Modelling Magic

In his third law Arthur C. Clark states that any sufficiently advanced technology is indistinguishable from magic. So, in some cases at least, magic doesn’t derive from an actual mystical or spiritual source; rather, it is technology in disguise. When we would be able to send a car a couple of ages back in time, driving our horseless carriages probably would have created a witch hunt. Not to mention flying an aircraft. Time travelling over shorter distances; our computer networks and phones that can do nearly everything must seem magic for someone living in the late 1960’s. So Arthur C. Clark is probably right. What does it imply for Operations Research? Is it sufficiently advanced technology to be indistinguishable from magic? Initiated only a few decades ago in World War II, Operations Research has enabled us to achieve some remarkable things that to the non-initiated seem to be magic. It has enabled us to solve the unsolvable and step by step it is entering our daily lives becoming an indispensable piece of technology, doing its magic every day.

The simple task of assigning activities to people can become very complex and unsolvable for a human. For small instances it’s a simple puzzle. In case of 2 activities and 2 people there are only 2 possible assignments. Deciding which one is best is therefore easy. But when the size of the instance increases, the number of possible assignments explodes which makes it impossible to find the best possible assignment. In optimising the assignment of 70 activities to 70 people, there are 70! different assignments to be evaluated. Constructing all of the 1.19785717 × 10¹⁰⁰ assignment possibilities would take forever. How to find the best possible one? Here is where Operations Research does its magic. One of the first optimisation techniques developed within Operations Research is the simplex method. It was discovered by George Dantzig in the late 1940’s and it still plays a very central role in Operations Research. With the simplex method the best possible assignment of 70 jobs to 70 people can be found within a few minutes or even seconds. Compared to what a human can do, this for sure is magic.

When we fast forward to our current era, Operations Research applications arise everywhere; in Finance & Accounting, Marketing, Procurement, Production management, Logistics, Personnel management, Government, Sports, etc, etc. It has become a deciding factor for companies to survive or become top players in their market. One of the areas where Operations Research has become a deciding factor is in the airline industry. In 1978 the Airline Deregulation act was signed, its purpose was to remove government control over commercial aviation. As a consequence competition increased with low-cost carriers seizing their opportunity to get a share of the commercial aviation market. The exposure to competition led to heavy losses for a number of carriers, some of them even went bankrupt. To counter low-cost airlines like People Express, several strategies were developed by the main carriers. American Airlines (AA) was the most successful one; using Operations Research they developed a pricing strategy now known as Revenue Management or Yield Management. According to AA it is “the single most important technical development in transportation management”. The essence of Yield Management is to use price to influence customer demand. As a consequence the price for a passenger seat may vary over time. This explains why the price for the same flight may vary between two visits to a booking site, leaving you clueless on the reason why. As if the airline uses a spell to maximise revenue. But because of this magic, we can fly cheap.

Operations Research is entering our daily lives more and more. It is responsible for the fact that we:

• have highly reliable electricity and gas supply networks,
• can use the internet,
• are able to develop reliable public transport schedules,
• have attractive soccer match schedules
• are able to operate global supply chains,
• have satellite navigation,
• can manage the risks of pension funds,
• have effective cancer treatments
• etc

It’s all possible because of Operations Research. It doesn’t matter if you understand why it is possible, just use it. Sit back and enjoy, let it do its magic!

Solving a Mayor’s dilemma; fact based environmental policy development

This week Rotterdam, one of the major cities of the Netherlands, was on the news. The city’s Court of Audit had analysed the city counsel’s policies on improving the environmental conditions of the inner-city and concluded that things weren’t going great. Rotterdam has set itself emission reduction goals, but with the selected policies it wasn’t going to achieve them according to the Court of Audit. The Court even concluded that the situation was getting worse. Compared to 2009 the number of hot spots on NO₂-emissions in the city has increased from 1 to 5 making the city a less healthy place to be in. The city council however is still convinced that they will achieve the goals set for 2015. Until now however, several countermeasures have been introduced with little or no effect on the air quality in the inner-city. One very drastic way to accomplish emission reductions would be to close down several parts of the inner-city; this would however impact the local economy heavily. Quite a dilemma for Mayor Aboutaleb.

Major part of the air pollution in inner-cities comes from the vehicles doing last mile distribution. Think of the replenishment of shops and stores but also of bars and restaurants. Many of them use a Just-in-time (JIT) based replenishment strategy, increasing the number of vehicle visits while reducing the drop size. JIT minimises the inventory levels in the shop and hence reduces costs. Counter side of it is that the inner cities become congested with vehicles and the emission levels rise. So, reducing the number of vehicles and/or the total distance travelled by those vehicles will lower emission levels and therefore improve air quality. Easy, thing is how to set a reasonable enough level of emission reduction to improve living conditions in the inner-city without harming economic activity and second decide on the necessary measures to achieve it.

It has been the subject of a project that I have been working on in the past months. Objective of the project was to provide decision support to the municipality of cities in deciding on logistical measures to better regulate inner-city logistics and reduce emission levels. One of the objectives of the project was to supply insights on the current sustainability of a city and assist in setting reasonable emission reduction goals. The project resulted in a mathematical model that supports these decisions, fact based. Also the model is capable of evaluating different measures (like a curfew, consolidated transport from city depot, electric vehicles, etc) on congestion and emission reduction effects. That way the most effective measure can be selected before putting it in practice.

Setting a realistic goal is difficult. Cities have different infrastructures and different distribution of shops, bars and restaurants. Taking all this into account would take a lot of modelling effort and detailed information on the route the vehicles take. Information that is not available (yes, even in these data rich times, we sometimes lack the data!). Therefore we decided to use a technique that doesn’t require a lot of detail on the “production” of emissions but would give a good estimate on the “environmental performance”. To achieve this we used Data Envelopment Analysis (DEA). DEA is a technique that is used to calculate and compare the efficiency of decision making units (DMU’s), for example factories, that makes no assumption on the underlying form of the production function. It focuses on the efficiency of the transition of inputs to outputs only. Differences in efficiency tell you how improvements can be achieved. In case of the environmental performance we looked at how vehicle movements and emissions were “produced” by number of deliveries and number of drop-off locations (shops, bars, etc) in the inner-city. The resulting relative environmental performance of the cities in the benchmark tells them how well they are doing compared to other cities and how much the emission levels should be lowered to be as “green” as the most efficient city in the benchmark.

When comparing Rotterdam with Amsterdam, Utrecht, The Hague, Enschede and Tilburg I found that Tilburg is the most environmental efficient city. This is no surprise, Tilburg has been working hard to improve inner-city environment for some years already, with all kinds of initiatives. So in reviewing and perhaps setting new goals for 2015, the city counsel of Rotterdam should have a talk with Tilburg, discussing the measures Tilburg has in place to improve the environmental conditions of the inner-city. Knowing what to aim for, the Mayor of Rotterdam can than make a fact-based trade of between the countermeasures to take to improve the inner-city environment and the economic impact of them. And Mayor Aboutaleb, …..010 is doing better than 020!