1. 4/12/2015 Management of Engineering Projects Limited Resources Dr. L. K. Gaafar

2. Example

3. 4/12/2015 Example A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 Critical path is CD. Minimum completion time is 13.

4. A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 Time Resources Activity Schedule 1 Resource Profile 1 5 needed Time

5. 4/12/2015 Example A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 Next slide shows 2 possible schedules to finish the project on time (13), and the associated resource profile in each case. Critical path is CD. Minimum completion time is 13.

6. A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 Time Resources Time Activity Schedule 1Schedule 2 Resource Profile 1 5 needed Resource Profile 2 4 needed Time

7. 4/12/2015 Single Resource Allocation Brooks’ Algorithm 1. Develop the activity network. 2. Determine the activity control time (ACTIM) for all activities. ACTIM is the longest path to the end of the project starting from the activity. 3. Rank activities in a descending order of their ACTIM with ties broken according to longest duration followed by largest resource requirements. 4. Set TNOW to 0. 5. Set the early start (TEARL) of all activities that may start at TNOW. 6. Schedule all possible activities that could be started and allocated enough resource units. Stop when all available activities are scheduled, or when you run out of resource units for the next available activity. Determine the finishing time for all scheduled activities (TFIN). 7. Update TEARL of remaining activities based on TFIN of scheduled activities. 8. Advance TNOW to next available TEARL or TFIN and repeat step 5. Continue until all activities are scheduled.

8. 4/12/2015 Order is CDAB D is ranked before A because it has a longer duration Resource allocation assuming 4 units are available Algorithm setup at TNOW = 0 C and A may start at time 0 and their TEARL is set accordingly. 4 units are available for assignment Since B depends on A, its TEARL cannot be determined at this time. Since D depends on C, its TEARL cannot be determined at this time.

9. 4/12/2015 After First Iteration Resource allocation assuming 4 units are available A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 C and A may be scheduled. C is allocated 3 units of the resource and its TSTART and TFIN are set to 0 and 6. TEARL of D is set to 6 (TFIN of C). A cannot be scheduled at this time as only one resource unit is left. TNOW will be set to 6 for next iteration TNOW = 0

10. 4/12/2015 After Second Iteration Resource allocation assuming 4 units are available A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 C is done and 3 units of the resource are recovered. Resource capacity upgraded to 4. D and A may be scheduled and enough resource units are available TSTART and TFIN of D and A are updated. TEARL of B is set to 9 (TFIN of A). TNOW will be set to 9 for next iteration TNOW = 6

11. 4/12/2015 After Third Iteration Resource allocation assuming 4 units are available A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 TNOW = 9 A is done and 2 units of the resource are recovered. Resource capacity upgraded to 2. B may be scheduled and enough resource units are available TSTART and TFIN of B are updated. All activities have been scheduled. The project completion time is the maximum TFIN (13).

12. 4/12/2015 A 3 (2) B4 (2) C 6 (3) D 7 (2) 0 3 6 13 A (2) B (2) C (3)D (2) 13 Time0 6 Resources 3 4 Time Schedule Resource Profile Results of applying Brooks’ algorithm Same as Schedule 2 before

13. 4/12/2015 Example Bus Shelter Construction Assume only 4 units of the resource are available.

14. 4/12/2015 Critical path is EABDCHI, completion time is 12 without resource constraints E(2,3) A(2,2) B(1,1) D(3,2) C(2,2) F(2,3) G(1,2) H(1,1)I(1,2) With resource constraints, completion time is 13.

15. 4/12/2015 I. Given the following Project: 1. Determine the Critical Path 2. What is the minimum Project completion time assuming no constraints? 16 3. Use Brooks' algorithm to schedule the project assuming 3 units of the resource are available. What is the project completion time? 4. Use Brooks' algorithm to schedule the project assuming 2 units of the resource are available. What is the project completion time? A 5 C 5 B 4 D 7 E 4 F 8 G 16 Example I

16. 4/12/2015 A 5 C 5 B 4 D 7 E 4 F 8 G 16 Assuming 3 resource units

17. 4/12/2015 A 5 C 5 B 4 D 7 E 4 F 8 G 16 Assuming 2 resource units