Resource histograms and schedulingEdexcel A-Level Further Maths: Subtopic test

1. 1
   A project has six activities. Each activity, its duration in days, the number of workers it needs and its immediate predecessors are: A 3 days, 2 workers (none); B 4 days, 1 worker (none); C 2 days, 3 workers (A); D 3 days, 2 workers (B); E 4 days, 2 workers (A); F 2 days, 4 workers (C, D, E). Every activity starts as soon as it can, and the project takes 9 days.

   (a)

   If every activity starts at its earliest start time, what is the greatest number of workers needed at any one time?

   [1 mark]

   • A6
   • B7
   • C8
   • D9

   (b)

   What is the total number of worker-days of work in the project?

   [1 mark]

   • A14
   • B9
   • C63
   • D38

   (c)

   State which activities are in progress when the greatest number of workers is needed, and the time interval for which this happens.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A project has six activities. Each activity, its duration in days, the number of workers it needs and its immediate predecessors are: A 3 days, 2 workers (none); B 4 days, 3 workers (none); C 2 days, 2 workers (A); D 5 days, 1 worker (A); E 3 days, 2 workers (B, C); F 2 days, 3 workers (D, E). Every activity starts as soon as it can, and the project takes 10 days.

   (a)

   What does a resource histogram show?

   [1 mark]

   • AThe critical path of the project
   • BThe earliest start time of each event
   • CThe total float of each activity
   • DThe number of workers required at each time

   (b)

   Which statement best describes resource levelling?

   [1 mark]

   • AMoving non-critical activities, within their floats, to reduce the greatest number of workers needed
   • BMoving critical activities to shorten the project
   • CAdding workers so that activities finish sooner
   • DRemoving the activities that need most workers

   (c)

   State the greatest number of workers needed at any one time, and the time interval during which it occurs.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A project has seven activities, each needing one worker. Each activity, its duration in days and its immediate predecessors are: A 3 (none); B 5 (none); C 4 (A); D 2 (A); E 6 (B, C); F 3 (D); G 4 (E, F). The minimum completion time of the project is 17 days, and the critical activities are A, C, E and G.

   (a)

   Show that at least 2 workers are needed to complete the project in 17 days.

   [3 marks]

   (b)

   Produce a schedule that completes the project in 17 days using 2 workers. State which activities each worker does, and when.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A project has seven activities. Each activity, its duration in days, the number of workers it needs and its immediate predecessors are: A 4 days, 2 workers (none); B 5 days, 1 worker (none); C 3 days, 3 workers (A); D 2 days, 2 workers (A, B); E 4 days, 1 worker (C, D); F 3 days, 2 workers (B); G 2 days, 2 workers (E, F). The earliest start times are A 0, B 0, C 4, D 5, E 7, F 5 and G 11, so the project takes 13 days. Activity F is the only non-critical activity, with a total float of 3 days.

   (a)

   Construct a resource histogram for the project with every activity starting at its earliest start time. Give the number of workers needed in each time interval.

   [6 marks]

   (b)

   Only 5 workers are available. Explain how resource levelling can reduce the greatest number of workers needed to 5, without delaying the project. State the new start time of the activity you move.

   [6 marks]

   Total for question 4: 12 marks

End of questions