Mathematical, Logical, Highly Efficient

Intelligent tools for managing the breadth of variants in automotive markets

German automobiles are offered in an exceptionally and still growing number of variants, which may lead to problems during production. The source of the problems are often errors in product data management (PDM). PDM includes the management of logical rules which capture the different configurations of optional extras offered in sales, and the supply of parts to production. Both kinds of rules typically consist of mathematical formulae. Modern Software tools, based on methods of Artificial Intelligence, employ highly efficient mechanical theorem proving algorithms to manage the complexity of the configuration rules.

PDM normally takes place on two levels and draws directly on mathematical logic (Boolean algebra). All optional extras, as well as important other factors such as countries, are represented as logical symbols (codes). Using operators of mathematical logic, such as AND, OR, NOT, it is possible to formulate the conditions that need to be fulfilled to configure a car and for using different kinds of parts.

On the upper configuration level, a customer’s configuration options are defined, i.e., which optional extras can be combined within a particular order. There are sometimes a gigantic number of possible vehicle configurations – typically somewhere between 1020 and 1040 per series – so it’s not possible to capture each one individually in a table. Instead, the configuration constraints are captured in thousands of formulae, such that each configuration option is the implicit result of the possible solutions to each set of formulae. Each of these solutions represents a valid configuration, in other words the actual list of optional extras and other production parameters for each vehicle.

On the lower configuration level, the exact parts required for the production of each individual vehicle have to be identified in the Bill-of- Materials (BOM) for the entire model series, i.e. in the list of all parts from which any vehicle of this series can be pieced together. For every material (part) on the BOM, the condition under which it is required for a car is Captured and documented in a formula. A part is required for a vehicle exactly when its condition is fulfilled for the relevant vehicle configuration.

Because of the huge number of different vehicle variants, a number of problems are encountered on both configuration levels. However, the language of mathematical logic makes it possible to solve many of these problems very efficiently and with scientific precision by using Artificial Intelligence, specifically mechanical theorem proving methods. The Steinbeis Transfer Center for Object and Internet Technologies (OIT) provides its program library Auto. Lib which offers a variety of verification and analysis procedures, as well as editors and display techniques, which are customized and optimized for the use in the automotive industry.

An example of a question that arises on the upper configuration level is which optional extras are permitted – or forbidden, or even compulsory – for a certain engine type and a specific country. This exact information is not specifically captured in individual configuration rules, but it can be worked out implicitly from the possible solutions of the entire set of rules. In addition, permitted combinations (for example pairs) of options can also be calculated efficiently. Overall, the solution makes it possible to submit any kind of query to the configuration rulebook (for example, if certain options make others compulsory) and to receive a quick answer, even if this answer is only an indirect logical consequence from a combination of rules.

On the BOM level, there are the classic problems with duplicate hits and missing parts. A parts list would admit duplicate hits if it were possible to configure a car that could select two alternative parts (e.g. two steering wheels). It would miss a part it were possible to configure a car that would not select any one out of a required set of parts (e.g. no steering wheel) In such cases, two separate rulebooks interact to produce undesirable contradictions. Because of the high number of variants, mechanical solution techniques have to be used as it is not possible to wade through huge numbers of possible configurations one by one to identify problem vehicles. The library provided by the Steinbeis Transfer Center for Object and Internet Technologies offers efficient out-of-thebox solutions to these classic problems with parts lists. The system contains a sophisticated “explanation component” that makes it possible to quickly and specifically analyze the sources of errors, even with highly complex rulebooks, and to make subsequent corrections.

The formulae used in product configuration play an important role in many areas, from sales and development to production and after sales. Based on the computational techniques devised by the Steinbeis Transfer Center OIT, many other problem-solving techniques and analytical methods are now possible, including an editor for correct, defect-free BOM positions, the analysis of assembly structure documentations, support with reconfigurations, configuration optimizations, and the conversion, simplification and graphical representation of logical formulae.


Professor Dr. Wolfgang Küchlin is director of the Steinbeis Transfer Center for Object and Internet Technologies at the University of Tübingen. His Transfer Center offers clients application-based research and protype development, the design and development of industrial software solutions in Java and C++ and consulting, expert reports, studies and training in these areas.

Professor Dr. Wolfgang Küchlin
Steinbeis Transfer Center Object and Internet Technologies (Tübingen)

Share this page