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

Richard Weinhold and Steven A. Gabriel

Journal of the Operational Research Society, 2020, vol. 71, issue 2, 237-249

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.

Date: 2020
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DOI: 10.1080/01605682.2018.1561163

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