Mixed binary interval goal programming

This paper focuses on the mixed binary preferences decision problem associated with the use of penalty functions in goal programming. In this sense, a new formulation approach for interval goal programming is derived, which is more efficient than the model of Jones and Tamiz. In addition, to enhance the usefulness of the proposed model, binary variables subject to the environmental constraints are added. This leads to the model of binary interval goal programming. Finally, examples to illustrate these models are given.