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The Product Matrix Traveling Salesman Problem: An Application and Solution Heuristic

Author

Listed:
  • Robert D. Plante

    (Purdue University, West Lafayette, Indiana)

  • Timothy J. Lowe

    (Purdue University, West Lafayette, Indiana)

  • R. Chandrasekaran

    (The University of Texas at Dallas, Richardson, Texas)

Abstract

In this paper we analyze an optimization problem that arises in the overhaul of a gas turbine engine. This problem involves the placement of nozzle guide vanes in the nozzle of the engine. The objective of the vane placement is to attain “uniform” flow (equalized distribution of hot fuel gases) about the circumference of the engine nozzle. We show that this placement problem is equivalent to a traveling salesman problem (TSP) whose cost matrix is a product matrix. Exploiting properties of the special form of the cost matrix, we give a heuristic algorithm for solving the problem, and derive a posteriori lower bounds for the heuristic. We show that the heuristic performs extremely well on both real and simulated data. Finally, we present and develop the theoretical results that are the foundation of the proposed heuristic.

Suggested Citation

  • Robert D. Plante & Timothy J. Lowe & R. Chandrasekaran, 1987. "The Product Matrix Traveling Salesman Problem: An Application and Solution Heuristic," Operations Research, INFORMS, vol. 35(5), pages 772-783, October.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:5:p:772-783
    DOI: 10.1287/opre.35.5.772
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    Citations

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    Cited by:

    1. Robert Plante & Herbert Moskowitz & Jen Tang & Jeff Duffy, 1999. "Improving Quality via Matching: A Case Study Integrating Supplier and Manufacturer Quality Performance," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 36-49.
    2. Robert D. Plante & Timothy J. Lowe & Richard T. Wong, 1988. "Partitioning and balancing for the assembly of nozzle guide vanes in gas turbine engines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(4), pages 585-603, August.
    3. Johanns, Patrick & Lowe, Tim & Plante, Robert, 2001. "Selection and sequencing heuristics to reduce variance in gas turbine engine nozzle assemblies," European Journal of Operational Research, Elsevier, vol. 132(3), pages 490-504, August.

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