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Discretely constrained mixed complementary problems: Application and analysis of a stylised electricity market

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  • Richard Weinhold
  • Steven A. Gabriel

Abstract

Recent research provides various methods to formulate and solve discretely constrained mixed complementary problems (DC-MCP) by relaxing complementarity. This paper provides insight into different areas of DC-MCPs. First, we look at three different solution methods for DC-MCPs from the literature and compare them in terms of solutions and usability. The methods discussed in this paper use disjunctive-constraints, SOS1 variables and an implementation of a certain median function. The methods are applied to a stylized electricity market including a minimum-generation constraint, making the problem a DC-MCP. Furthermore, the paper discusses the mathematical and economic implications of solutions. It is shown that a relaxed version of the discrete restrictions on variables combined with MCP conditions may not lead to an equilibrium where no player has a unilateral incentive to deviate. To overcome this problem, this paper presents a method to implement a two-stage DC-MCP to find solutions which are in line with the economic definition of an equilibrium.

Suggested Citation

  • Richard Weinhold & Steven A. Gabriel, 2020. "Discretely constrained mixed complementary problems: Application and analysis of a stylised electricity market," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(2), pages 237-249, February.
    • Handle: RePEc:taf:tjorxx:v:71:y:2020:i:2:p:237-249
    DOI: 10.1080/01605682.2018.1561163
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    Cited by:

    1. Marianna De Santis & Sven de Vries & Martin Schmidt & Lukas Winkel, 2022. "A Penalty Branch-and-Bound Method for Mixed Binary Linear Complementarity Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3117-3133, November.
    2. Dimitri J. Papageorgiou & Francisco Trespalacios & Stuart Harwood, 2021. "A Note on Solving Discretely-Constrained Nash-Cournot Games via Complementarity," Networks and Spatial Economics, Springer, vol. 21(2), pages 325-330, June.

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