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Developing a Maximum Inscribed Rectangle Heuristic to Satisfy Rush Orders for Heavy Plate Steel

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Listed:
  • M. Muntazir Mehdi

    (Microsoft Corporation, Redmond, Washington 98052)

  • Le Wang

    (Amazon.com, Seattle, Washington 98109)

  • Sean P. Willems

    (Haslam College of Business, University of Tennessee, Knoxville, Tennessee 37996)

Abstract

Steel service centers receive rush orders that must be fulfilled on very short notice. Each order only consumes a portion of one steel plate, so plate selection and job placement are the critical factors that affect the service center’s primary performance metric: plate yield. In conjunction with a steel service center, Artco Steel, we model this problem as a two-dimensional online bin-packing algorithm. Unique in the online bin-packing literature, we calculate the maximum inscribed rectangle (MIR) before and after job placement as the basis for heuristics that assign each job to a plate and position the job on the plate. Our work is the first paper to extend the online two-dimensional bin-packing problem to incorporate scrap, rectangular bin sizes, and a finite number of bins. The MIR procedure significantly outperformed Artco’s existing practice of giving priority to the most recently used plate, and the heuristic’s straightforward nature allowed easy adoption in 2010.

Suggested Citation

  • M. Muntazir Mehdi & Le Wang & Sean P. Willems, 2022. "Developing a Maximum Inscribed Rectangle Heuristic to Satisfy Rush Orders for Heavy Plate Steel," Interfaces, INFORMS, vol. 52(3), pages 283-294, May.
  • Handle: RePEc:inm:orinte:v:52:y:2022:i:3:p:283-294
    DOI: 10.1287/inte.2021.1086
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    References listed on IDEAS

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    1. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    2. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    3. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    4. Andrea Lodi & Silvano Martello & Daniele Vigo, 1999. "Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 345-357, November.
    5. Anantaram Balakrishnan & Joseph Geunes, 2003. "Production Planning with Flexible Product Specifications: An Application to Specialty Steel Manufacturing," Operations Research, INFORMS, vol. 51(1), pages 94-112, February.
    6. Mark A. Vonderembse & Robert W. Haessler, 1982. "A Mathematical Programming Approach to Schedule Master Slab Casters in the Steel Industry," Management Science, INFORMS, vol. 28(12), pages 1450-1461, December.
    7. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
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