Every morning I take my children to school by car. The ride isn’t very long but all the same, to make use of this time, we play a game to find licence plates that read the same forwards as backwards. They are palindromes. It is a simple game that they can easily understand, and it is plain and unambiguous.

The problem arises when, suddenly, one of my children says: “That licence plate is almost a palindrome”. And often when this happens, my other child will say, “No, that’s not almost a palindrome. It’s very different.” Actually, they are both right.

In this case, we have no simple criterion to determine whether a number is almost a palindrome. What for one person is almost a palindrome can be very different for someone else.

In fact, to determine if a number is almost a palindrome, we would need to define a function that allows us to measure the distance from being a palindrome. Once such as measure were defined, we would need to define a threshold of values for which we would consider the licence plate to be almost a palindrome.

For example, if our function measures the minimum number of digits that we have to alter so that the number becomes palindrome, we will find that the licence plate numbers 0121, 0101 and 0127 have exactly the same distance (i.e. 2) from being a palindrome. If we decide that the licence plates whose distance from being a palindrome is less than or equal to 1 will be considered “almost a palindrome”, then none of these three fulfil this criteria and, moreover, the three will be exactly the same as being nearly a palindrome.

Even in this simple case, if we present it to several people, we will most likely hear several different views:

- Some would say that 0101 is almost a palindrome, because by swapping the last two digits it becomes a palindrome.

Others will say that, obviously, the licence plate 0121 is even closer to being a palindrome than 0127 since, although the same number of digits are changed, the digits changed are closer. - …

And so, we would have all kinds of different opinions for the definition of “almost a palindrome”.

As much as we refine the function of distance, as well as the threshold, there will always be opinions for and against the results. While the definition of a palindrome is simple and specific, that of being nearly a palindrome is highly subjective, so you would need to sit down with each individual to define the function of distance and its threshold.

## So, why am I telling you all this?

Typically our optimisation work consists of building optimisation engines that propose solutions to our customers’ problems. Depending on the sector, these may be Workshift Allocators, Production Planners, Route Optimisers, etc.

In all these cases, the initial approach is to build an engine which, upon inputting data, returns a good workable solution (see previous post). Although this approach may seem theoretically sufficient, when asked

What if someone gets sick? What if a machine breaks down?

The answer is always the same:

Then we need to re-plan and to try to fill the gap by making minimal changes to the existing plan.

Upon hearing these words, a consultant without a great deal of experience would register the answer and be pleased to have this information.

However, since we earlier took a look at the subjectivity involved behind the question of how to determine whether a licence plate was almost a palindrome, one can imagine the complexity that lies behind the phrase

… modify the existing plan as little as possible

What does ‘as little as possible’ mean for our customer? Is it better to make a minimal number of changes, or is it better to make a greater number of changes that will have a lower impact? In the second case, how do we define impact? Do we mean the impact on the worker, or the impact on the company? Or both?

When an experienced consultant receives such a response, a better reaction would possibly be to take note of this and put it to one side, but by no means to think that the matter is closed. Actually, instead of closing the matter off, another has been opened, and the scale of this new issue must not be underestimated. Compiling all the subjectivity hidden behind this innocent phrase can be a task which could take weeks to sort out, if the consultant is lucky.