Separable programming deals with such nonlinear programming problem in which the objective function as well as constraints are separable. For solving Separable nonlinear programming problem (SNPP) is reduced first to Linear programming problem (LPP) by approximating each separable function by a piecewise linear function and than usual graphical, simplex method applied. A new form of Gauss elimination technique for inequalities has been proposed for solving a Separable nonlinear programming problem. The technique is useful than the earlier existing methods because it takes least time and calculations involve in are also simple. The same has been illustrated by a numerical example of SNPP.

Goal linear programming(GP) is one of the important techniques for solving multi-objective linear programming (MOLP) problems so that for every objective aspiration level is considered by the decision maker. A special kind of GP problem is the multi-choice goal programming, where some aspiration level is considered for the targets. The multi-choice goal programming the first time was presented by chang. T. C in the year 2007. Then in 2008 change expired another kind of multi choice goal programming entitled, the revised multi-choice goal programming where its goal aspersion levels are a closed interval. The first paper of the Fuzzy multi-choice goal programming was introduced by the Bankian et al. in the year 2012, which uses triangular Fuzzy number as the aspiration level. In this paper, we are going to present two new models of the flexible Fuzzy multi-choice goal programming: 1) revised multi-choice goal programming with flexible Fuzzy constraints and 2) revised multi-choice goal programming with flexible Fuzzy objective functions. For both models, we propose a new approach for solving them based on a multi-parametric linear goal programming and minimum degree membership technique. Finally, we illustrate our approach by solving some numerical examples.

In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using Fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, Fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.