Gantt diagrams Example 1The table below shows the tasks involved in a project, with their durations and immediate predecessors.

TaskDurationImmediate predecessorsA3-B4-C6-D5AE1BF6BG7C, D, E

Gantt diagrams Example 1The precedence network for this project, shown below, was found in Section 1.

Gantt diagrams - Example 1246810121416HoursThe critical activities, A, D and G are placed at the top of the chart.

Gantt diagrams - Example 1The earliest that activity B can start is at time 0, and the latest that it can finish is at time 7.246810121416Hours

Gantt diagrams - Example 1The earliest that activity C can start is at time 0, and the latest that it can finish is at time 8.246810121416Hours

Gantt diagrams - Example 1The earliest that activity E can start is at time 4, and the latest that it can finish is at time 8.246810121416Hours

Gantt diagrams - Example 1The earliest that activity F can start is at time 4, and the latest that it can finish is at time 15.246810121416Hours

Gantt diagrams Example 1A and B both require the use of the same piece of equipment. Can the project still be completed in 15 hours?Problem 1

Gantt diagrams - Example 1At present, A and B are both scheduled at the same time.Since A is a critical activity, moving A would result in the project being delayed.Moving B means that E and F must also move.246810121416Hours

Gantt diagrams - Example 1The project can still be completed in 15 hours.246810121416Hours

Gantt diagrams Example 1A and C must both be done by a qualified person. There is only one qualified person available. Can the project still be completed in 15 hours?Problem 2

Gantt diagrams - Example 1At present, A and C are scheduled at the same time.Again, as A is a critical activity, it is better to move C.Neither E nor F depend on C, but G does depend on C.246810121416HoursC can be moved by two hours

Gantt diagrams - Example 1246810121416HoursAt present, A and C are scheduled at the same time.Again, as A is a critical activity, it is better to move C.Neither E nor F depend on C, but G does depend on C.C can be moved by two hoursbut if it moves a further hour to avoid overlap with A, then G must also move.

Gantt diagrams - Example 1The project can be completed in 16 hours.246810121416Hours

Gantt diagrams and schedulingThe table below shows the tasks involved in a project, with their durations, immediate predecessors and number of workers required.How many workers are needed if all activities are scheduled to start as early as possible?

TaskDurationImmediate predecessorsNumber of workersA2-2B3-1C5-2D6A, B2E8C2F2C2G4D, E2

Gantt diagrams and schedulingThe precedence network shown below was found in Section 1.

Gantt diagrams and schedulingPut the critical activities along the top.C (2) E (2)G (2)(The numbers in brackets show the number of workers required)

Gantt diagrams and schedulingThe earliest start time for activity A is at time 0, and the latest finish time is at time 7.C (2) E (2)G (2)A (2)

Gantt diagrams and schedulingThe earliest start time for activity B is at time 0, and the latest finish time is at time 7.C (2) E (2)G (2)A (2)B (1)

Gantt diagrams and schedulingThe earliest start time for activity D is at time 3, and the latest finish time is at time 13.C (2) E (2)G (2)A (2)B (1)D (2)

Gantt diagrams and schedulingThe earliest start time for activity F is at time 5, and the latest finish time is at time 17.C (2) E (2)G (2)A (2)B (1)D (2)F (2)If this schedule is used, 6 workers are needed. (6 are needed on days 6 and 7).

Gantt diagrams and schedulingProblemOnly four workers are available.Is it possible to complete the project in the same amount of time?

Gantt diagrams and schedulingWe need to move some tasks so that only four workers are needed at any given time.At present 5 workers are needed for the first two days. Task B can be moved so that it starts after A has finished. This means that D must also move.C (2) E (2)G (2)A (2)F (2)

Gantt diagrams and schedulingWe need to move some tasks so that only four workers are needed at any given time.At present 6 workers are needed for days 6 and 7. Task F can be moved so that it starts after D has finished.C (2) E (2)G (2)A (2)F (2)

Gantt diagrams and schedulingNow only four workers are needed at any given time.C (2) E (2)G (2)A (2)F (2)Workers 1 and 2 could do activities C, E and G.Worker 3 could do A, B, D and FWorker 4 could do A, D and F (with 3 days off between A and D).