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For more about Aldo Rustichini's research go here: http://www.econ.umn.edu/~arust/

Engineering Design Theory and Manufacturing

Professor Beth Allen is pursuing research in an endeavor is to use knowledge gained from interdisciplinary work on rigorous theoretical foundations for engineering design and manufacturing (the disciplines of mechanical and industrial engineering) to improve our understanding of production in microeconomic theory.

  • The treatment of production in economics has remained somewhat of a black box as our understanding of other issues has advanced rapidly. We still model firms by their "technologies," which are formalized by sets of feasible net input-output vectors. Indeed, most economists have never visited a factory since childhood school and vacation trips and many of us imagine assembly lines like the ones Henry Ford developed.
  • Modern manufacturing has evolved greatly and has fundamentally changed our economy, yet economic theorists focus their research efforts in this area on the strategic behavior of firms (for example, price or quantity-setting oligopolists) and markets for their financial assets under uncertainty, or possibly the regulation of monopolists or aggregate research and development.
  • How production really occurs and the related question of how a technology is chosen have largely been ignored despite major advances in product development (the design of project lines and the means to fabricate these items) such as automation, robotics, mass customization, CAD/CAM systems, and so forth.
One current project involves the study of the mathematical structure for a space of geometric objects or "shapes." This represents the simplest class of manufactured objects - indivisible items that are fabricated from a single homogeneous material. Some examples include wine glasses, computer casings, and the millions of metal parts from which automobiles and airplanes are assembled. A metric is designed for an (infinite dimensional) space of such geometric objects which reflects the extent to which different items are close substitutes for each other. Then the classes of objective functions (utilities, costs, profits, etc.) that can be rigorously optimized are identified and the classes of feasible sets over which such optimization can occur are also characterized. The key to obtaining a tractable feasible set is a "real world" manufacturing consideration that restricts the class of objects that can be fabricated by processes like machining.

The objective of a second research project is to suggest how manufacturing process planning systems should be designed. In automated manufacturing, process planning is the intermediate step that transforms a design into an ordered list of instructions for fabrication. For instance, in machining, a block of homogeneous metal (the stock or initial workpiece) must be transformed by removing material appropriately. For each step, the position of the workpiece, how it is held in place (fixturing), the specific tool to be used, the tool access direction, and the price tool path must be specified. A computer aided process planning system takes a computer file defining the design in a standard format - the output of a computer aided design system - and finds computerized instructions for computer assisted manufacturing equipment to make the desired artifact. Increasingly, such process planning systems contain multiple artificially intelligent agents (or distributed decision makers). Process planners (and multi-agent systems in general) define particular games. The examination of such games helps one to understand how process planners and multi-agent systems work, why they can fail, and how they can be improved. Game-theoretic mechanism design analyzes how games can be designed so that the desired outcomes arise as equilibria in the games. The research first uses existing results in game theory and mechanism design to study process planners and multi-agent systems. Then new results are derived for network and distributed games and the potential disaggregation of agents. The goal is to establish rigorous theoretical principles, based on strategic optimization behavior, to guide the design of multi-agent process planning systems and multi-agent process planning systems and multi-agent systems in general.

This research project will provide principles to improve the design of process planning systems.

  • Process planning can be time-consuming and expensive; when it fails, it can lead to further costs and delays due to redesign.
  • Process planning is a crucial step on a manufacturing industry (machining) that typically represents about five percent of gross domestic product in developed economies.
  • It is important to design process planning systems well, so that they successfully find feasible-and ideally, good, where "good" means relatively inexpensive to manufacture to tolerance specifications-process plans quickly on average when the design is manufacturable (and don't waste excessive amounts of time and resources if the design is not manufacturable).

Broader impacts include the initiation of a new course at the University of Minnesota on game theory for engineers. Moreover, the project is inherently interdisciplinary and involves novel applications of game theory in manufacturing.

These projects are funded by the National Science Foundation's Engineering Design Program in the Division of Design, Manufacturing and Industrial Innovation, Directorate for Engineering. This research has benefited from participation in Minnesota's Supply Chain Research Center and in the Geometric Design and Optimization Programs of Minnesota's Institute for Mathematics and Its Applications. To date, the research has resulted in about twenty publications in engineering outlets. For an introduction to this projects potential to economics, see the article entitled "On the Differentiated Products in the Real World," forthcoming in Economic Theory.

 

 
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July 16, 2007

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