Critical Paths and Scheduling Tasks Circuits, Paths, and Schedules

Critical Path Analysis Sometimes we cannot simply choose our route as we have to do things in a certain order. A path is a logical progression from one task to the next. A task is an action that takes a certain amount of time. The total time to complete any task will depend completely on the critical path.

The critical path is the path with the longest time completion as this is the shortest time in which EVERYTHING can get completed.

Scheduling Tasks Processors may be machines or they may be humans. Either way, they are assigned a task. Once that task is completed, they move on to the next available task. Our goal is to schedule processors in such a way that they have as little idle (unproductive) time as possible.

The Rules 1. Once a processor begins a task it will continue that task without interruptions until the task is completed. 2. A processor cannot opt to skip a task that is available and remain idle. 3. We must abide by the order-requirement digraph. (A diagram-graph that has order restrictions built in.) 4. We will have a priority list.

List-Processing Algorithm A viable algorithm, even if not the optimal solution. We must know the number of processors, have a priority list, and have an order-requirement digraph. Assign the first ready task on the priority list that has not already been assigned to the lowest-numbered processor that is not currently working on a task.

Circuits, Paths, and Schedules Independent Tasks

Some tasks have no order required and therefore no order requirement-digraph. These are called independent tasks. Decreasing-time-list algorithm – List all completion times in decreasing order (biggest to smallest) and then assign tasks to processors in order.

Bin Packing Next-fit-decreasing Use the decreasing time list and place first item on first shelf. Continue as long as an item fits, otherwise move on to the next shelf. You can never return to a previous shelf. First-fit-decreasing Use the decreasing time list and place first item on first shelf. Continue as long as an item fits, otherwise move on to the next shelf. You CAN return to previous shelves. Worst-fit-decreasing Use the decreasing time list and place items in shelves with most space available first.