International OR
Translating OR into Success
German institute tackles a variety of problems, including life-saving cancer radiation project
By Horst W. Hamacher
The "Institut für Techno- und Wirtschaftsmathematik," located in Kaiserslautern, Germany, was founded in November 1995 with the strong financial support of the state government of Rheinland-Pfalz, a state best known for its fine wines and as the home of former Chancellor Helmut Kohl. The English translation of the institute's name has been the source of many hours of deliberations, a debate that continues to this day. Some claim we should translate it as the "Institute for Industrial Mathematics," which is probably a good description of what is mostly practiced. Staff purists (including the author) use "Institute of Techno- and Econo-Mathematics," a translation that, as far as I know, has never found the unambiguous support of any native-English speaking person.
At ITWM (www.itwm.fhg.de) we develop mathematical models to tackle technological problems, or problems in econometrics and management science. The two branches are also part of the curriculum of the Department of Mathematics of the University of Kaiserslautern, which has close ties with the ITWM. If you just think of the ITWM as a research and consulting institute doing industrial mathematics and operations research, you've got the right idea.
The goal of the Institute is to show that mathematics can be used to solve all kinds of problems arising in industry and public institutions, and to convince decision-makers in these institutions to use our services (and, as you may have guessed, to pay us for these services). In a publication like OR/MS Today, this may sound obvious, but in Germany, where 70 percent of the adults described themselves as "math-haters" in a recent poll, it takes a lot of convincing to overcome the bias against mathematically-based methods.
When ITWM started out, public financial support accounted for 60 percent of the institute's overall budget. Our goal was to reduce that figure to 25 percent by bringing in money from consulting and research.
After five years the institute has reached its financial goal; 75 percent of the $5 million budget comes from contracted work. The staff, meanwhile, has grown to include 120 full- and part-time employees. Most of the full-time staffers hold a Ph.D. in mathematics, computer science, physics or engineering.
As of Jan. 1, 2001, we entered the prestigious Fraunhofer Association (FhG) (www.fhg.de). This means that we are part of the largest German research organization devoted to developing new methods and transferring knowledge to the public in order to improve service and production. Although the FhG is the head organization of 48 institutes, each of us is fully responsible for our respective budget and business decisions.
Although the ITWM is completely independent of the University of Kaiserslautern, we take advantage of the intensive contacts. Some of us work both at the University and at the ITWM, and have access to the 500 mathematics students, who in turn profit form the project-oriented mathematics education influenced by ITWM. Some 20 students are involved in a Ph.D. program closely related to the ITWM.
ITWM's Role
Within the OR group (www.itwm.fhg.de/opt) we focus on four areas of research and consulting:
- in-house logistics,
- facility location planning and supply chain management,
- traffic planning, and
- optimization of resources in the public sector.
Other departments of the ITWM deal with adaptive systems, flows in complex structures, models and algorithms in image processing and transportation processes.
We have been successful in using and developing tools of the OR trade — mostly simulation and optimization — to design supply chains, to plan warehouses, to organize commissioning systems, to model casting of iron and to develop vision systems for the car industry. We have saved our industrial partners considerable time and money through more reliable planning and better quality products. And yes, the 120 full- and part-time ITWM staffers make a living from these modeling activities. In short, we have compiled a record of achievement with classical applications of operations research. But our success is perhaps best illustrated by an ITWM project that might seem to be off the traditional OR path, but serves, in fact, as a model for the potential of modern operations research.
The Cancer Radiation Project
The success of the Cancer Radiation Project involving OR activities at the ITWM and its mirror group at the University of Kaiseriautern is easy to describe, but difficult to measure. By any account, however, the project is of tremendous importance to our society: the fight against cancer, in particular, the optimization of radiation therapy systems that are needed to destroy cancer. Figure 1 indicates the relevance of this problem using data from the German cancer index: Out of 100,000 patients with a realistic chance to successfully fight cancer using radiation therapy, more than 20,000 nevertheless die.
Figure 1: Out of an annual number of 350,000 new cancer patients (red), 210,000 are treated with radiation therapy (blue), 100,000 have a positive prognosis (green), but nevertheless, 27,000 (grey) die.
Source: German cancer index
What are possible reasons for this phenomenon, and can OR help to change this situation? In order to answer this question, we restrict ourselves in this article to the case of radiation applied from the outside of the body using a linear accelerator attached to some gantry.
The gantry can move around the couch, on which the patient is fixed, in order to keep the patient in a stable position. The goal of a "good" radiation plan is to provide radiation that mirrors the shape of the tumor in the best possible way (conformal radiation). This means that the radiation should be strong and homogeneous within the target/tumor (in order to destroy malignant cells) and weak outside (in order not to harm any of the organs at risk).
In order to design radiation plans of good quality, technicians and physicians have to make various decisions that influence each other. Examples of such decisions include the ones indicated in Figure 2 (a 2-dimensional cross section of the human body). Where and how often does the gantry stop (radiation geometry problem)? How much and in which form is radiation released when the gantry stops (intensity profile problem)? How can these intensity profiles be realized using modern technology (realization problem)?
Figure 2: OR problems related to the radiation problem.
The radiation geometry problem can be looked at as a location problem, where the position of the gantry is characterized by the angle at which it is stopping. Depending on the technology of the gantry, models from discrete or continuous location theory can be used as a starting point of suitable OR models.
Various authors have formulated the intensity profile problem. Due to the contradictory objectives (high radiation in the target, low radiation in the organs at risk), a multicriteria model is very plausible, but has only been suggested recently. The goal of this approach is to provide oncologists with a database of Pareto solutions corresponding to high-quality radiation plans. These individually custom-designed plans avoid the time consuming (and therefore often cancelled) interaction between radiation planners and oncologists.
Intensity profiles are realized by modulating the homogeneous radiation using technical devices. The most effective way of doing this is with a multileaf collimator, a device that consists of several rows, each with a pair of metal leaves. These pairs build a filter that blocks out part of the radiation (see Figure 3). The sequence of MLC set-ups must correspond to the intensity profile computed using the methods described above. The goal is to find a sequence yielding the smallest possible radiation or treatment time. We use integer programming and network flow methods to model feasible positions of the right and left leaves in each row.
Figure 3: Example of a multileaf collimator (MLC).
In contrast to "standard" OR problems, the reward of using OR models is difficult to measure in this project. Using methods sketched above, one can show that the treatment time is improved considerably compared with times found by previous methods. (This argument is obviously sufficient to justify a fair amount of scientific publications.) But this objective is obviously only a substitute for the actual goal in radiation planning - to design "better" radiation plans and save lives. To see the effect of OR models positively reflected in the mortality frequency (see Figure 1) is the ultimate goal. Actually, if and when this happens, we as OR people may not even get the credit for it, since the interrelation between improved radiation plans and lower mortality may not be easy to establish.
Modeling Limits
The radiation project shows the well-known strengths of the OR approach to solving problems. Operations research (and applied mathematics as such) provides a tool box that can be successfully applied in various contexts. It should also be noted that it shows the limits of modeling. In most cases, we may be able to help tackle problems, but in most of them we are far from actually solving them. Promising too much based on the application of OR methods really does hurt our community.
Multicriteria optimization was used in the radiation project to provide oncologists with custom-made, patient-dependent databases to find high quality radiation profiles. Most of the real-world problems are multicriteria by nature. At the ITWM we deal, for instance, with hospital management problems, an area in which Germany is years behind the United States as far as the implementation of OR models is concerned. Patient flow in hospitals (with models similar to material flow), design of hospitals (with models taken from facility layout), time scheduling and rostering, etc. are problems that obviously should be considered in a multicriteria context.
We need to come up with a well-justified set of Pareto solutions stored in a database to help decision-makers. Some of my colleagues will claim that it is better to provide them with an interactive software tool, such that they can produce suitable solutions by themselves. For various reasons, I find the database approach more promising. In order to make this idea a success in any application context, we need to know more about representative systems for Pareto solutions. The hospital management project at ITWM is supported by a grant of the state Rheinland-Pfalz. Cooperation with hospitals is a must, but the implementation of results is often obstructed by medical staff members, who are afraid of loosing their privileges as a result of quantitative planning methods based on OR.
The location model for the radiation geometry is obviously transferred from well-known methods in management science and econometrics. At ITWM we work in this area with various partners. Based on our experiences with the software package LoLA (Library of Location Algorithms) we are partners of SAP and contribute a location module to their worldwide distribution of APO (Advanced Planner and Optimizer). The combination of geographical information systems and location planning is obviously one of the main areas in this context. In order to have realistic models, i.e. models that can, indeed, be used to tackle problems from industry and public institutions, ITWM and its mirror group at the University of Kaiserslautern have developed in the past various new approaches. One of the main challenges here is to look at complex, integrated OR models in which location is just one part. While this has been done, for instance, with location and routing quite extensively, combinations with scheduling, timetabling, rostering, etc. are just beginning.
The integer programming and network flow approach, and its potential in solving real-world problems, might be the hottest item on the current OR market. As such, the solution approach to the MLC problem in the radiation project is only one of many in which this approach proves to be successful. At ITWM we apply IP models to solve warehouse problems (for instance, to model the parallel warehouse device rotastor; see Figure 4), to solve load balancing problems, to improve production (Miele), to optimize holiday planning (Lufthansa), to optimize the purchasing process (Markant Suedwest), to design supply chain management systems (ICON) and to tackle evacuation problems.
Figure 4: The parallel warehouse unit rotastore. Transportation units can be stored in, and taken from, the warehouse in parallel on all layers of rotastore.
In traffic planning, we cooperate with the Deutsche Bahn (German Railway) on some projects. Additionally, a consortium of public transportation companies and ITWM is working on a delay management system. Several regions of Germany have designed their tariff zones according to models developed at ITWM and its mirror group of the university.
Conclusion
The classical OR approach — real-world problem -> model -> model solution -> real-world implementation and check — still proves successful. Let's all be careful to keep the credit, which we have attained through our achievements by being aware that we still work with models, and that we very rarely will achieve a complete one-to-one correspondence between model and reality.
ITWM has been lucky enough to be able to contribute to the success of OR in various projects. The German system of starting applied research institutions with public funds with the goal of replacing most of these funds by project money has again proven to be a success.
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Horst W. Hamacher is a director at the Institut fuer Techno- und Wirtschaftsmathematik and a professor in the Department of Mathematics, University of Kaiserslautern, Germany.
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