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Hillier and Lieberman Chapter 22: Reliable Construction Co. critical path and PERT
| Tool | Project Schedule |
| Source | Hillier, F. S., and Lieberman, G. J. (2021). Introduction to Operations Research, 11th ed. McGraw-Hill, New York. Chapter 22, Tables 22.1–22.6 and Figure 22.5. |
| Level | Undergraduate |
Problem
Reliable Construction Co. must build a plant from the fourteen activities A–N of Table 22.1 (excavate, lay the foundation, rough wall, roof, plumbing, siding, painting, electrical work, wallboard, flooring, fixtures) with the predecessor list and the optimistic, most likely and pessimistic durations of Table 22.4. Find the early and late schedule, the slack of every activity, the critical path and the project duration, and the probability of meeting the 47-week deadline.
Inputs to Enter
- Three-point estimates, 14 activities (loaded by default): A 1/2/3; B 2/3.5/8 after A; C 6/9/18 after B; D 4/5.5/10 after C; E 1/4.5/5 after C; F 4/4/10 after E; G 5/6.5/11 after D; H 5/8/17 after E, G; I 3/7.5/9 after C; J 3/9/9 after F, I; K 4/4/4 after J; L 1/5.5/7 after J; M 1/2/3 after H; N 5/5.5/9 after K, L
- Time unit weeks, deadline 47 weeks, confidence 95 %
Answers
- PERT means and variances as Table 22.4 (A 2 and 1/9, B 4 and 1, C 10 and 4, E 4 and 4/9, H 9 and 4, K 4 and 0, N 6 and 4/9)
- Project duration 44 weeks; one critical path A-B-C-E-F-J-L-N (Figure 22.5); slack D 4, G 4, H 4, I 2, K 1, M 4 (Table 22.3)
- Six paths with lengths 40, 31, 43, 44, 41, 42 weeks (Table 22.2); with every pessimistic estimate the longest path is A-B-C-D-G-H-M at 70 weeks (Table 22.5)
- μ_p = 44, σ_p² = 9 (Table 22.6); K_α = (47 − 44)/3 = 1, P(T ≤ 47) = 0.8413
- Deadline met with 95 % confidence: 44 + 1.645 × 3 = 48.93 weeks
Notes
The tool's default activity list is this example; press Submit. The Monte Carlo section (PERT-beta durations) gives a mean of about 44.3 weeks and P(T ≤ 47) about 0.82 (numpy 400,000 runs 44.33 / 0.816), which is not in the book.