The paper presents an optimisation scheme for the economic dispatch of electric and steam demands to a cogeneration plant with a tieline and auxiliary boiler facilities. The primary objective of the optimisation scheme is to share both the electric and thermal load demands among the in-plant generating units and the energy purchase facilities to minimise the total energy cost. Depending on the cost parameters, optimum cogeneration can result in selling electricity during utility peak demand hours while purchasing electricity during the local peaks of either electricity and/or steam to reduce the overall cost of the unit product. The optimisation scheme is based on generalized network programming (GNP) which can often solve problems with significantly more variables and constraints that can not be easily solved by other optimisation techniques. This scheme is capable of handling the nonlinear cost functions and the dependent relations between the electric power and steam generation for the cogeneration unit. It is possible to represent the price of selling electricity as well as the cost evaluation of satisfying each steam and electric demand. Also, the proposed scheme has the capability to handle multiple objectives which is beneficial for the system operator.