The manufacturing industry consumes electricity and natural gas to provide the power and heat required for manufacturing. Additionally, large amounts of electric energy and heat energy are used, and the electricity cost, amount of environmental pollution, and equipment maintenance cost are high. Thus, optimizing the management of equipment with new energy is important to satisfy the load demand from the system. This paper formulates the scheduling problem of these multiple energy systems as a multi-objective linear regression model (MLRM), and an energy management system is designed focusing on the economy and on greenhouse gas emissions. Furthermore, a variety of optimization objectives and constraints are proposed to make the energy management scheme more practical. Then, grey theory is combined with the common MLRM to accurately represent the uncertainty in the system and to make the model better reflect the actual situation. This paper takes load fluctuation, total grid operation cost, and environmental pollution value as reference standards to measure the effect of the gray optimization algorithm. Lastly, the model is applied to optimize the energy supply plan and its performance is demonstrated using numerical examples. The verification results meet the optimized operating conditions of the multi-energy microgrid system.