Modified signomial geometric programming (MSGP) and its applications

A "signomial" is a mathematical function, contains one or more independent variables. Richard J. Duffin and Elmor L. Peterson introduced the term "signomial". Signomial geometric programming (SGP) optimization technique often provides a much better mathematical result of real-world nonlinear optimization problems. In this research paper, we have proposed unconstrained and constrained signomial geometric programming (SGP) problem with positive or negative integral degree of difficulty. Here a modified form of signomial geometric programming (MSGP) has been developed and some theorems have been derived. Finally, these are illustrated by proper examples and applications

Fuzzy E.O.Q model with constant demand and shortages: A fuzzy signomial geometric programming (FSGP) approach

In this paper, a fuzzy economic order quantity (E.O.Q) model with shortages under fully backlogging and constant demand is formulated and solved. Here the model is solved by fuzzy signomial geometric programming (FSGP) technique. Fuzzy signomial geometric programming (FSGP) technique provides a powerful technique for solving many non-linear problems. Here we have proposed a new idea that is fuzzy modified signomial geometric programming (FMSGP) and some necessary theorems have been derived. Finally, these are illustrated by some numerical examples and applications

Proof without Words: (a+b+c)^2,(a+b-c)^2,(a+b+c)^2-(a+b-c)^2

In this proof without words, we prove wordlessly the following theorems,(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca(a+b-c)^2=a^2+b^2+c^2+2ab-2bc-2ca(a+b+c)^2-(a+b-c)^2=4c(a+b

Proof Without Words: Arithmetic Mean / Geometric Mean Inequality

The author proves almost wordlessly the Arithmetic Mean / Geometric Mean Inequality

Modified signomial geometric programming (MSGP) and its applications

A "signomial" is a mathematical function, contains one or more independent variables. Richard J. Duffin and Elmor L. Peterson introduced the term "signomial". Signomial geometric programming (SGP) optimization technique often provides a much better mathematical result of real-world nonlinear optimization problems. In this research paper, we have proposed unconstrained and constrained signomial geometric programming (SGP) problem with positive or negative integral degree of difficulty. Here a modified form of signomial geometric programming (MSGP) has been developed and some theorems have been derived. Finally, these are illustrated by proper examples and applications

Fuzzy geometric programming techniques and applications

This book develops the concepts of various unique optimization techniques in the crisp and fuzzy environment. It provides an extensive overview of geometric programming methods within a unifying framework, and presents an in-depth discussion of the modified geometric programming problem, fuzzy geometric programming, as well as new insights into goal geometric programming. With numerous examples and exercises together with detailed solutions for several problems, the book also addresses fuzzy multi-objective geometric programming techniques. Geometric programming, which falls into the general class of signomial problems, has applications across disciplines, from engineering to economics, and is extremely useful in applications of a variety of optimization problems. Organized into thirteen chapters, this book is a valuable resource for graduate and advanced undergraduate students and researchers in applied mathematics and engineering

Multiobjective Geometric Programming Problem Under Uncertainty

Multiobjective geometric programming (MOGP) is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Generally, the parameters of a multiobjective geometric programming (MOGP) models are assumed to be deterministic and fixed. However, the values observed for the parameters in real-world MOGP problems are often imprecise and subject to fluctuations. Therefore, we use MOGP within an uncertainty based framework and propose a MOGP model whose coefficients are uncertain in nature. We assume the uncertain variables (UVs) to have linear, normal or zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained multiobjective geometric programming (UCCMOGP) problems can be transformed into conventional MOGP problems to calculate the objective values. The paper develops a procedure to solve a UCCMOGP problem using an MOGP technique based on a weighted-sum method. The efficacy of this procedure is demonstrated by some numerical examples. (original abstract

Fuzzy E.O.Q model with constant demand and shortages: A fuzzy signomial geometric programming (FSGP) approach

In this paper, a fuzzy economic order quantity (E.O.Q) model with shortages under fully backlogging and constant demand is formulated and solved. Here the model is solved by fuzzy signomial geometric programming (FSGP) technique. Fuzzy signomial geometric programming (FSGP) technique provides a powerful technique for solving many non-linear problems. Here we have proposed a new idea that is fuzzy modified signomial geometric programming (FMSGP) and some necessary theorems have been derived. Finally, these are illustrated by some numerical examples and applications

A fuzzy inventory model with unit production cost, time depended holding cost, with-out shortages under a space constraint: a parametric geometric programming approach

In this paper, an Inventory model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. We have considered here a single objective inventory model. In most real world situation, the objective and constraint function of the decision makers are imprecise in nature, hence the coefficients, indices, the objective function and constraint goals are imposed here in fuzzy environment. Geometric programming provides a powerful tool for solving a variety of impreciseoptimization problem. Here we have used nearest interval approximation method to convert a triangular fuzzy number to an interval number then transform this interval number to a parametric interval-valued functional form and solve the parametric problem by geometric programming technique. Here two necessary theorems have been derived. Numerical example is given to illustrate the model through this Parametric Geometric-Programming method.