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Introducing Covering Problems for the Electronic Wafer Test

Author

Listed:
  • Dominic Deckert

    (Hochschule für Technik und Wirtschaft Dresden – University of Applied Sciences)

  • Dirk Reichelt

    (Hochschule für Technik und Wirtschaft Dresden – University of Applied Sciences)

  • Peter Holland-Moritz

    (Hochschule für Technik und Wirtschaft Dresden – University of Applied Sciences)

Abstract

Semiconductor manufacturing is an essential area of modern industry. Its yield is influenced by a wide variety of different factors, among them machining precision as well as scheduling and processing concerns. To minimize the amount of faulty products, the semiconductors are examined at several steps in the manufacturing process. This paper presents the wafer covering problem, an optimization problem that arises during the multi-site electrical wafer test. Foundational research in this area is minimal, which this paper aims to amend. Mathematical definitions are introduced for the underlying decision problem. An objective function is presented to minimize probe mark damage and increase manufacturing yield while considering test efficiency as well. The problem is analyzed and references to similar problems in the literature are drawn. It is shown that even the decision version is NP-complete, using a reduction from the well-known set covering problem. The paper concludes by presenting a suite of practically relevant test problems for use in further research. Optimal solutions for many of these test instances are calculated using a constraint satisfaction solver.

Suggested Citation

  • Dominic Deckert & Dirk Reichelt & Peter Holland-Moritz, 2025. "Introducing Covering Problems for the Electronic Wafer Test," SN Operations Research Forum, Springer, vol. 6(3), pages 1-20, September.
    • Handle: RePEc:spr:snopef:v:6:y:2025:i:3:d:10.1007_s43069-025-00504-2
    DOI: 10.1007/s43069-025-00504-2
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    References listed on IDEAS

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    1. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    2. Repede, John F. & Bernardo, John J., 1994. "Developing and validating a decision support system for locating emergency medical vehicles in Louisville, Kentucky," European Journal of Operational Research, Elsevier, vol. 75(3), pages 567-581, June.
    3. Beasley, J. E. & Chu, P. C., 1996. "A genetic algorithm for the set covering problem," European Journal of Operational Research, Elsevier, vol. 94(2), pages 392-404, October.
    4. Alberto Caprara & Paolo Toth & Matteo Fischetti, 2000. "Algorithms for the Set Covering Problem," Annals of Operations Research, Springer, vol. 98(1), pages 353-371, December.
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