Örnek-2Örnek-2 2

FinishFinish StartStart CG B 10 D 35 H J E 24 I 15 A F K ABCDEFGHIJKABCDEFGHIJK — — A B B A C D A E,G,H F,I,J Immediate Predecessor Örnek-2Örnek-2 3 Figure 7.2

4 Analyzing Cost-Time Trade- Offs Determining the Minimum Cost Schedule: 1.Determine the project’s critical path(s). 2.Find the activity or activities on the critical path(s) with the lowest cost of crashing per week. 3.Reduce the time for this activity until… a.It cannot be further reduced or b.Another path becomes critical, or c.The increase in direct costs exceeds the indirect and penalty cost savings that result from shortening the project. 4.Repeat this procedure until the increase in direct costs is larger than the savings generated by shortening the project.

Örnek-2Örnek-2 DIRECT COST AND TIME DATA FOR THE ST. JOHN’S HOSPITAL PROJECT Activity Normal Time (NT) (weeks) Normal Cost (NC)($) Crash Time (CT)(week s) Crash Cost (CC)($) Maximu m Time Reductio n (week) Cost of Crashing per Week ($) A12$12,0001$13,00011,000 B950,000764,00027,0007,000 C104,0004,00057, D1016,000820,00022,0002,000 E24120, , ,0008,000 F1010,000616,00041,5001,500 G35500, , ,0003,000 H401,200, ,260,000512,00012,000 I1540, ,50052,5002,500 J410,000113,00031,0001,000 K630,000534,00014,0004,000 Totals$1,992,000$2,209,500 5

Örnek-2Örnek-2 Determine the minimum-cost schedule for the St. John’s Hospital project. Project completion time = 69 weeks. Project cost = $2,624,000 Direct =$1,992,000 Indirect = 69($8,000) = $552,000 Penalty = (69 – 65)($20,000) = $80,000 A–I–K A–F–K A– C–G–J–K B–D–H–J–K B–E–J–K 6 33 weeks 28 weeks 67 weeks 69 weeks 43 weeks

7 Örnek-2Örnek-2 STAGE 1 Step 1. The critical path is B–D–H–J–K. Step 2. The cheapest activity to crash per week is J at $1,000, which is much less than the savings in indirect and penalty costs of $28,000 per week. Step 3. Crash activity J by its limit of three weeks because the critical path remains unchanged. The new expected path times are A–C–G–J–K: 64 weeks B–D–H–J–K: 66 weeks The net savings are 3($28,000) – 3($1,000) = $81,000. The total project costs are now $2,624,000 – $81,000 = $2,543,000.

Örnek-2Örnek-2 Finish K 6K 6 I15I15 F10F10 C10C10 D10D10 H40H40 J1J1 A12A12 B9B9 StartStart G35G35 8 E24E24 STAGE 1

9 Örnek-2Örnek-2 STAGE 2 Step 1. The critical path is still B–D–H–J–K. Step 2. The cheapest activity to crash per week is now D at $2,000. Step 3. Crash D by two weeks. The first week of reduction in activity D saves $28,000 because it eliminates a week of penalty costs, as well as indirect costs. Crashing D by a second week saves only $8,000 in indirect costs because, after week 65, no more penalty costs are incurred. Updated path times are A–C–G–J–K: 64 weeks and B–D–H–J–K: 64 weeks The net savings are $28,000 + $8,000 – 2($2,000) = $32,000. Total project costs are now $2,543,000 – $32,000 = $2,511,000.

Örnek-2Örnek-2 FinishFinish K 6K 6 I15I15 F10F10 C10C10 D8D8 H40H40 J1J1 A12A12 B9B9 StartStart G35G35 10 E24E24 STAGE 2

11 Örnek-2Örnek-2 STAGE 3 Step 1. The critical paths are B–D–H–J–K and A-C-G-J-K Step 2. Activities eligible to be crashed: (A, B); (A, H); (C, B); (C, H); (G, B); (G, H)—or to crash Activity K We consider only those alternatives for which the costs of crashing are less than the potential savings of $8,000 per week. We choose activity K to crash 1 week at $4,000 per week. Step 3. Updated path times are: A–C–G–J–K: 63 weeks and B–D–H–J–K: 63 weeks Net savings are $8,000 – $4,000 = $4,000. Total project costs are $2,511,000 – $4,000 = $2,507,000.

Örnek-2Örnek-2 FinishFinish K 5K 5 I15I15 F10F10 C10C10 D8D8 H40H40 J1J1 A12A12 B9B9 StartStart G35G35 12 E24E24 STAGE 3

13 Örnek-2Örnek-2 STAGE 4 Step 1. The critical paths are still B–D–H–J–K and A–C–G–J–K. Step 2. Activities eligible to be crashed: $7,600 per week. Step 3. Crash activities B and C by two weeks. Updated path times are A–C–G–J–K: 61 weeks and B–D–H–J–K: 61 weeks The net savings are 2($8,000) – 2($7,600) = $800. Total project costs are now $2,507,000 – $800 = $2,506,200.

Örnek-2Örnek-2 Finish K 5K 5 I15I15 F10F10 C 8C 8 D8D8 H40H40 J1J1 A12A12 B 7B 7 StartStart G35G35 14 E24E24 STAGE 4

15 Örnek-2Örnek-2 Stage Crash Activit y Time Reduction (weeks) Resultin g Critical Path(s) Project Duratio n (weeks) Project Direct Costs, Last Trial ($000) Crash Cost Adde d ($000 ) Total Indirec t Costs ($000) Total Penalty Costs ($000) Total Project Costs ($000) 0——B-D-H-J-K69691,992.0— , J3B-D-H-J-K61, , D2B-D-H-J-K64641, ,511.0 A-C-G-J-K 3K1B-D-H-J-K63631, ,507.0 A-C-G-J-K 4B, C2B-D-H-J-K61612, ,506.2 A-C-G-J-K