Answer To: Assignment 1 (20 marks) Question 1. A shop works a 400-minute day. The manager of the shop wants an...
Banasree answered on Mar 22 2023
To construct the precedence diagram, we can use the information given in the table to create a network diagram that shows the sequence in which the tasks must be completed.
The nodes of the network diagram represent the tasks, and the arrows connecting the nodes represent the sequence in which the tasks must be completed. The duration of each task and its immediate predecessors are also indicated in the table.
Using this information, we can create the following precedence diagram:
In this diagram, the task nodes are represented by rectangle box, and the duration of each task is shown in parentheses next to the task node. The arrows connecting the task nodes indicate the order in which the tasks must be completed. The immediate predecessors of each task are shown above the task node. The task e has two immediate predecessors, b and c, and task j has two immediate predecessors, e and i. These dependencies are indicated by multiple incoming arrows to the task nodes.
To assign tasks according to the most following tasks rule, prioritize the tasks based on the number of immediate successors that each task has. The task with the most immediate successors should be given the highest priority.
In case of ties, use the greatest positional weight rule to break them. This means that prioritize the task with the highest immediate predecessor, i.e., the task that comes first in the precedence diagram. Using this approach:
Task a has no immediate successors, so it is assigned first.
Task e has two immediate successors (g and i), which is the highest number, so it is assigned next.
Tasks b, c, and d each have one immediate successor, so they are tied for the next priority. Among these, task b has the highest immediate predecessor (a), so it is assigned next, followed by tasks c and d.
Task i has one immediate successor (j), which is the same as tasks b, c, and d, but it has the highest immediate predecessor (f), so it is assigned next.
Task j has one immediate successor (k), so it is assigned next.
Task f has one immediate successor (i), so it is assigned next.
Task h has one immediate successor (k), so it is assigned next.
Task k has one immediate successor (m), so it is assigned next.
Task g has no immediate successors, but it has already been assigned as part of the e branch.
Task m has no immediate successors, so it is assigned last.
The final task assignment, with the assigned tasks in parentheses, is:
a (a) -> b -> c -> d -> e (e) -> g...