When Solving Tomorrow's Problem Is Better Than Solving Today's Problem
JeanFrancoisPuget 2700028FGP Visits (7760)
As good as it may be, mathematical optimization needs to be applied to the right problem in order to yield business value. This may sound obvious, but it is not, surprisingly enough. Several authors have warned about it. For instance I like this citation taken from a paper by Steve Sashihara: "An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem" , John Tuckey.
Another variant I heard (but I don't know who the original author is), was : It is better to provide an approximate answer to today's problem than to perfectly solve yesterday's problem.
So, what is the right problem to solve? There are many answers to that question, and finding good ones are definitely what differentiates good OR practitioners from the rest of the crowd.
Let us use an example to illustrate what makes a good problem to solve. We are working with IBM Research on a solution to the Empty Container Repositioning (ECR) problem.
Containers are the primary mean of transporting finished goods. Containers are filled in countries that export goods, then unloaded at countries that import goods. Containers move on trucks to a given harbor, then they move on one or several ships, then they are unloaded at another harbor where they are picked up and emptied. This is a great way to move goods efficiently, and it led to major changes in international commerce. However, a nasty side effect is occurring: there is an imbalance, more containers move from Asia to North America and Europe than the other way round. This results in an accumulation of empty containers in US and Europe harbors, wile there is a shortage of containers in Asia harbors. This is depicted on Figure 1. What makes the issue nasty (read interesting to solve using optimization) is that no one wants to pay for moving empty containers. Shipping companies, who own these containers, need to move them at minimal cost for them.
Figure 1. Empty Container Imbalance.
A red circle means a shortage, a green one a surplus, and the size of the circle represents the number of containers. These numbers are in millions of unit.
We then have a nice (and simple) problem to solve: how can we move at minimal cost empty containers from where they are in excess to where they are needed? The response is to use the ships that are going back to where they loaded containers in the first place.
Ships follow fixed routes (called lines) in the container shipping industry, going round and round along the same string of harbors. An example ship route is shown in Figure 2. We are then facing a kind of flow problem, where flow capacity is defined by the ships moves along these fixed routes
Figure 2.A ship route
Is it that simple? Are we providing business value there?
Well, we are not.
Why? Because it takes weeks to move containers across oceans. It means that when we move an empty container, we must move it to where it will be needed when its travel ends. We cannot use the current shortage in empty containers because of travel time. We need to know the shortage in few weeks, when the container can arrive at the harbors lacking containers. It means that we must take into account time in our optimization models. It also means that we must take as input some forecasts on where empty containers will be needed in the future. Such forecasts are usually provided by some data analytics application, where one looks at history and tries to extract trend.
Once we take into account the current excess of empty containers, the forecast demand of empty containers where there will be shortage, all scheduled ship movements, their capacities, the various transshipment and storage costs, the result of optimization is a plan, or schedule (see Figure 3) by which we move empty containers to where they will be needed. And this has great value. One of our customers is saving 7.5% on the cost of moving empty containers thanks to our solution. Given that the number of containers is in hundreds of million of thousands this translates into savings of tens of millions of US $ per year.
Figure 3. Part of a schedule
The bar on each ship indicates the number of empty containers on that ship.
As a summary, solving today's problem is of limited value in the ECR case. We need to solve tomorrow's problem, which is of much greater value. This is true of many industries, not just transportation. And the business value is achieved by a combination of forecast and optimization. Once we get demand forecasts from data analytics (here, trends in empty container usage at various harbors), then we can plan against these forecasts (here, move empty containers where they will be used). It is an instance of the pattern I described in my post : Is Optimization part of Analytics?