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the optimal pace problem
Econometrie Economie Operations Research Samenleving Statistiek Wiskunde

The Optimal Pace

For professional athletes, the goal of running a marathon is to complete it as fast as possible. However, this does not mean that the athletes are running as hard as they can all the time, as one cannot maintain this pace the entire marathon. Hence they need to find a maintainable pace at which they finish the marathon as fast as possible: the optimal pace problem.

It turns out that this very general problem is occurring far more often in normal day life and in business than most of us realise. Furthermore, it turns out that more often than not, the optimal pace is not equal to the maximum pace, like in the marathon example.

To give some insight on the broad application of the pace problem, I have some examples of everyday situations where we encounter it.

 

Traffic jams on the highway are a frustration for many people. Driving maximum speed, on the other hand, is beloved by many. However, traffic psychologists and researcher in the Netherlands have concluded that the speed limit had to be lowered to improve the flow of traffic. It turns out that 95 kilometres per hour is the optimal pace on the highway, which is way lower than the current speed limit of 130 kilometres per hour on some highways.

However, there are some massive advantages to the lower velocity. Firstly, it leads to less speed differences between vehicles, which are the main cause of traffic jams. Secondly, vehicles can drive closer to each other, so the highway can be used more efficiently. Thirdly, the number of accidents likely decreases, also due to lower speed differences as we have to brake less. Lastly but certainly not least, the lower pace leads to lower carbon dioxide emission and vehicles are using their fuel more efficiently. This is of course a huge benefit for the environment.

Of course, it takes some more time to reach your final destinations, but since there will be far less traffic jams, the difference in driving time is almost neglectable.

 

A second example can be found in the phone industry. Companies design new phones to keep customers happy and to get new users. Of course, releasing new phones all the time would not be the smartest strategy. A new phone must realize a good revenue and a sufficient demand to make it a profitable product. Customers won’t buy a phone if they know a new one will already be released shortly afterwards. Furthermore, a high pace of releases probably implies that the difference in quality between phones is insufficient to make it an appealing product. Therefore, phone companies set the pace of releases to a certain rate to make sure the old release makes enough profit and that there is enough demand for the new release.

 

A third and last example can be found in the supermarket, in the form of cash registers. For a customer, it would be ideal if you never had to wait in line before you got helped. However, to obtain this maximum pace of service, it would mean that the supermarket would need an enormous number of cash registers, all available at every moment. Obviously, it is not surprising that this costs a huge amount of money, leading to a huge increase in costs, while the revenue is not increasing. Hence supermarkets have to make the consideration between service time for customers and the costs of these services. This problem of the rate of serving customers and the costs of serving is a far wider problem than just supermarkets. It can, for example, also be applied in customer service, restaurants and car manufacturing.

 

As seen in the examples above, the optimal pace clearly does not need to be equal to the maximum pace. This often is due to the negative effects of a high velocity. These negative effects are often relative higher costs, missing out on possible profit or bad effects on the environment. Finding the optimal pace mind sound extremely vague but it is applicable to a lot of situations in our world. Therefore, solving this problem in the particular cases, by using data and econometric research, can be very important to improve our life, our world, or in some cases, to improve our bank account.


This article was written by  Casper de Vries

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