Covers Lessons 4–6: Gantt charts, resource allocation, dummy activities, multiple critical paths, cost-time trade-offs, and mixed project problems.
Multiple Choice
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Short Answer
1. A project has: A(3,-), B(4,A), C(2,A), D(5,B), E(5,C), F(2,D,E). (a) Find all critical paths. (b) If D's duration increases to 6, what happens? (c) Draw a Gantt chart showing both paths. (d) From the original durations, crash D by 1 ($\$500$) and E by 1 ($\$400$). New duration and cost? 5 MARKS
2. (a) Explain why a Gantt chart is better than an AOA network for presenting a project schedule to a client. (b) A project has two critical paths that share only their starting activity; the branches otherwise share no activities. You have a budget to crash one activity on each path by 1 day. Crashing the shared starting activity by 1 day costs the same as the two separate crashes. Is the shared crash necessarily better? Explain. (c) What is the difference between a lag and a lead? 3 MARKS
Q1 (5 marks): (a) Path correct [1]. (b) Effect [1]. (c) Gantt [1.5]. (d) Cost [1.5].
Q1 worked model: The two start-to-finish routes are A–B–D–F=3+4+5+2=14 days and A–C–E–F=3+2+5+2=12 days. Thus A–B–D–F is the only critical path. If D increases to 6, its route becomes 15 days and the project finishes in 15 days. A Gantt schedule at the original durations is A 0–3, B 3–7, C 3–5, D 7–12, E 5–10, and F 12–14; E finishes at day 10 and waits until day 12, when D also finishes and F can start. The A–C–E route therefore has 2 days of float. After D increases, D runs 7–13 and F runs 13–15. If D and E are each reduced by one day from the original schedule, the two route lengths are 13 and 11 days, so the new duration is 13 days. The stated crash costs total $500+$400=$900.
Q2 (3 marks): (a) Explanation [1]. (b) Reason [1]. (c) Difference [1].
Q2 worked model: (a) A Gantt chart places activities on a time line, making start/finish dates, overlaps and progress easier for a client to read; an AOA network shows precedence more directly but is less familiar. (b) Crashing the shared start activity shortens both critical routes by one day in a single change. Since it costs the same as crashing one activity on each route separately, it is not strictly better on cost or duration; it may be simpler to coordinate, but that depends on the project. (c) A lag is a required waiting interval before a successor starts; a lead is an allowed overlap in which the successor starts before the predecessor is fully complete.
Tick when you have finished all questions and checked your answers.