The modern decision environment is characterized by the presence of multiple objectives or goals, which are generally competing or conflicting. Therfore, it has been well established that virtually every decision making problem involves several key criteria. Mathematical programming techniques based on a single objective criterion such as cost minimization or profit maximization are restricted in application to real-world problems. Radford (14) contended that the goal of a global optimum solution should be discarded when considering complex and multiple objective decision problems. Under the modern complex decision environment, it is necessary to simultaneously consider all of the multiple and often conflicting objectives appropriately in selecting a best strategy or policy. Among the various techniques which have been developed to handle multicriteria decision making problems, goal programming is perhaps the most promising approach as it is an appropriate, powerful, flexible, and pragmatic tool. This technique was originally introduced by Charnes and Cooper (2, 3), and further developed by Ijiri (g) and Lee (11). The goal programming model can be solved through the use of a computer program based on an iterative algorithm. Currently, the most widely used computer program is Lee`s program (11) written in Fortran. Another popular algorithm was developed by Ignizio (7). Lee`s and Ignizio`s programs were designed using the modified simplex method. Lee`s and Ignizio`s programs did not consider efficiency in terms of the running time and storage requirements. Computational inefficiency results from unnecessary information being computed from iteration. to iteration. Recently Arthur (1) attempted to design a more efficient algorithm. This algorithm was tested in comparison with Lee`s algorithm in terms of computational time. Arthur`s goal partitioning algorithm is more efficient than the other two algorithms because it reduces the number of computations by modifying the matrix size when the number of subproblems increases and by eliminating unnecessary nonbasic variables. The critical disadvantage of this algorithm is its inability to provide the final optimal simplex tableau required to perform sensitivity analysis. This paper presents a new efficient GP algorithm based on the product represenation of the revised simplex method in order to overcome deficiencies of computational inefficiency on the part of the Lee and Ignizio algorithms and the lack of the final simplex tableau on the part of the Arthur algorithm.