Thursday, 27 December 2012

Providing a bicycle for the mind; Mathematical modelling in portfolio decision making

Today's economy is driven by global uncertainties such as exchange rates, oil and energy prices, layered upon local uncertainties involving individual projects. These uncertainties create an unprecedented number of interdependent risks that hamper high quality decision making. Most Oil & Gas companies lack a consistent approach to modelling these uncertainties and risks, specifically in core decisions like exploration and production portfolio selection. Instead, they typically use averages to represent uncertainties. This leads to a class of systematic errors known as the ‘flaw of averages’.

In March 2012 Stanford University professor Sam Savage and I were interviewed on managing uncertainty in portfolio decisions by Paragon. In this interview we shared our views on portfolio optimisation and how to coherently manage uncertainties and improve decision making in portfolio decisions.

As we discuss in the interview complexity of decision making in Oil & Gas has increased in the last decade. There is a need to find new sources of oil and gas as the production level of the current portfolios is diminishing. Because these new sources of oil and gas are more difficult to reach (like deep sea, arctic or shale) new and more complex techniques are required which have high investment costs. Together with the uncertainty of finding oil and the amount of oil found, uncertainty in decision making has increased a lot. As the stakes have risen, also the risks have increased.

The Oil & Gas industry has a history of failing to deliver on promised performance. A survey of Bickel and Bratvold among petroleum engineers shows that many executives are dissatisfied with their companies’ performance, citing budget and cost overruns. They therefore require more brains per barrel to understand the impact of uncertainty and improve decision making. Prof Savage and I conclude that mathematical models will be the enabling technology that will make it easier to get a grip on the increased complexity, include uncertainty in decision making and therefore improve decision quality. Also mathematical modelling will improve consistency in decision making and reduce time to reach a decision; it will provide a bicycle for the mind in portfolio decisions.

We argue that in mathematical modelling one should focus on understanding the impact of uncertainty and how it will influence the decision that needs to be made, as it doesn’t make sense to model uncertainty if it doesn’t impact your decision. Using mathematical modelling to support decision making under uncertainty is like using a paper plane to learn how to fly. It doesn’t take very long, it’s easy and although it doesn’t look much like the real thing it teaches you the basics of flying. Instead of trying to build a model that captures all the details (engineer-like) time should be spent on building paper planes. Once the basics are understood, the level of complexity can increase and we can go for the real thing, leading to better quality portfolio decisions. Enjoy the videos.

Sunday, 4 November 2012

Managing Fuel Price Uncertainty in Logistics

Recently the low cost carrier Allegiant Travel announced that it would like to introduce a way of sharing the risk of fuel price fluctuations with its customers. (See Businessweek) It will offer its customers to either go for a fixed high fare or choose a lower ticket price in exchange for sharing the risk that the cost of fuel may increase before takeoff. Taking the latter option customers will pay an additional amount depending on the fuel price developments in the period between booking and flying. FAA regulations don’t allow this way of pricing at this time, but things might change. In logistics carriers typically transfer the risk of severe fuel price fluctuations to their customers, the shippers, using fuel price surcharges. The use of a surcharge on the fuel price introduces uncertainty into the shipper’s decision making and exposes it to the risk of additional costs due to rising fuel prices. This risk became apparent in 2008, when fuel prices skyrocketed, causing many shippers to exceed their transportation budgets by millions of euros. To better manage this fuel price risk, shippers need to make better decisions when selecting carriers.

In a typical supply chain one or more carriers are used by a shipper to transport materials from manufacturing centers to warehouses, distribution centers and/or retail outlets. In selecting a carrier a shipper invites carriers to quote prices at which they are willing to haul loads on the lanes in the shipper’s network. Based on the quotes the shipper selects the carriers and signs a contract with them for a certain amount of time. This contract contains the agreement on the price per shipment the carrier asks for transporting the loads, consisting of a base price plus a fuel surcharge. In most cases a shipper estimates the increase in cost due to the fuel surcharge using the average fuel price of the previous year maybe with a small mark up. This is why things can go very wrong.

Let me illustrate with a small example of a shipping company that wants to organize its logistics between Amsterdam, Berlin, Paris, Madrid and Rome. Each week it is required to transport material between each pair of cities. The shipper has asked 3 carriers for quotes for the lanes in scope. The cost per kilometer, including the surcharge for fuel price is shown in the graph. For small distances (like Amsterdam-Berlin) a higher cost is incurred, than for long distance hauls. The shipper selects its carriers based on the average fuel cost of 2009 (€0.89/Liter) with a markup of 15% (resulting in €1.023/Liter) to capture the uncertainty on the fuel price. Bases on this business rule the Shipper will select Carrier 1 for its long hauls (>1000 km) and Carrier 3 for its short hauls. Now take a look at how the logistic cost develops during 2010.

Although the shipper used a markup on the fuel price to try and capture the fuel price uncertainty, it still faces an increase of weekly shipping cost during 2010 of over 4%. This is due to the way the increase in fuel price kicks in on the line haul cost charged by each of the selected carriers. At a fuel price of €1.08 and above, Carrier 1 even becomes cheaper on the short hauls than Carrier 3 which was selected initially. But at that time the shipper can no longer switch carriers. With hindsight it would have been better to select Carrier 1 for all line hauls.

Fuel prices are uncertain and cannot be influenced by shippers. But they can improve the quality of their decisions by better incorporating fuel price uncertainty. A straight forward way would be to test the robustness of their choice of carriers under various fuel price assumptions, or use more advance modeling methods like Monte Carlo simulation or Robust Optimization that explicitly incorporate the fuel price uncertainty when identifying the best choice of carriers. Also, knowing the negative effect fuel price can have on shipping cost, the shipper can negotiate better conditions on how fuel surcharges are imposed. An example could be to put a cap on the fuel surcharge at a certain fuel price level, so further fuel price are at the carrier’s risk. Again mathematical models can help both the shipper and the carrier decide what would be a fair way of sharing the risk. This of course depends on their risk appetite and the possibility to diversify this risk.

Friday, 19 October 2012

Would you entrust your daughter to a decision professional?

Last week the European Decision professionals (EDPN) had its first conference. Theme of the conference was competing through quality of strategic decisions. Reidar Bratvold, one of the speakers, touched upon the fact that we as humans are unfit to deal with uncertainty in reasoning. The examples he used, reminded me of a book that I recently read, The Drunkard's Walk: How Randomness Rules Our Lives by Mlodinow. Bratvold had asked decision professionals in Oil and Gas industry about a well-known puzzle in statistics which is also in Mlodinow’s book. It goes like this:

You are told that a family, completely unknown to you, has two children and that one of the children is a daughter. What is the chance that the other child is also a daughter?
About 80% of the people Bratvold asked responded that the chance is equal to ½. Bratvold repeats the question making explicit that no statement whatsoever is made on the birth order of the children. With that remark, still 80% of the people responded that the chance is equal to ½.
The correct answer however is 1/3. With two children in a family there are obviously four possibilities: {Girl, Girl}, {Girl, Boy}, {Boy, Girl} and {Boy, Boy}. Since one of the children is a girl, the {Boy, Boy} possibility must be eliminated. That leaves us with 3 possible options. The chance that the other child is a girl as well therefore is 1/3. To come to the correct answer I used Cardano’s method. As he explains in “Book on Games of Chance” it is best to construct a sample space to calculate the odds of even the simplest events. Trust your instincts instead and you’re bound to go wrong, even the decision professional.
To test your instincts, what if we add a seemingly irrelevant remark to the above question? Suppose that the daughter is born on a Friday. What are the chances of both children being girls?
Let’s follow Cardona’s advice and built a sample space. We had three possible combinations, {Girl, Girl}, {Girl, Boy}, and {Boy, Girl}. For each combination count the possible combinations of weekdays of birth:
  • {Girl, Girl} = {Mon, Fri}, {Tue, Fri}, {Wed, Fri}, {Thu, Fri}, {Sat, Fri}, {Sun, Fri}, {Fri, Mon}, {Fri, Tue}, {Fri, Wed}, {Fri, Thu}, {Fri, Sat} {Fri, Sun}
  • {Boy, Girl} = {Mon, Fri}, {Tue, Fri}, {Wed, Fri}, {Thu, Fri}, {Fri, Fri}, {Sat, Fri}, {Sun, Fri}
  • {Girl, Boy} = {Fri, Mon}, {Fri, Tue}, {Fri, Wed}, {Fri, Thu}, {Fri, Fri}, {Fri, Sat}, {Fri, Sun}
The {Fri, Fri} outcome for the combination of two girls is not valid, because we know that only one girl was born on a Friday. In total there are 26 possible outcomes of which 12 are favorable. So the chance of two girls in this case becomes 6/13.
My and probably your intuition as well would have been to discard the additional information on the weekday of birth as irrelevant. But it isn’t! The probability even rises because of it, with whopping 38%! Imagine the impact of this is when it comes to real world decisions like exploring new oil fields, medical decisions or investing in the development of new drugs. So my advice would be before you entrust your daughter to a decision professional to ask him if is knows Gerolamo Cardano. As irrelevant that question may be, it can have a large impact.

Friday, 31 August 2012

Fair Elections?

Elections for Dutch parliament are only a couple of weeks away. The papers, television, internet and social media are swamped with election rhetoric, opinions and polls. Not much different from the election circus in the States I guess. For the Dutch this election is of high importance. The national economy is under pressure because of rising national debt, sluggish domestic demand and the housing market slump. The next government needs to come up with measures to control and reduce the national debt without hurting economic growth. Which government that will be is up to the voters. But will an election result in a government that represents the preferences of voters? There are many examples of voting systems in which that is not the case, and I am not talking about elections in a banana republic.

To give an example; in 2005 the Labour party got 57% of the seats in the British House of Commons with only 36% of the votes. Is that fair? This outcome is a consequence of the first-past-the-post electoral system, or winner-takes-all system, in multiple districts. In this case, the candidate that gets the most votes, whether he/she reaches a majority of votes or not ("first past the post") wins the seat in parliament. It was designed to support for a two-party electoral contest. It worked well when there were only Whigs and Tories it is however ill-suited to a multi-party political landscape. It thwarts the will of the voters, leaving millions without political representation in parliament.

In the Netherlands the House of Commons is elected using a system of open party lists and only one district (the whole nation), resulting in proportional representation. Question is if this results in a fair representation of the voters preferences. Unfortunately this is also not the case. In 1994 the majority of the voters preferred the Democrats 66 party (D66) to the Dutch Labour Party (PvdA), Christian Democratic Appeal (CDA) and People's Party for Freedom and Democracy (VVD) so you would expect that the D66 would also have the majority of the seats in the House of Commons. However PvdA, CDA, VVD all ended up with more seats that D66. Is this fair?

Take a look at the vote and seat distribution of the 1994 elections. As you can see, CDA and PvdA suffered great losses, D66 and VVD won a lot of votes. Now consider the election matrix as retrieved prior to the elections (source Dutch Parliament Elections Studies). The cell (D66, PvdA) in this matrix contains the number of 655 while the cell (PvdA, D66) contains the number of 580. This means that 655 respondents strictly prefer D66 to PvdA and that 580 strictly prefer the PvdA.

Using this matrix a majority ranking can be constructed in such a way that the party higher in rank holds a majority over all parties at lower ranks. From the majority ranking it is immediately clear that although D66 has the majority vote it is only ranked fourth based on number of seats. This is an example of what is called The More-Preferred-Less-Seats Paradox.

Can’t we improve voting systems to overcome these kinds of paradoxes? Unfortunately not. Like Kurt Gödel's proof that there will always be facts which cannot be proved or disproved in any mathematical system, the Impossibility Theorem on social choice of Arrow precludes the ideal of a perfect democracy. So abolish democracy? Of course not! The perfect democracy doesn’t exist, the challenge is to find the best possible. With Arrow’s theorem available a trade-off can be made on the properties a voting system should have and whether the above paradox is acceptable or not. But how to decide on that? Take a vote?

Sunday, 24 June 2012

May the best team win? Chances are they will not

In an attempt to understand and come to terms with the early exit of the Dutch football team from the European Championships I started to review the team’s performance during the qualification phase. They must have been a poor team in that phase as well. But I found an amazing track record. The Dutch team scored 37 goals in ten matches, which was the highest of the 53 teams in the competition. Ranking all the teams of the qualification phase the Dutch came in second with 27 points, just after Germany who totalled 30 points. During the qualification phase we only lost one game, at that time we already had qualified for the finals. How come such a great team, with top players like Wesley “The Sniper” Sneijder and Klaas Jan “The Hunter” Huntelaar, didn’t make it to the finals?  They didn’t even manage to score a single point in the group phase.  I found the answer in basic probability analysis.

The European Football Championship starts with a pool phase of 4 groups. In each group 4 countries play against each other to determine first and second in the group. After the group phase the knock out phase starts with quarter finals, semi-finals and finals for the 8 remaining teams. The Netherlands was up against Denmark, Germany and Portugal. Given the tough competition, this group was called the group of death. Trying to figure out what the probability of surviving the group phase was I started with some basic calculations. To estimate the probability of winning, losing or a draw when playing against these countries I looked at their ranking in the UEFA list . Germany and the Netherlands score about the same (40860 for the Netherlands, 40446 for Germany) Based on this score I thought it reasonable that the probability of a draw when playing against Germany would be about 50%. I set the probability of winning or losing from Germany at 25% each. Denmark and Portugal both had a much lower score than Germany and the Netherlands in the UEFA list. A reasonable probability of wining from the Danish and Portuguese team would be 40%, losing the game at 30% with the same probability for a draw. Note that the probability of winning all the games in the pool phase for the Dutch team than becomes 40%*40%*25%, or only 4%. Based on these assumptions the probability the Dutch would survive the pool phase (for simplicity reasons, scoring at least 6 points) is 28%.  Thus surviving the pool phase for the best team (The Netherlands has the highest UEFA ranking of all countries in the group) is slightly better than one in four; this is similar to drawing a random name from a set of four. It’s a lottery.

Assuming the Dutch team would have managed to get to the knock out phase, the teams they would have been up against would be the strongest in the competition. The probability of winning a game would have been similar to the flip of a coin. Thus the probability of making it to the finals would have been 28%*50%*50%=7%, winning the championship even worse, only 3.5%.  Thus, although the Dutch were one of the favourites, qualifying as second for the final round of the European Championship, it was tough luck that led to their early exit. As basic probability analysis shows, the probability of the best team not winning the championship is high; winning the championship is more like wining a lottery. This insight helps to sooth the pain a little and not only supports me, but any country that didn’t make it to the finals. 

Wednesday, 25 April 2012

What does it take to win a Super Bowl?

The scene:  April 16th, Regency Hyatt Grand Ballroom in Huntington Beach, California. INFORMS President Terry Harrison walks towards the podium on the stage and says: “And now the moment of truth. Srinivas, may I have the judges’ decision please? Ladies and gentlemen, please welcome to the stage to receive the first place 2012 Franz Edelman Award for outstanding achievement in Operations Research, the team representing……..TNT Express". At table 23 there is excitement and cheers. We did it! We won the Franz Edelman Award 2012! 

Winning the Franz Edelman award really is amazing. I know the work of previous Edelman Award winners like Sloan-Kettering, Hewlett Packard, the Netherlands Railways and Midwest ISO. Being ranked among these top OR accomplishments is a great honour to me. The Edelman rewards outstanding examples of applied Operations Research. It’s the Super Bowl of OR, and I’m very proud that this year the team of TNT Express was selected first place. It’s not what we set off to accomplish when we started our first project at TNT Express back in 2005. That first project didn’t even contain much OR.

The first time we considered applying for the Franz Edelman Award was at the beginning of 2011. Several of Hein Fleuren’s colleagues at Tilburg University and some of my colleagues at ORTEC had suggested that we should submit our work with TNT Express for the Edelman Award competition. At first we had our doubts. Did the OR we had used at TNT Express match the level of sophistication of past Edelman Award winners? Were the accomplished savings significant enough? However, what appealed to us is that the Edelman Award rewards implemented work. After seven years of hard work on different levels of decision making within TNT Express a lot had been accomplished. After discussing it with TNT Express and thinking about it, we decided to go for it.

Applying for the Edelman Award gave us the opportunity to share TNT’s approach in applying OR and why it was successful. Of course it requires sound OR. As an OR consultant you have to construct the right model at the right level of detail to support the business decision at hand, an art in itself. However, that’s not the complete story. A key aspect of TNT’s success in my opinion is that from the start TNT had a strong focus on the organisational embedment of the programme, a reason for many projects (not only OR projects) to fail when that’s not taken care of. This embedment was accomplished by not just focussing on tools and technology (the OR) but also with strong project- and change management principles in place and a focus on the development of analytical skills and supply chain thinking. Marco Hendriks, Hein Fleuren and Jan Salomons developed a special training programme together with Tias Nimbas Business School to achieve that, the GO-Academy.

When we started the Global Optimisation (GO) programme in 2005, TNT Express wasn’t accustomed to using mathematical models or formal methods to support decision making. Based on our experience with other customers we started with easy to understand analysis tools that supported the visual identification of bottlenecks and provided suggestions to resolve them. As the awareness and understanding of optimisation methods increased at TNT Express, we also increased the level of sophistication of the models, making sure to keep pace with the decision making maturity level of the TNT operating units. That way, decision making quality improved and OR models and tools became standard equipment for decision making. One of our biggest challenges was in 2008 when TNT Express faced major challenges as a result of the financial crisis. Shipping volumes had gone down drastically which required immediate action. Being aware of the GO accomplishments thus far, Marie-Christine Lombard asked Hein Fleuren to work on this challenge.  Supported by OR modelling and analysis, TNT Express was able to counter the challenges of 2008 and reduced costs significantly with minimal impact in service. With this success, OR modelling became a key asset for senior management decision making. Today, fact-based decision making capabilities have become available at the core of TNT’s business, the primary objective of GO.

In preparing for the Edelman competition, we worked as a team, as we did in the GO projects. Winning the award strengthens our bonds even more. Standing on the stage, receiving the cheers and applause really does something to you. Not to mention all the emails, text messages and tweets with congratulations.  It proves that the GO programme really is special. Reading the takeaways from the conference on the internet, one appealed to me very much. Rob Ende states: “My biggest takeaway from their (TNT Express) presentation had nothing to do with their network optimization models.  Rather, it was how they built an entire optimization “ecosystem” centred on their GO (Global Optimisation) Academy.” I guess that is what it takes to win a Super bowl, you have to live what you want to accomplish. With GO-Academy and Communities of Practice, we were able to build an ecosystem that allowed optimisation to flourish within TNT.

Sunday, 11 March 2012

On Eggs and Baskets

Reading the papers the last couple of weeks, the reported rise of investments in both the chemical and the oil & gas industry caught my attention. The top 20 European chemical companies had doubled their investments from 1.5% of total revenue in 2008 to more than 3.1% in 2011, which is about €5 billon. The oil & gas industry also displays an increase of investments driven by the race for new production wells. Petrobras is investing a stunning $225 billion in exploration of new oil fields over the period 2011-2015, making it one of the world’s biggest corporate investment programmes. Not only Petrobras, other major oil companies report a significant rise in investments as well. Royal Dutch Shell for example reported a€12 billion investment to explore the Prelude-gas field in Australia. Chemical and oil & gas companies have to make numerous investment decisions, each of them concerning large initial investments and uncertain returns. Business executives in both industries therefore require rigor in decision making when deciding on their capital investments. One lesson they all know too well is to make sure that they diversify their investments and not place all of their eggs in one basket.  But how do they decide which baskets to invest in and how many eggs to put in each of them?

Diversification of investments is not an idea that came out of the modern portfolio theory as Harry Markowitz developed it. The knowledge was already available 3000 year ago as the book of Ecclesiastes (about 935 B.C) advices you to "divide your investments among many places, for you do not know what risks might lie ahead". It’s even part of classical English literature. Antonio in Shakespeare’s Merchant of Venice tells Salarino that his ventures are not in one bottom trusted, nor to one place. The work of Harry Markowitz however gave us a formal method for deciding on the best possible portfolio of investments, minimizing risk given a required return. He was rewarded the Nobel Prize for Economics in 1990 for this work.  Key in the work of Markowitz work is the concept of diversification which reduces the risk of an investment portfolio, but can appear counterintuitive.

To illustrate imagine two projects, a safe and a risky one, with independent probabilities of success. Each project requires an initial investment of €10 million. The table above summarizes the probabilities and pay offs for each of the projects. Note that the expected pay off for each of the projects is €30 million. Investing in the higher risk project will not increase the expected return, so the safe project is the obvious better choice.  Now suppose that it would be possible to split the €10 million investment in two and invest €5 million in the safe project and €5 million in the risky project. Would that be a better choice? Intuitively it would seem like a bad idea to take money invested in the save project and invest in the risky project and I expect that many business executives also follow that instinct. However, diversification of the investment, spreading the eggs over the two baskets, will reduce overall risk. Let me show you how. Instead of just two outcomes, we now have 4 possible outcomes as summarized in the table below. The expected value of the 50/50 split remains €30 million but compared to investing solely in the safe project the probability of losing €10 million is reduced from 33% to 22%, a significant reduction of risk. Although moving money from a safe investment to a more risky one seems counterintuitive, doing so will reduce risk showing the effect of diversification.

Note that when the projects would have been positively correlated (for example when drilling for oil in the same area) this risk reduction would have been less significant. If the safe project fails, because of the positive correlation, the risky project has a greater probability of failure resulting in a higher than 22% probability of losing €10 million. On the other hand if they would have been negatively correlated the risk reduction would have been even more significant. In deciding on which projects to invest in, the executives in the chemical and oil & gas industry therefore need to spread their investments seeking the negatively correlated projects, and avoiding the positively correlated ones. A challenge that can be solved well with the optimisation techniques of Operations Research. 

Sunday, 5 February 2012

A Billion in Need

A red cup makes the difference between life and starvation for one billion people every day. One of every seven people on earth suffers from chronic hunger, every 10 seconds a child dies of hunger.  These are horrifying facts, which become even worse when we realize that there is enough food and technology available to feed everybody.  Last November I was in Rome, at the head office of the World Food Program (WFP), the world’s largest humanitarian agency fighting hunger worldwide.  My visit coincided with the 50th anniversary celebration of WFP. I listened to Josette Sheeran, Executive Director of the World Food Program (WFP), and several other officials talk about the work and the challenges of WFP. At that meeting my already strong belief (see my earlier posts) that Operations Research can contribute to fighting global hunger became even stronger.

WFP manages a global supply chain for food aid, moving food to where it is needed most. This can be emergency response due to manmade or natural disasters or instances of chronic hunger.  Every day WFP fills the red cups of over 90 million people in more than 70 countries.  It is a complex task, in which decisions need to be made fast and with confidence since lives are at stake. The complexity of the WFP operations is, as Van Wassenhove describes in Humanitarian Logistics, comparable to planning an event like the Olympics. But imagine planning the event not knowing when or where it will take place, how many spectators will attend or how many athletes will compete. The near impossibility of this task gives some insight into what the WFP is up against.

During my visit, I talked with several WFP officials and learned in more detail the challenges they face in managing their supply chains.  WFP recognizes that logistics is the part in their supply chain that can mean the difference between a successful or failed operation.  It also is the most expensive part; in emergency relief 80% of the cost is due to logistics. WFP must design and manage its logistics in such a way that they get the right goods to the right place and distribute to the right people at the right time. These decisions are more complex than in private sector logistics, because WFP operates in a highly uncertain environment and has many stakeholders (Donors, Military, NGO’s, local government, etc). Things become even more complex; road infrastructure can be a serious problem. In South Sudan (a country as large as France) no more than 4,100 km of all-weather roads are available. For comparison, neighboring Kenya has 160.000 km’s of roads. The absence of all-weather roads can be a serious bottleneck when transporting food into a country, especially when the country is land-locked and no other modalities are available to get the food in.

To feed a billion people WFP needs to be successful at designing and managing its supply chain. It has to act fast, make decisions in a complex and uncertain environment with scarce resources. It is an environment in which Operations Research is at its best. With our analytical skills we Operations Researchers can develop and apply tools and techniques to solve the decision problems WFP faces with the rigor they require.  From past projects I already know that this is true. Following my visit to the WFP head office we started a project to support the South Sudan operation of WFP.  Our aim is to increase the decision power of WFP in the supply chain design for South Sudan, working towards a generic model that will support decision making in organizing aid in land-locked countries.  With support from the Operations Research society WFP can become better, smarter and faster in providing aid to those who need it most. Let’s get to work and make sure that there is no need to celebrate the 60th anniversary.


Wednesday, 4 January 2012

Losing weight fact based

Made any New Year resolutions this year? What’s your #1 on the list? I bet it is losing weight. In the Netherlands it is the number one resolution for 2012 and I expect in many other countries as well. Research from ING Banking & Insurance indicates that about 80% of the Dutch have made New Year resolutions this year. By equating the fulfillment of a resolution to an economic value ING was even able to calculate that on average the Dutch would give €450 to keep their resolution, resulting in a total economic value of €4.5 billion in the Netherlands alone. Given the economic crisis we are in, a serious amount of money. To stimulate keeping the resolution, maybe the government could introduce a tax in case of failure. This could be a very interesting idea, since not many of us seem to be able to keep our resolutions. To illustrate, 88% will fail to stop smoking, 95% will keep the same weight or even gain weight.

So you want to lose weight, but how much? One way of making that estimate is to use the Body Mass Index. It is a much used number in the medical profession to measure if you’re overweight. It divides your weight in kilograms by the square of your length in meters. So if you’re 1.86 meter tall and weigh 92 kg, a BMI results of 26.6. A BMI score lower than 18.5 kg/m2 implies underweight, above 25 kg/m2 overweight. Interesting to note is that the BMI would put Schwarzenegger (in his Conan years, 1.83 m tall and about 107 kg) in the serious overweight category. I can’t imagine that to be correct. Let’s take an analyst view at this way of assessing overweight.

To calculate the BMI, only height and weight are required. Would that be enough to decide if a person is overweight? It’s important to know that the density of fat is less than that of muscle which in turn has a smaller density than bone. In other words, the less fat you have, and the more your body is made up of muscle and bone (meaning you’re a fit person), the greater the numerator in the BMI formula, and therefore the higher the BMI. So when you start to exercise to lose weight and build up muscle, you will be worse of according to the BMI. This can’t be right, the BMI model must be wrong.

The concept of BMI is the work of a Belgian mathematician, Adolphe Quetelet . He was one of the first to use statistics to draw conclusions about society. He published his "Quetelet Index" in 1832, later known as BMI. Quetelet had no interest in studying overweight when he developed his index. His main interest was to apply probability calculus to human physical characteristics which led him to develop the BMI formula. He found that during normal growth, weight tends to increase in relation to height in meters squared. So for a population as a whole, the BMI is an easy to calculate number that helps study weight issues. There is no rationale or medical evidence that explains why the model is right on indicating whether you are overweight or not. So the BMI was initially developed to measure a societally trend, not as a diagnostic tool to draw conclusions on an individual level. But that is the way in which it is now used, even by doctors. Statistical speaking, that’s rubbish.

So if not the BMI, than what indicator should you use to determine the weight you should lose? You could take a look in the mirror, or ask your partner. But for sure these are not very objective measures. So maybe the best measure is to put on your favorite jeans and feel if they still fit, not to tight. That probably is the best model to use to optimize your weight. Keeping your resolution will also become easier, because buying a complete new wardrobe will probably cost you more than €450.