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A Constrained Capital Budgeting Problem with Applications to Repair Kit Selection

Author

Listed:
  • John W. Mamer

    (Graduate School of Management, University of California, Los Angeles, California 90024)

  • Andrew W. Shogan

    (School of Business Administration, University of California, Berkeley, California 94720)

Abstract

We consider a capital budgeting problem in which each potential project requires the performance of a known set of activities. In general, these sets of activities are not mutually exclusive. However, when a particular activity is common to the requirements of multiple projects, a single performance of the activity simultaneously satisfies the requirements of the multiple projects. Associated with the performance of each activity are two quantities: a known fixed cost and a consumption of a known amount of a scarce resource. Because the sets of activities required by the projects are not mutually exclusive, we cannot apportion an activity's fixed cost or resource consumption to a single project. In this paper, we formulate this capital budgeting problem (and a slight variant) as a maximal network flow problem with a side constraint, and we report computational experience using Lagrangian relaxation to find an optimal solution. We also discuss an application to the selection of parts and tools to include in a field repair kit used to fix a variety of types of breakdowns.

Suggested Citation

  • John W. Mamer & Andrew W. Shogan, 1987. "A Constrained Capital Budgeting Problem with Applications to Repair Kit Selection," Management Science, INFORMS, vol. 33(6), pages 800-806, June.
    • Handle: RePEc:inm:ormnsc:v:33:y:1987:i:6:p:800-806
    DOI: 10.1287/mnsc.33.6.800
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    Citations

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    Cited by:

    1. Mark S. Hillier & Margaret L. Brandeau, 1998. "Optimal Component Assignment and Board Grouping in Printed Circuit Board Manufacturing," Operations Research, INFORMS, vol. 46(5), pages 675-689, October.
    2. Vliegen, I.M.H. & Kleingeld, P.A.M. & van Houtum, G.J., 2010. "Separate tools or tool kits: An exploratory study of engineers' preferences," International Journal of Production Economics, Elsevier, vol. 125(1), pages 173-184, May.
    3. Crama Yves & Klundert Joris van de, 1996. "The approximability of tool management problems," Research Memorandum 019, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Rippe, Christoph & Kiesmüller, Gudrun P., 2023. "The repair kit problem with imperfect advance demand information," European Journal of Operational Research, Elsevier, vol. 304(2), pages 558-576.
    5. K Liu & J-A Li & Y Wu & K K Lai, 2005. "Analysis of monitoring and limiting of commercial cheating: a newsvendor model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(7), pages 844-854, July.
    6. Jayashankar M. Swaminathan & Sridhar R. Tayur, 1998. "Managing Broader Product Lines through Delayed Differentiation Using Vanilla Boxes," Management Science, INFORMS, vol. 44(12-Part-2), pages 161-172, December.
    7. Anabela Costa & José Paixão, 2010. "An approximate solution approach for a scenario-based capital budgeting model," Computational Management Science, Springer, vol. 7(3), pages 337-353, July.
    8. Prak, Dennis & Saccani, Nicola & Syntetos, Aris & Teunter, Ruud & Visintin, Filippo, 2017. "The Repair Kit Problem with positive replenishment lead times and fixed ordering costs," European Journal of Operational Research, Elsevier, vol. 261(3), pages 893-902.
    9. Crama, Y. & van de Klundert, J., 1996. "The approximability of tool management problems," Research Memorandum 034, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Gerald G. Brown & Robert F. Dell & Alexandra M. Newman, 2004. "Optimizing Military Capital Planning," Interfaces, INFORMS, vol. 34(6), pages 415-425, December.
    11. Jing-Sheng Song, 1998. "On the Order Fill Rate in a Multi-Item, Base-Stock Inventory System," Operations Research, INFORMS, vol. 46(6), pages 831-845, December.
    12. Christoph Rippe & Gudrun P. Kiesmüller, 2023. "The added value of advance demand information for the planning of a repair kit," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 311-335, March.
    13. Crama, Yves, 1997. "Combinatorial optimization models for production scheduling in automated manufacturing systems," European Journal of Operational Research, Elsevier, vol. 99(1), pages 136-153, May.
    14. Rachel Q. Zhang, 1999. "Expected time delay in multi‐item inventory systems with correlated demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 671-688, September.
    15. Vliegen, I.M.H. & van Houtum, G.J., 2009. "Approximate evaluation of order fill rates for an inventory system of service tools," International Journal of Production Economics, Elsevier, vol. 118(1), pages 339-351, March.
    16. Liu, Ke & Li, Jing-An & Lai, Kin Keung, 2004. "Single period, single product newsvendor model with random supply shock," European Journal of Operational Research, Elsevier, vol. 158(3), pages 609-625, November.

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