Schedule with limited workers - create schedule/chart

4 The table lists tasks which are involved in adding a back door to a garage. The table also lists the duration and immediate predecessor(s) for each task. Each task is undertaken by one person.

1. Draw an activity on arc network for these activities.
2. Mark on your diagram the early time and the late time for each event. Give the minimum completion time and the critical activities.
3. Produce a schedule to show how two people can complete the project in the minimum time. Soon after starting activity D , the marble step breaks. Getting a replacement step adds 4 hours to the duration of activity D.
4. How does this delay affect the minimum completion time, the critical activities and the minimum time needed for two people to complete the project? \section*{Question 5 begins on page 6}

7. This question should be answered on the sheet provided. \begin{figure}[h] \end{figure} Figure 2 shows an activity network modelling the tasks involved in widening a bridge over the B451. The arcs represent the tasks and the numbers in brackets gives the time, in days, to complete each task.

1. Find the early and late times for each event.
2. Determine those activities which lie on the critical path and list them in order.
3. State the minimum length of time needed to widen the bridge. Each task needs a single worker.
4. Show that two men would not be sufficient to widen the bridge in the shortest time.
   (2 marks)
5. Draw up a schedule showing how 3 men could complete the project in the shortest time. \section*{Please hand this sheet in for marking}
   1. Complete matching:

      \(P\)	\(\bullet\)	\(\bullet\)	\(D\)
      \(Q\)	\(\bullet\)	\(\bullet\)	\(G\)
      \(R\)	\(\bullet\)	\(\bullet\)	\(E\)
      \(S\)	\(\bullet\)	\(\bullet\)	\(L ( H )\)
      \(T\)	\(\bullet\)	\(\bullet\)	\(L\)

      \section*{Please hand this sheet in for marking}

   2. \(x\)	\(a\)	\(b\)	\(( a - b ) < 0.01\) ?
      100	50	26	No
      -	26	14.923	No

      Final output
   3. \(\_\_\_\_\)

   4. \(x\)	\(a\)	\(b\)	\(( a - b ) < 0.01 ?\)
      100

   5. \(\_\_\_\_\) \section*{Please hand this sheet in for marking}
   6. \includegraphics[max width=\textwidth, alt={}, center]{1e518ab0-9852-4d1d-a4c9-344a5edf9547-11_768_1689_427_221}
   7. \(\_\_\_\_\)
   8. \(\_\_\_\_\)

   9. 0	5	10	15	20	25	30	35	40	45	50	55	60
      Worker 1
      Worker 2

   10. 0	5	10	15	20	25	30	35	40	45	50	55	60
       Worker 1
       Worker 2
       Worker 3

6.

1. Draw the activity network for the project described in the precedence table, using activity on arc and the minimum number of dummies. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{ba9337bf-7a3c-49aa-b395-dd7818cf1d13-10_880_1154_1464_452} \captionsetup{labelformat=empty} \caption{Grid 1}
   \end{figure} A cascade chart for all the activities of the project, except activity \(\mathbf { L }\), is shown on Grid 1. The time taken to complete each activity is given in hours and each activity requires one worker. The project is to be completed in the minimum time using as few workers as possible.
2. State the critical activities of the project.
3. Use the cascade chart to determine the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to time and activities. (You do not need to provide a schedule of the activities.) The duration of activity L is \(x\) hours. Given that the total float of activity L is at most 7 hours,
4. determine the range of possible values for \(\chi\).

6. \begin{figure}[h] \end{figure} A building project is modelled by the activity network shown in Fig. 4. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, taken to complete the activity. The left box entry at each vertex is the earliest event time and the right box entry is the latest event time.

1. Determine the critical activities and state the length of the critical path.
2. State the total float for each non-critical activity.
3. On the grid in the answer booklet, draw a cascade (Gantt) chart for the project. Given that each activity requires one worker,
4. draw up a schedule to determine the minimum number of workers required to complete the project in the critical time. State the minimum number of workers.
   (3)

3. \begin{figure}[h] \end{figure} A project is modelled by the activity network shown in Figure 3. 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 H. You must make the numbers you use in your calculation clear.
3. Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. Show your calculation. Diagram 2 in the answer book shows a partly completed scheduling diagram for this project.
4. Complete the scheduling diagram, using the minimum number of workers, so that the project is completed in the minimum time.

2. \begin{figure}[h] \end{figure} A project is modelled by the activity network shown in Figure 2. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, to complete the corresponding activity.

1. Complete Diagram 1 in the answer book to show the early event times and the late event times. Each activity requires one worker and the project must be completed in the shortest possible time using as few workers as possible.
2. Calculate a lower bound for the number of workers needed to complete the project in the shortest possible time. You must show your working.
3. Schedule the activities using Grid 1 in the answer book.

6. The precedence table below shows the 12 activities required to complete a project.

1. Draw the activity network described in the precedence table, using activity on arc. Your activity network must contain the minimum number of dummies only.
   (5) Each of the activities shown in the precedence table requires one worker. The project is to be completed in the minimum possible time. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{7f7546eb-0c1a-40da-bdf0-31e0574a9867-11_303_1547_296_260} \captionsetup{labelformat=empty} \caption{Figure 3}
   \end{figure} Figure 3 shows a schedule for the project using three workers.
2. 1. State the critical path for the network.
   2. State the minimum completion time for the project.
   3. Calculate the total float on activity B.
   4. Calculate the total float on activity G. Immediately after the start of the project, it is found that the duration of activity I, as shown in Figure 3, is incorrect. In fact, activity I will take 8 hours.
      The durations of all the other activities remain as shown in Figure 3.
3. Determine whether the project can still be completed in the minimum completion time using only three workers when the duration of activity I is 8 hours. Your answer must make specific reference to workers, times and activities.

5. This question should be answered on the sheet provided in the answer booklet. \begin{figure}[h] \end{figure} Figure 2 shows the activity network used to model a small building project. The activities are represented by the edges and the number in brackets on each edge represents the time, in hours, taken to complete that activity.

1. Calculate the early time and the late time for each event. Write your answers in the boxes on the answer sheet.
2. Hence determine the critical activities and the length of the critical path. Each activity requires one worker. The project is to be completed in the minimum time.
3. Schedule the activities for the minimum number of workers using the time line on the answer sheet. Ensure that you make clear the order in which each worker undertakes his activities.
   (5 marks)

5. This question should be answered on the sheet provided in the answer booklet. \begin{figure}[h] \end{figure} Figure 2 shows the activity network used to model a small building project. The activities are represented by the edges and the number in brackets on each edge represents the time, in hours, taken to complete that activity.

1. Calculate the early time and the late time for each event. Write your answers in the boxes on the answer sheet.
   (6 marks)
2. Hence determine the critical activities and the length of the critical path.
   (2 marks)
   Each activity requires one worker. The project is to be completed in the minimum time.
3. Schedule the activities for the minimum number of workers using the time line on the answer sheet. Ensure that you make clear the order in which each worker undertakes his activities.
   (5 marks)

Kirstie has bought a house that she is planning to renovate. She has broken the project into a list of activities and constructed an activity network, using activity on arc. \includegraphics{figure_1}

1. Construct a cascade chart for the project, showing the float for each non-critical activity. [7]
2. Calculate the float for remodelling the internal layout stating how much of this is independent float and how much is interfering float. [3]

Kirstie needs to supervise the project. This means that she cannot allow more than three activities to happen on any day.

1. Describe how Kirstie should organise the activities so that the project is completed in the minimum project completion time and no more than three activities happen on any day. [3]