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Optimal Facility Location with Concave Costs

Author

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  • Richard M. Soland

    (The University of Texas at Austin, Austin, Texas)

Abstract

The following problem is considered: select plant sites from a given set of sites and choose their production and distribution levels to meet known demand at discrete points at minimum cost. The construction and operating cost of each plant is assumed to be a concave function of the total production at that plant, and the distribution cost between each plant and demand point is assumed to be a concave function of the amount shipped. There may be capacity restrictions on the plants. A branch-and-bound algorithm for identifying an optimal solution is described; it is equivalent to the solution of a finite sequence of transportation problems. The algorithm is developed as a particular case of a simplified algorithm for minimizing separable concave functions over linear polyhedra. Computational results are cited for a computer code implementing the algorithm.

Suggested Citation

  • Richard M. Soland, 1974. "Optimal Facility Location with Concave Costs," Operations Research, INFORMS, vol. 22(2), pages 373-382, April.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:2:p:373-382
    DOI: 10.1287/opre.22.2.373
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    Cited by:

    1. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. Christensen, Tue Rauff Lind & Klose, Andreas, 2021. "A fast exact method for the capacitated facility location problem with differentiable convex production costs," European Journal of Operational Research, Elsevier, vol. 292(3), pages 855-868.
    3. Mario Vanhoucke, 2002. "Optimal due date assignment in project scheduling," Vlerick Leuven Gent Management School Working Paper Series 2002-19, Vlerick Leuven Gent Management School.
    4. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    5. Sangwon Moon, 1989. "Application of generalized benders decomposition to a nonlinear distribution system design problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 283-295, June.
    6. Wooseung Jang & J. George Shanthikumar, 2002. "Stochastic allocation of inspection capacity to competitive processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 78-94, February.
    7. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    8. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.
    9. Harold P. Benson & S. Selcuk Erenguc, 1990. "An algorithm for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 515-525, August.
    10. Harold P. Benson, 2004. "Concave envelopes of monomial functions over rectangles," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 467-476, June.
    11. Li Xia & Zhe George Zhang & Quan‐Lin Li, 2022. "A c/μ‐Rule for Job Assignment in Heterogeneous Group‐Server Queues," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1191-1215, March.
    12. Alejandro Montoya & Mario C. Vélez–Gallego & Juan G. Villegas, 2016. "Multi-product capacitated facility location problem with general production and building costs," Netnomics, Springer, vol. 17(1), pages 47-70, July.
    13. Sun, Zhuo & Zheng, Jianfeng, 2016. "Finding potential hub locations for liner shipping," Transportation Research Part B: Methodological, Elsevier, vol. 93(PB), pages 750-761.
    14. Vedat Verter & M. Cemal Dincer, 1995. "Facility location and capacity acquisition: An integrated approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1141-1160, December.
    15. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    16. Jianzhe Zhen & Ahmadreza Marandi & Danique de Moor & Dick den Hertog & Lieven Vandenberghe, 2022. "Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2410-2427, September.
    17. Fontes, Dalila B.M.M. & Hadjiconstantinou, Eleni & Christofides, Nicos, 2006. "A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1205-1219, October.
    18. Baumgartner, Kerstin & Fuetterer, André & Thonemann, Ulrich W., 2012. "Supply chain design considering economies of scale and transport frequencies," European Journal of Operational Research, Elsevier, vol. 218(3), pages 789-800.
    19. Takahito Kuno, 2022. "A revision of the rectangular algorithm for a class of DC optimization problems," Journal of Global Optimization, Springer, vol. 83(2), pages 187-200, June.
    20. Ioannis Avgerinos & Ioannis Mourtos & Georgios Zois, 2022. "Multi-type facility location in printing and parcel delivery services," Annals of Operations Research, Springer, vol. 309(1), pages 365-393, February.
    21. Natarajan, Ramachandran & Sethuraman, Kannan & Surysekar, Krishnamurthy, 2005. "Reducing incremental costs associated with the delegation of incentive contracting decisions: An analysis of planning and control decisions in a manufacturing setting in the presence of moral hazard," European Journal of Operational Research, Elsevier, vol. 162(3), pages 816-838, May.
    22. Zhengguan Dai & Kathleen Xu & Melkior Ornik, 2021. "Repulsion-based p-dispersion with distance constraints in non-convex polygons," Annals of Operations Research, Springer, vol. 307(1), pages 75-91, December.
    23. Vanhoucke, Mario & Demeulemeester, Erik & Herroelen, Willy, 2003. "Progress payments in project scheduling problems," European Journal of Operational Research, Elsevier, vol. 148(3), pages 604-620, August.

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