Queuing Theory

In mathematics, Queuing Theory is the study of waiting lines or queues as they are often called. With queuing theory, mathematicians are able to analysis several related processes such as joining the (back of the) queue, waiting in the queue, and being served at the front of the queue.  

In this article, we will look at using queuing theory to systematically organise a production process to improve productivity and save time and wait. However, before we dig deep into the concept, there are a number of things that should be noted. First, it should be understood that queuing theory takes into consideration a number of variable such as: the position where the queue is joined, the time it took to stand in line before being served, the time it takes to get served, who serves, and a host of other variables. For this reason, it is safe to conclude that queuing theory is more of a statistical theory than an actual mathematical theory.

Without Further ado, consider the following sections:

Queuing Theory and an Organisational Setting:

Since queuing theory is based on joining queues, waiting, and getting served, how can this be related to an organisational setting? For simplification, we’ll only consider a manufacturing process such as pen, bottle, or other product manufacturing. Say for instance, in a simple bottle manufacturing plant for a fruit juice packaging company, the process for getting the bottles ready for the fruit juice to be poured into them may be as follows:

1. Bottle arrives at the start point of the process and joins the queue.
2. The bottle waits for its turn to get processes; i.e. cleaned, disinfected, dried, and labelled.
3. The bottle moves slowly in line until it gets to its turn to undergo cleaning.
4. The cleaning, disinfecting etc process begins.
5.  The process is completed, hence the end of this example process.

Now, queuing theory can be used to analyse a number of issues that can possibly affect the bottle preparation process. For instance, how long does it take the bottle to make it to the queue? Once it gets to the queue, how long does it have to wait before it undoes the cleaning process and how long does the cleaning take? In addition to that, knowing how many bottles get cleaned at a time is another question that needs an answer.  These issues and more, once discovered, will help the management staff understand the process more and come up with ways to improve it.

The aim is to get the line moving as fast as possible because, the faster a line (of bottles in this case) can move and get served, the faster the manufacturing process, and hence the more productive the entire process will be.

Based on the above, we can conclude that understanding the possible variables present in a manufacturing process such as that described above will make it a lot easier to improve or speed up the process while maintaining good quality to meet customers’ expectations.