This paper presents an integrated production and marketing planning model. The model aims at maximizing production and minimizing the cost of production and marketing expenditure. The resulted model which is highly nonlinear and non-convex is solved by geometric programming (GP) in order to provide the closed form solution. The solution of the proposed model is analyzed in different cases in order to study the behavior of the marketing planning. A Numerical example is used to demonstrate the implementation of the closed form solution.

Generally, an engineering design problem has multiple objective functions. Some of these problems can be formulated as multiobjective geometric programming models. On the other hand, often in the real world, coefficients of the objective functions are not known precisely. Coefficients may be interpreted as fuzzy numbers, which lead to a multiobjective geometric programming with fuzzy parameters. In this paper, we solve the multiobjective geometric programming problem with fuzzy parameters by applying a linear ranking function. The linear ranking function is used to compare fuzzy numbers. Finally, a numerical example is given.

One of the fundamental concepts in convex analysis and optimization is the relative interior of a set. This concept is used when the interior of a set is empty due to the incompleteness of its dimension. In this paper, first, we propose a linear programming model to find a relative interior point of a polyhedral set. Then, we discuss the application of this model to geometric programming. Specifically, we show that a special form of our proposed model can determine the degeneracy of a geometric programming problem by identifying a relative interior point of the feasible region of its dual. Finally, we present two numerical examples for describing the applications of the proposed model.

Nonlinear programming is one of the most common models in optimization which is useful for solving many of the problems in the real world. On the other hand, in formulating engineering problems we face some practical kinds of nonlinear optimization which is called geometric programming. In fact, geometric program is a method for solving nonlinear problems with nonlinear or linear constraints. Many applications of geometric programming are engineering design problems in which some of the problems parameters are estimates of actual values. Intuitively, when the parameters are imprecise values, the derived objective value is imprecise as well. The aim of this paper is to develop a solution procedure for solving geometric programming with fuzzy triangular numbers.

geometric programming is a mathematical technique, which has been developed for nonlinear optimization problems. This technique is based on the dual program with linear constraints. Determination of species concentrations in chemical equilibrium conditions is one of its applications in chemistry and chemical engineering fields. In this paper, the principles of geometric programming and its computational method are presented. Also, for a chemical equilibrium, as an example, the concentrations of species for the ammonia synthesis reaction are determined. The obtained results are compatible with the experimental data available in the literature. This leads to the application of the geometric programming to estimate the concentrations in the equilibrium conditions for reactions where the experimental data are not available.