Grouping algorithm for linear goal programming problems

An algorithm called grouping algorithm for linear goal programming problems has been suggested. The algorithm considers all goal and real constraints together as a one group with the objective function being the sum of all weighted deviations and solves a sequence of linear programming subproblems, each using the optimal solution of the previous subproblems. The simplex method and sensitivity analysis are applied to obtain the solution of the subproblems. In the case of the objective function being nonzero in the optimal table of the subproblem, the goal constraints having the lowest priority are deleted and then the optimal table is examined. The deletion of goal constraints starting from the lowest priority to the highest priority levels continues till the objective function reaches to zero value or the relative cost of some nonbasic variables assumes zero value whichever occurs earlier. The proposed algorithm also reallocates the priority levels to the goals with the requirements of the decision maker to have the maximum goals satisfied.