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The fixed charge problem

Author

Listed:
  • Warren M. Hirsch
  • George B. Dantzig

Abstract

A fundamental unsolved problem in the programming area is one in which various activities have fixed charges (e.g., set‐up time charges) if operating at a positive level. Properties of a general solution to this type problem are discussed in this paper. Under special circumstances it is shown that a fixed charge problem can be reduced to an ordinary linear programming problem.

Suggested Citation

  • Warren M. Hirsch & George B. Dantzig, 1968. "The fixed charge problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 15(3), pages 413-424, September.
    • Handle: RePEc:wly:navlog:v:15:y:1968:i:3:p:413-424
    DOI: 10.1002/nav.3800150306
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    Citations

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    Cited by:

    1. Shyamali Ghosh & Karl-Heinz Küfer & Sankar Kumar Roy & Gerhard-Wilhelm Weber, 2023. "Type-2 zigzag uncertain multi-objective fixed-charge solid transportation problem: time window vs. preservation technology," 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 337-362, March.
    2. Mojtaba Akbari & Saber Molla-Alizadeh-Zavardehi & Sadegh Niroomand, 2020. "Meta-heuristic approaches for fixed-charge solid transportation problem in two-stage supply chain network," Operational Research, Springer, vol. 20(1), pages 447-471, March.
    3. Jesús Sáez Aguado, 2009. "Fixed Charge Transportation Problems: a new heuristic approach based on Lagrangean relaxation and the solving of core problems," Annals of Operations Research, Springer, vol. 172(1), pages 45-69, November.
    4. Ling Gai & Ying Jin & Binyuan Zhang, 2022. "An integrated method for hybrid distribution with estimation of demand matching degree," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2782-2808, November.
    5. Lara, Cristiana L. & Koenemann, Jochen & Nie, Yisu & de Souza, Cid C., 2023. "Scalable timing-aware network design via lagrangian decomposition," European Journal of Operational Research, Elsevier, vol. 309(1), pages 152-169.
    6. Gurwinder Singh & Amarinder Singh, 2021. "Solving fixed-charge transportation problem using a modified particle swarm optimization algorithm," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(6), pages 1073-1086, December.
    7. Sagratella, Simone & Schmidt, Marcel & Sudermann-Merx, Nathan, 2020. "The noncooperative fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 373-382.
    8. Alex Scott & Chris Parker & Christopher W. Craighead, 2017. "Service Refusals in Supply Chains: Drivers and Deterrents of Freight Rejection," Transportation Science, INFORMS, vol. 51(4), pages 1086-1101, November.
    9. Rajeev Das & Kedar Nath Das & Saurabh Mallik, 2024. "An effective evolutionary algorithm for solving uncertain fixed charge transportation problem with damageable items," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(11), pages 5231-5245, November.
    10. Alexey Sorokin & Vladimir Boginski & Artyom Nahapetyan & Panos M. Pardalos, 2013. "Computational risk management techniques for fixed charge network flow problems with uncertain arc failures," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 99-122, January.
    11. Zhu, Kai & Ji, Kaiyuan & Shen, Jiayu, 2021. "A fixed charge transportation problem with damageable items under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    12. Aristide Mingozzi & Roberto Roberti, 2018. "An Exact Algorithm for the Fixed Charge Transportation Problem Based on Matching Source and Sink Patterns," Transportation Science, INFORMS, vol. 52(2), pages 229-238, March.
    13. Gaudioso, Manlio & Monaco, Maria Flavia & Sammarra, Marcello, 2021. "A Lagrangian heuristics for the truck scheduling problem in multi-door, multi-product Cross-Docking with constant processing time," Omega, Elsevier, vol. 101(C).
    14. Amy B. Gore & Mary E. Kurz & Matthew J. Saltzman & Blake Splitter & William C. Bridges & Neil J. Calkin, 2022. "Clemson University’s Rotational Attendance Plan During COVID-19," Interfaces, INFORMS, vol. 52(6), pages 553-567, November.
    15. Sharmistha Halder Jana & Biswapati Jana & Barun Das & Goutam Panigrahi & Manoranjan Maiti, 2019. "Constrained FC 4D MITPs for Damageable Substitutable and Complementary Items in Rough Environments," Mathematics, MDPI, vol. 7(3), pages 1-26, March.

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