Effect of activity delay/change

1 Figure 1 below shows an activity diagram for a construction project. The time needed for each activity is given in days.

1. Find the earliest start time and latest finish time for each activity and insert their values on Figure 1.
2. Find the critical paths and state the minimum time for completion of the project.
3. On Figure 2 opposite, draw a cascade diagram (Gantt chart) for the project, assuming that each activity starts as early as possible.
4. A delay in supplies means that Activity \(I\) takes 9 days instead of 2 .
   1. Determine the effect on the earliest possible starting times for activities \(K\) and \(L\).
   2. State the number of days by which the completion of the project is now delayed.
      (1 mark) \section*{Figure 1}
      1. \includegraphics[max width=\textwidth, alt={}, center]{c4dc61a7-47ee-4d5c-bf6d-30a5da2ee8dd-02_815_1337_1573_395}
      2. Critical paths are \(\_\_\_\_\) Minimum completion time is \(\_\_\_\_\) days. QUESTION PART REFERENCE
      3. \begin{figure}[h]
         \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{c4dc61a7-47ee-4d5c-bf6d-30a5da2ee8dd-03_978_1207_354_461}
         \end{figure}

1 Figure 1 opposite shows an activity diagram for a project. The duration required for each activity is given in hours. The project is to be completed in the minimum time.

1. Find the earliest start time and the latest finish time for each activity and insert their values on Figure 1.
2. Find the critical path.
3. Find the float time of activity \(E\).
4. Given that activities \(H\) and \(K\) will both overrun by 10 hours, find the new minimum completion time for the project.
   \includegraphics[max width=\textwidth, alt={}]{5123be51-168e-4487-8cd3-33aee9e3b23f-02_1515_1709_1192_153}
   \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{5123be51-168e-4487-8cd3-33aee9e3b23f-03_1656_869_627_611}
   \end{figure}

2 A project is represented by this activity network. The weights (in brackets) on the arcs represent activity durations, in minutes. \includegraphics[max width=\textwidth, alt={}, center]{fc01c62e-64bd-4fbc-ac1e-cdfa47c07228-3_645_1235_356_415}

1. Complete the table in the answer book to show the immediate predecessors for each activity.
2. Carry out a forward pass and a backward pass through the activity network, showing the early event time and the late event time at each vertex of your network. State the minimum project completion time and list the critical activities. Suppose that the start of one activity is delayed by 2 minutes.
3. List each activity which could be delayed by 2 minutes with no change to the minimum project completion time.
4. Without altering your diagram from part (ii), state the effect that a delay of 2 minutes on activity \(A\) would have on the minimum project completion time. Name another activity which could be delayed by 2 minutes, instead of \(A\), and have the same effect on the minimum project completion time.
5. Without altering your diagram from part (ii), state what effect a delay of 2 minutes on activity \(C\) would have on the minimum project completion time.

4 A project is represented by the activity network below. The activity durations are given in minutes. \includegraphics[max width=\textwidth, alt={}, center]{6f64abca-108c-4b81-8ccf-124dfd9cc2f6-5_447_1020_392_246}

1. Give the reason for the dummy activity from event (3) to event (4).
2. Complete a forward pass to determine the minimum project completion time.
3. By completing a backward pass, calculate the float for each activity.
4. Determine the effect on the minimum project completion time if the duration of activity A changes from 2 minutes to 3 minutes. The duration of activity C changes to \(m\) minutes, where \(m\) need not be an integer. This reduces the minimum project completion time.
5. By considering the range of possible values of \(m\), determine the minimum project completion time, in terms of \(m\) where necessary.

1 The table below shows the activities involved in a project together with the immediate predecessors and the duration of each activity.

1. Model the project using an activity network.
2. Determine the minimum project completion time. The start of activity C is delayed by 2 hours.
3. Determine the minimum project completion time with this delay.

7. \begin{figure}[h] \end{figure} \section*{[The sum of the duration of all activities is 172 days]} A project is modelled by the activity network shown in Figure 5. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires one worker. The project is to be completed in the shortest possible time.

1. Complete Diagram 1 in the answer book to show the early event times and late event times.
2. Calculate the total float for activity M. You must make the numbers you use in your calculation clear.
3. For each of the situations below, explain the effect that the delay would have on the project completion date.
   1. A 2 day delay on the early start of activity P.
   2. A 2 day delay on the early start of activity Q .
4. Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. Diagram 2 in the answer book shows a partly completed cascade chart for this project.
5. Complete the cascade chart.
6. Use your cascade chart to determine a second lower bound on the number of workers needed to complete the project in the shortest possible time. You must make specific reference to times and activities.
7. State which of the two lower bounds found in (d) and (f) is better. Give a reason for your answer.
   (Total 17 marks)

3 Deva Construction Ltd undertakes a small building project. The activity network for this project is shown below in Figure 1, where each activity's duration is given in hours. \begin{figure}[h] \end{figure} 3

1. Complete the activity network for the building project. 3
2. Deva Construction Ltd is able to reduce the duration of a single activity to 1 hour by using specialist equipment. State, with a reason, which activity should have its duration reduced to 1 hour in order to minimise the completion time for the building project.
   3
3. State one limitation in the building project used by Deva Construction Ltd. Explain how this limitation affects the project.
   [0pt] [2 marks]

4 Deva is having some work done on his house. The table shows the activities involved, their durations and their immediate predecessors.

1. Model this information as an activity network.
2. Find the minimum time in which the work can be completed.
3. Describe the effect on the minimum project completion time of each of the following happening individually.
   1. The duration of activity A is increased to 3.5 hours.
   2. The duration of activity D is increased to 4 hours.
   3. The duration of activity F is decreased to 2 hours. The decorators working on activity H cannot work for 3 hours without a break.
   4. How would you adapt your model to incorporate the break?

1 [Figures 1 and 2, printed on the insert, are provided for use in this question.]
The following diagram shows an activity network for a project. The time needed for each activity is given in days. \includegraphics[max width=\textwidth, alt={}, center]{f98d4434-458a-4118-92ed-309510d7975a-02_940_1698_721_164}

1. Find the earliest start time and the latest finish time for each activity and insert their values on Figure 1.
2. Find the critical paths and state the minimum time for completion.
3. On Figure 2, draw a cascade diagram (Gantt chart) for the project, assuming each activity starts as early as possible.
4. Activity \(C\) takes 5 days longer than first expected. Determine the effect on the earliest start time for other activities and the minimum completion time for the project.
   (2 marks)

1 [Figure 1, printed on the insert, is provided for use in this question.]
A decorating project is to be undertaken. The table shows the activities involved.

1. Complete an activity network for the project on Figure 1.
2. On Figure 1, indicate:
   1. the earliest start time for each activity;
   2. the latest finish time for each activity.
3. State the minimum completion time for the decorating project and identify the critical path.
4. Activity \(F\) takes 4 days longer than first expected.
   1. Determine the new earliest start time for activities \(H\) and \(I\).
   2. State the minimum delay in completing the project.

3 A project consists of 11 activities \(A , B , \ldots , K\) A completed activity network for the project is shown in the diagram below. \includegraphics[max width=\textwidth, alt={}, center]{ecbeedf5-148e-40ad-b8a2-a7aa3db4a115-04_972_1604_445_219} All times on the activity network are given in days.
3

1. Write down the critical path.
   [0pt] [1 mark] 3
2. Due to an issue with the supply of materials, the duration of activity \(G\) is doubled. Deduce the effect, if any, that this change will have on the earliest start time and latest finish time for each of the activities \(I , J\) and \(K\)

Bill Durrh Ltd undertake a construction project. The activity network for the project is shown below. The duration of each activity is given in weeks. \includegraphics{figure_7}

1. 1. Find the earliest start time and the latest finish time for each activity and show these values on the activity network above. [3 marks]
   2. Identify all of the critical activities. [1 mark]
2. The manager of Bill Durrh Ltd recruits some additional temporary workers in order to reduce the duration of one activity by 2 weeks. The manager wants to reduce the minimum completion time of the project by the largest amount. State, with a reason, which activity the manager should choose. [2 marks]