# Activity-on-Arrow (AOA) Diagram Construction Given the activity table: | Activity | Immediate Predecessor(s) | |----------|:-----------------------:| | A | — | | B | — | | C | A | | D | A | | E | B | | F | B | | G | C, E | | H | D, F | Let's build the AOA diagram step by step. --- ## Step 1: Start Nodes **Explanation:** Activities **A** and **B** have no predecessors, so they both start from the initial event (node). - Draw a start node (Node 1). - Draw arrows from Node 1 to two new nodes (Node 2 for A, Node 3 for B), representing activities A and B. --- ## Step 2: Activities after A **Explanation:** Activities **C** and **D** depend only on **A**. - From the end node of A (Node 2), draw arrows to new nodes (Node 4 for C, Node 5 for D). --- ## Step 3: Activities after B **Explanation:** Activities **E** and **F** depend only on **B**. - From the end node of B (Node 3), draw arrows to new nodes (Node 6 for E, Node 7 for F). --- ## Step 4: Activity G (Depends on C, E) **Explanation:** **G** requires both **C** and **E** to be completed. - Both C (Node 4) and E (Node 6) need to converge before G can start. - Draw arrows from Node 4 and Node 6 to a new node (Node 8), with a dummy arrow from Node 6 to Node 8 (since E is not directly connected to C). - From Node 8, draw the arrow for G to a new node (Node 9). --- ## Step 5: Activity H (Depends on D, F) **Explanation:** **H** requires both **D** and **F** to be completed. - Both D (Node 5) and F (Node 7) need to converge before H can start. - Draw arrows from Node 5 and Node 7 to a new node (Node 10), with a dummy arrow if necessary. - From Node 10, draw the arrow for H to a new node (Node 11). --- ## **Full AOA Diagram Structure** ```plaintext (Start) | [A] [B] | | (Node2) (Node3) | \ | \ [C] [D] [E] [F] | | | | (Node4)(Node5) (Node6)(Node7) | \ / \ \ \ / \ \ [dummy] [dummy] \ / / [G] (Node8) [H](Node10) | | (Node9) (Node11) ``` (Dummy arrows are used to maintain correct precedence when more than one activity depends on two or more predecessors.) --- ## **Conclusion** The AOA diagram visually represents the sequence and interdependencies among the activities. - **Start:** Activities A and B begin the project. - **Parallel Paths:** After A and B, activities branch out and proceed in parallel where possible. - **Convergence:** Activities G and H require completion of two prior activities each, necessitating dummy arrows to illustrate these convergences. - **End:** The project concludes after activities G and H. This structure is useful for identifying the project’s critical path, managing dependencies, and scheduling tasks efficiently.