Getting Things Done With Weight

In my last article titled Scheduling and Moore’s Algorithm, I had mentioned that sometimes we just want to get things done and without the need of meeting any deadline, that there is no particular limit when you want things to get done but you just want it all to get done at the earliest as possible. In such a situation, it’s hard to explicitly impose “the most efficient” scheduling strategy here to solve the problem.

But what we can and might want to do is take a different perspective. Let’s assume that you’re a freelancer and you are given two projects on Monday. You make some assumptions and decide that it takes roughly 4 days for the first project to complete and merely 1 day for the second project to complete. Now going by the “complete difficult tasks first” principle stated by many gurus, you should essentially be starting with the 4 day project first which obviously is relatively complex than the other. But let’s look back and analyze. If you start with the 4 day project first and deliver it on Thursday afternoon (4 days elapsed) and then deliver the 1-day project on Friday (5 days elapsed), the clients would’ve waited for a total of 4+5 = 9 days. Now, this is with regard to the start time, i.e. Sunday and the summation is done as both are individual projects from different clients. The first client would be satisfied with completion of project in 4 days but what about the client who handed out the second project ? Now, if we reverse the order and complete the second project first and then do the first project, the clients have to wait for just 1+5 = 6 days. Ultimately, it’s consuming a full week for you but in terms of the client’s, you saved three days of their combined time. In scheduling theory, this metric of adding up completion times with respect to different tasks is called as “sum of completion times”.

Of course, the most intuitive way to have a better strategy is to minimize the completion time and this can be done using a very simple and optimal algorithm called as “Shortest Processing Time (SPT) ”. This algorithm literally says “always do the quickest task you can”. Once again, the total amount of time it’ll take for you to work will be the same but SPT eases your mind by reducing the number of tasks as quickly as possible and provides a little bit of mental and psychological strength to get other things off your checklist.

Checklist, argh. Now if you think about a checklist, you might have different tasks written and it’s understood that not all tasks will be of equal importance. There might a “do a health checkup” and “complete the final project” listed in your checklist. The first task might take more time than the other but it demands importance. This brings us to understanding what “weight” means in Scheduling. One can also associate “weight” in literal terms and associate it with his/her checklist. You can think about checking off an important task with max weight as putting down a heavy load off your shoulders. A tasks completion time shows how long you can carry this burden and now you want to minimize the sum of weighted completion times.

This however, can be done with a minor adjustment to the Shortest Processing Time (SPT) algorithm. It makes sense to divide the weight of each task by the time taken for it to finish and then work in order from the highest to lowest.

The term “weight” can be interpreted to any situation accordingly. In terms of business as explained above, you can look at weight as something that divides reward over duration. In the above mentioned example of a Freelancer, you can interpret weight as the total fee divided by total time taken taken to complete the project. But in terms of debt over incomes, this essentially says to simply get done with the debt with highest interest rate as this logically carries the most weight.

And once again, as things proceed it’s up to us to choose in what way we wish to see and work on things. Do you want to reduce the “number” of tasks off your checklist or reduce the weight of your burden? Although the second makes more sense, if you still wish go for reducing the number of tasks to gain an increased mental health to fuel completion of other tasks, then you might as well choose that. Either way, whatever works for you, go for it.

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