Example of Decreasing Time Algorithm

Davenport University MATH200 – Planning and Scheduling

Example of Decreasing Time Algorithm for Independent Tasks

Problem: We must create a schedule for independent tasks using the decreasing time algorithm with two processors to complete the eight task project with times given in figure 1 below.

Figure 1 - The Task List (Task times in circles)

T-1 T-2 T-3 T-4

8 7 5 3

5 6 9 4

T-5 T-6 T-7 T-8

Optimal Time for Independent Task Problem: Recall that among our goals in creating a schedule is to both minimize total project time and minimize the amount of down (or idle) time experienced by the processors. Unlike the other cases, determining the optimal time for an independent task project happens to be fairly straightforward: Sum the task times, divide by the number of processors, and then round up to the next whole number if necessary.

In our example, the total of the task times is 47 and dividing it by 2 (number of processors) gives us 23.5. So, if our method below yields a project schedule that is complete at time 24 (23.5 rounded up to the next whole number), then our schedule will be optimal.

Solution: As we begin the scheduling process, we need to place the tasks in descending order with respect to time: T-7, T-1, T-2, T-6, T-3*, T-5*, T-8, and T-4

*Note: Tasks that take an equal amount of time can be scheduled in any order. Instead of listing T-3 before T-5 above, we could have chosen T-5 before T-3 and it would still result in the identical project completion time.

With just the two processors, we can only start the top two tasks on the priority list: T-7 and T-1. T-1 finishes first (at time 8) and we can immediately start T-2. T-7 is complete soon after (at time 9), and we can begin T-6. T-2 and T-6 finish simultaneously (at time 15) and are followed by T-3 and T-5 (it is coincidence that these items ended up being started at the same time). T-3 and T-5 also end concurrently (time 20) and the final two tasks, T-8 and T-4, now begin. T-8 is the last task to be completed at time 24 (see Figure 2 below for complete schedule).

Figure 2 - Processor Schedule Machine 1 T-7 T-6 T-3 T-8 Machine 2 T-1 T-2 T-5 T-4 Time 8 9 15 20 23 24

Reflection: In this instance we were able to create an optimal schedule. Again, please remember that we will not always be so fortunate.