Local and Global Objectives

In the business world it is common to fix objectives defined at different levels, for example some personal, others local and others global. These objectives are often defined by different people or teams and it is very important that they are aligned with each other in order to avoid undesired situations. If we think of local objectives as those that focus on improving a particular aspect of a situation, while global objectives seek to maximize the overall result, it is important to understand that a local maximum is not always a global maximum. Achieving an optimal solution in one part of the problem does not guarantee that it is the best solution for the entire problem. In the following, we will explore why this is so.

A simple example to understand this is the problem of finding the highest point on a hill. If we only look at the small section of the hill directly in front of us, we can easily find the highest point on that section, but that does not mean that point is the highest point on the entire hill. To find the highest point on the whole hill, we need to consider all the sections and look for the highest point among all of them.

In a more complex problem, there are many variables and factors that need to be considered to achieve an optimal solution. If we focus only on a local objective, we may not consider other important factors that could have a significant impact on the overall outcome. For example, in the design of an automobile, it is important to consider not only engine performance, but also safety, energy efficiency, and driver and passenger comfort. If we only focus on improving engine performance, we could end up with a car that is fast but dangerous and inefficient.

Mathematically we could have something like the figure above where two functions have their local maximums for certain values, but the global maximum (the sum of the two) is given for values in which there are no local maximums. That is to say, we would have the greatest profit when none of the other areas has its greatest profit. Curious, isn’t it? When setting objectives, it must be taken into account that they are not excessively influenced by other objectives set at another level, because everything is interrelated.

When we take the interdependence of objectives to the extreme, it is when they can clash and be directly incompatible. In this situation we have that a local optimal objective is not compatible with other local optimal objectives. For example, we may have a quarterly global objective to make a higher than normal quantity of products, and on the other hand a local objective for the maintenance team to overhaul all machines. In this case two teams would conflict because the team in charge of the first objective needs to keep the machines running as long as possible while the second team needs to stop the machines in order to overhaul them. In this case, it is like a game of tug-of-war with two teams each pulling towards their goal and usually the outcome is that there is friction between the teams, neither goal is achieved and everyone is disappointed in some way.

We can say then that it is important to keep in mind that local and global objectives are equally important in the search for optimal solutions to complex problems, but they must be aligned. A local optimal objective may not be compatible with other local (or global) optimal objectives and, therefore, does not guarantee the best global solution. Therefore, it is necessary to consider all relevant objectives, ensure that they are aligned and not contradictory, and seek a balance to achieve the globally optimal solution.