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The Piecewise Concave Function

Author

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  • Willard I. Zangwill

    (University of California, Berkeley)

Abstract

An important function which is neither concave nor convex often arises in production and inventory models. This function is herein called piecewise concave and can be considered to be a generalization of the concave function. Essentially it is the maximum of a collection of concave functions. Various properties of piecewise concave functions are explored in this paper. In particular, a theory is developed to locate the point at which such functions are minimized. A short discussion of applications is included.

Suggested Citation

  • Willard I. Zangwill, 1967. "The Piecewise Concave Function," Management Science, INFORMS, vol. 13(11), pages 900-912, July.
    • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:11:p:900-912
    DOI: 10.1287/mnsc.13.11.900
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    Cited by:

    1. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    2. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    3. Aguiar, Victor H. & Hjertstrand, Per & Serrano, Roberto, 2020. "A Rationalization of the Weak Axiom of Revealed Preference," Working Paper Series 1321, Research Institute of Industrial Economics.
    4. Jop Schouten & Mirjam GrooteSchaarsberg & Peter Borm, 2024. "Cost sharing methods for capacity restricted cooperative purchasing situations," Review of Economic Design, Springer;Society for Economic Design, vol. 28(2), pages 347-390, June.
    5. Berman, Oded & Sanajian, Nima & Wang, Jiamin, 2017. "Location choice and risk attitude of a decision maker," Omega, Elsevier, vol. 66(PA), pages 170-181.
    6. Esra Koca & Hande Yaman & M. Selim Aktürk, 2014. "Lot Sizing with Piecewise Concave Production Costs," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 767-779, November.
    7. Bhattacharjee, Sudip & Ramesh, R., 2000. "A multi-period profit maximizing model for retail supply chain management: An integration of demand and supply-side mechanisms," European Journal of Operational Research, Elsevier, vol. 122(3), pages 584-601, May.

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