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In this work, we present a promising and emerging energy supply chain type based on decentralized energy generation through domestic microgeneration using micro combined heat and power generators, which produce electricity as well as heat. In particular, several of those microgenerators are connected so as to form a residential energy micro-grid. By constructing such a micro-grid while integrating various energy alternatives in a residential scale, residents can trade and consume the power flexibly with each other. The micro-grid administrator should realize the energy production planning of this energy supply chain so as to: mainly satisfy the heat and electrical energy demand of every household, interchange electrical energy among the network members, and sell excessive electricity production to the central electricity macro-grid. In order to facilitate the planning and the management of such micro-grids, we develop a linear mixed integer programming framework for the energy production planning of micro-grids consisting of interconnected residential micro combined heat and power generators. Finally, we apply the proposed approach to a number of cases studies in order to highlight its potential benefits and reveal future research lines.