. Rate: Cost/Duration Minimum Total Cost With the shortest duration 155
- 156. Bar Chart with Cost/Duration Minimum Total Cost With the shortest duration 156
- 157. Bar Chart with Cost/Duration 157
- 158. Sum Direct, Indirect, and Total Cost 158
- 160. Time-Cost Tradeoff by Examples THANK YOU 160