This paper develops a model and optimization method for multi-area heat and power production with power transmission and storage. The objective function of the model is to minimize the operating costs of the system. The model can be used both for planning optimal system operation, and for simulating the effects of extended production, transmission and storage capacity. The proposed parametric decomposition method is fast enough to solve problems with a large number of hourly models. The parametric decomposition method works in two phases. First, the problem is decomposed into hourly local energy production models without storages and transmission. Parametric linear programming analysis is applied to these models for determining the optimal marginal operating costs as a function of power production. In the second phase, the optimal marginal cost functions are encoded as a linear transshipment network model including storages and transmission network. The network model is solved using generic sparse linear programming software. The operation of each production plant is determined based on the network solution. The decomposition method was validated by comparing it against an integrated linear programming model. The decomposition method demonstrates good accuracy and solves yearly models up to 30 times faster than the integrated model.