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Parallel Replacement under Capital Rationing Constraints

Author

Listed:
  • Nejat Karabakal

    (Faculty of Business Administration, Bilkent University, 06533 Bilkent, Ankara, Turkey)

  • Jack R. Lohmann

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • James C. Bean

    (Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, Michigan 48109)

Abstract

Contrary to serial replacement, parallel replacement problems require a decision maker to evaluate a portfolio of replacement decisions in each time period because of economic interdependencies among assets. In this paper, we describe a parallel replacement problem in which the economic interdependence among assets is caused by capital rationing. The research was motivated by the experience gained from a vehicle fleet replacement study where solutions to serial replacement problems could not be implemented since they violated management's budget plan. When firms use budgets to control their expenditures, competition for the limited funds creates interdependent problems. In this paper, we formulate the problem as a zero-one integer program and develop a branch-and-bound algorithm based on Lagrangian relaxation methodology. A multiplier adjustment method is developed to solve one Lagrangian dual.

Suggested Citation

  • Nejat Karabakal & Jack R. Lohmann & James C. Bean, 1994. "Parallel Replacement under Capital Rationing Constraints," Management Science, INFORMS, vol. 40(3), pages 305-319, March.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:3:p:305-319
    DOI: 10.1287/mnsc.40.3.305
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    Citations

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    Cited by:

    1. Kevin Spiritus & Etienne Lehmann & Sander Renes, "undated". "Optimal Taxation with Multiple Incomes and Types," Tinbergen Institute Discussion Papers 22-000/IVI, Tinbergen Institute.
    2. Peiling Wu & Joseph C. Hartman & George R. Wilson, 2005. "An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets," Transportation Science, INFORMS, vol. 39(1), pages 87-103, February.
    3. Ishwar Murthy & Sumit Sarkar, 1998. "Stochastic Shortest Path Problems with Piecewise-Linear Concave Utility Functions," Management Science, INFORMS, vol. 44(11-Part-2), pages 125-136, November.
    4. Guerrero, Sebastian E. & Madanat, Samer M. & Leachman, Robert C., 2013. "The Trucking Sector Optimization Model: A tool for predicting carrier and shipper responses to policies aiming to reduce GHG emissions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 59(C), pages 85-107.
    5. Lim, Seung-Kil & Kim, Yeong-Dae, 1998. "Capacity planning for phased implementation of flexible manufacturing systems under budget restrictions," European Journal of Operational Research, Elsevier, vol. 104(1), pages 175-186, January.
    6. Paul R. Kleindorfer & Andrei Neboian & Alain Roset & Stefan Spinler, 2012. "Fleet Renewal with Electric Vehicles at La Poste," Interfaces, INFORMS, vol. 42(5), pages 465-477, October.
    7. Amiri, Ali, 2002. "An integrated approach for planning the adoption of client/server systems," European Journal of Operational Research, Elsevier, vol. 142(3), pages 509-522, November.
    8. Hartman, Joseph C., 2004. "Multiple asset replacement analysis under variable utilization and stochastic demand," European Journal of Operational Research, Elsevier, vol. 159(1), pages 145-165, November.
    9. Ansaripoor, Amir H. & Oliveira, Fernando S. & Liret, Anne, 2014. "A risk management system for sustainable fleet replacement," European Journal of Operational Research, Elsevier, vol. 237(2), pages 701-712.
    10. Yuri Yatsenko & Natali Hritonenko, 2016. "Asset replacement under improving operating and capital costs: a practical approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(10), pages 2922-2933, May.
    11. Zhang, Le & Gu, Weihua & Fu, Liangliang & Mei, Yu & Hu, Yaohua, 2021. "A two-stage heuristic approach for fleet management optimization under time-varying demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    12. Stasko, Timon H. & Oliver Gao, H., 2012. "Developing green fleet management strategies: Repair/retrofit/replacement decisions under environmental regulation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1216-1226.
    13. Joseph C. Hartman, 2000. "The parallel replacement problem with demand and capital budgeting constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(1), pages 40-56, February.
    14. Scarf, Philip A. & Martin, Harry H., 2001. "A framework for maintenance and replacement of a network structured system," International Journal of Production Economics, Elsevier, vol. 69(3), pages 287-296, February.
    15. Rafic Faddoul & Abdul-Hamid Soubra & Wassim Raphael & Alaa Chateauneuf, 2013. "Extension of dynamic programming models for management optimization from single structure to multi-structures level," Post-Print hal-01006860, HAL.
    16. Suzanne Childress & Pablo Durango‐Cohen, 2005. "On parallel machine replacement problems with general replacement cost functions and stochastic deterioration," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 409-419, August.
    17. Zhi‐Long Chen, 1998. "Solution algorithms for the parallel replacement problem under economy of scale," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 279-295, April.
    18. Spiritus, Kevin & Lehmann, Etienne & Renes, Sander & Zoutman, Floris T., 0. "Optimal taxation with multiple incomes and types," Theoretical Economics, Econometric Society.
    19. Bollapragada, Srinivas & Gupta, Aparna & Lawsirirat, Chaipat, 2007. "Managing a portfolio of long term service agreements," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1399-1411, November.

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