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Approximation Algorithms for Pick-and-Place Robots

Author

Listed:
  • Anand Srivastav
  • Hartmut Schroeter
  • Christoph Michel

Abstract

In this paper we study the problem of finding placement tours for pick-and-place robots, also known as the printed circuit board assembly problem with m positions on a board, n bins containing m components and n locations for the bins. In the standard model where the working time of the robot is proportional to the distances travelled, the general problem appears as a combination of the travelling salesman problem and the matching problem, and for m=n we have an Euclidean, bipartite travelling salesman problem. We give a polynomial-time algorithm which achieves an approximation guarantee of 3+ε. An important special instance of the problem is the case of a fixed assignment of bins to bin-locations. This appears as a special case of a bipartite TSP satisfying the quadrangle inequality and given some fixed matching arcs. We obtain a 1.8 factor approximation with the stacker crane algorithm of Frederikson, Hecht and Kim. For the general bipartite case we also show a 2.0 factor approximation algorithm which is based on a new insertion technique for bipartite TSPs with quadrangle inequality. Implementations and experiments on “real-world” as well as random point configurations conclude this paper. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Anand Srivastav & Hartmut Schroeter & Christoph Michel, 2001. "Approximation Algorithms for Pick-and-Place Robots," Annals of Operations Research, Springer, vol. 107(1), pages 321-338, October.
    • Handle: RePEc:spr:annopr:v:107:y:2001:i:1:p:321-338:10.1023/a:1014923704338
    DOI: 10.1023/A:1014923704338
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    Cited by:

    1. Jingyang Xiang & Lianguo Wang & Li Li & Kee-Hung Lai & Wei Cai, 2024. "Classification-design-optimization integrated picking robots: a review," Journal of Intelligent Manufacturing, Springer, vol. 35(7), pages 2979-3002, October.
    2. García, Alfredo & Tejel, Javier, 2017. "Polynomially solvable cases of the bipartite traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 429-438.

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