# Is Near Enough Ever Good Enough?

A mountain climber generally wishes to reach the highest point of a mountain, and for a mountain such as the Matterhorn the summit is very well defined, making it easy to tell whether the peak has been attained. However, if you were allowed to climb Merrick Butte in the USA’s Monument Valley, it would be much more difficult to ensure the precise location had been found.

Identifying the optimal solution to a problem is a common requirement in business. An obvious need is to maximise profits, but other problems include minimising time spent or maximising quality. Generally the mathematical approach is to develop a model for what is being optimised and then find the combination of inputs that gives the best answer from that model.

The complexity can vary markedly, from where there is only a single input that can be varied to where dozens of interconnected inputs could be changed. Once multiple inputs are involved, the effort and cost to develop a model and then determine the optimal solution rapidly increase. Sometimes it is necessary to ask whether the cost of finding the optimum is worth it.

Data Analysis Australia consultants are experienced in solving complex optimisation questions, but we also recognise that solutions must be ‘fit for purpose’.  We work with clients to understand the background behind the question, and advise on the implications of accepting a level of imperfection, or uncertainty, in results.  While a purist mountaineer may be unwilling to settle for anything less than the absolute maximum, for many others the sense of achievement in climbing Merrick Butte would be the same as long as the plateau was reached.

In a numerical sense, having a large area that is almost optimal makes it particularly difficult to identify the overall or global optimum.  However, in a practical sense it can be ideal, reducing the risk inherent in accepting a sub-optimal solution – near enough is good enough.

Compare this to climbing the Matterhorn, when a small error can result in falling off, or seeing the view from only halfway up – near enough is not good enough.  Knowing which mountain you are climbing is critical!

An example of Data Analysis Australia’s work in this area is an investigation of the potential location of court facilities, where we used demand projections, travel models and linear programming to give optimal locations for Courts.  By reducing the detail of the model to suburbs we saved enormous effort in modelling.  And suburbs were good enough for Court locations since many other, more subjective factors could then influence final decisions.