**Methods of feasible directions : a study in linear and non-linear programming**

Problems, referred to as strategies of possible directions, that use the simplex methodology as function ; three. the institution of associate degree equivalence between several existing strategies for the linear, quadratic or lentiform programming drawback and therefore the strategies of possible directions. The author offers an entire survey of the strategies in such the simplest way that programming for associate degree computer becomes simple. it’s going to safely be declared that another vital contribution has been created to the present speedily growing upshot of the mathematical sciences.** [1]**

**Fuzzy programming and linear programming with several objective functions**

In the recent past varied models and ways are advised to resolve the vectormaximum downside. Most of those approaches center their attention on applied mathematics issues with many objective functions. with the exception of these approaches the idea of fuzzy sets has been utilized to formulate and solve fuzzy applied mathematics issues. This paper presents the appliance of fuzzy applied mathematics approaches to the linear vectormaximum downside. It shows that solutions obtained by fuzzy applied mathematics square measure invariably economical solutions. It additionally shows the implications of mistreatment other ways of mixing individual objective functions so as to see associate “optimal” compromise resolution. **[2]**

**Linear Programming Under Uncertainty**

This chapter originally appeared in Management Science, April–July 1955, Vol. 1, Nos. 3 and 4, pp. 197–206, printed by The Institute of Management Sciences. this text was conjointly reprinted in a very special issue of , emended by Wallace Hopp, that includes the “Ten Most prestigious Papers of Management Science´s 1st Fifty Years,” Vol. 50, No. 12, Dec., 2004, pp. 1764–1769. For this special issue patron saint B. Dantzig provided the subsequent commentary: “I am very happy that my 1st paper on designing below uncertainty is being republished in spite of everything these years. it’s a elementary paper in a very growing field.” **[3]**

**Shaping the topology of folding pathways in mechanical systems**

Disordered mechanical systems, once powerfully distorted, have complicated configuration areas with multiple stable states and pathways connecting them. The topology of such pathways determines that states square measure swimmingly accessible from any a part of configuration house. dominant this topology would enable United States to limit access to unwanted states and choose desired behaviors in metamaterials. Here, we have a tendency to show that the topology of such pathways, as captured by bifurcation diagrams, are often tuned exploitation imperfections like stiff hinges in elastic networks and wrinkled skinny sheets. we have a tendency to derive Linear Programming-like equations for coming up with fascinating pathway topologies. These ideas square measure applied to eliminate the exponentially some ways of misfolding self-folding sheets by creating some creases stiffer than others. **[4]**

**On Application of Two- Stage Stochastic Fully Fuzzy Linear Programming for Water Resources Management Optimization**

In this paper, a two- stage random absolutely fuzzy applied math is developed for a management downside in terms of water resources allocations for example the pertinency of a projected approach. A projected approach converts {the downside|the matter} into a triple- objective problem so a coefficient technique is employed for finding it. The advantage of the approach is to come up with a group of solutions for water resources coming up with that facilitate the choice maker to create tradeoffs between the potency of economic and also the risk violation of the constrains. A case study is given for illustration. **[5]**

**Reference**

**[1]** Zoutendijk, G., 1960. Methods of feasible directions: a study in linear and non-linear programming. Elsevier. (Web Link)

**[2]** Zimmermann, H.J., 1978. Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), (Web Link)

**[3]** Dantzig, G.B., 2010. Linear programming under uncertainty. In Stochastic programming (pp. 1-11). Springer, New York, NY. (Web Link)

**[4]** Shaping the topology of folding pathways in mechanical systems

Menachem Stern, Viraaj Jayaram & Arvind Murugan

Nature Communications volume 9, Article number: 4303 (2018) (Web Link)

**[5]** Khalifa, H. A. and Al- Shabi, M. (2018) “On Application of Two- Stage Stochastic Fully Fuzzy Linear Programming for Water Resources Management Optimization”, Journal of Advances in Mathematics and Computer Science, 29(6), (Web Link)