The article presents solution procedure of geometric programming to solve the structural model with imprecise coefficients. We have considered a single objective structural optimization model with weight as an objective function. Geometric programming provides a powerful tool for solving a variety of imprecise optimization problems. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval number. In this paper, we transform this interval number to a parametric interval-valued functional form and then solve the parametric problem by geometric programming technique. The advantage of this technique is that we can find directly optimal solution of the objective function without solving two-level mathematical programs. Numerical example is given to illustrate the model through this approximation method.

Cash flow analysis is one of the most popular methods for investigating the outcome of an economical project. The costs and benefits of a construction project are often involved with uncertainty and it is not possible to find a precise value for a particular project. In this paper, we present a simple method to calculate the net present value of a cash flow when both costs and benefits are given as triangular numbers. The proposed model of this paper uses Delphi method to figure out the fair values of all costs and revenues and then using fizzy programming techniques, it calculates the fuzzy net present value. The implementation of the proposed model is demonstrated using a simple example.

Ranking fuzzy numbers is one of the most important phases in any decision making process in fuzzy environments. In most cases, we deal with fuzzy numbers in the field of evaluating alternatives with fuzzy information or linguistic variables. This paper investigates ranking fuzzy numbers using the concept of preference ratio, introduces the weakness of this method, and proposes a new approach that overcomes the shortcoming of existing method. The proposed approach which is based on the concept of utility function takes the opinion of DM for ranking fuzzy numbers into account.

In this article, we consider a single-unit unreliable production system which produces a single item. During a production run, the production process may shift from the in-control state to the out-of-control state at any random time when it produces some defective items. The defective item production rate is assumed to be imprecise and is characterized by a trapezoidal fuzzy number. The production rate is proportional to the demand rate where the proportionality constant is taken to be a fuzzy number. Two production planning models are developed on the basis of fuzzy and stochastic demand patterns. The expected cost per unit time in the fuzzy sense is derived in each model and defuzzified by using the graded mean integration representation method. Numerical examples are provided to illustrate the optimal results of the proposed fuzzy models.

:In this paper, we present a multi-objective possibilistic programming model to locate distribution centers (DCs) and allocate customers' demands in a supply chain network design (SCND) problem. The SCND problem deals with determining locations of facilities (DCs and/or plants), and also shipment quantities between each two consecutive tier of the supply chain. The primary objective of this study is to consider different risk factors which are involved in both locating DCs and shipping products as an objective function. The risk consists of various components: the risks related to each potential DC location, the risk associated with each arc connecting a plant to a DC and the risk of shipment from a DC to a customer. The proposed method of this paper considers the risk phenomenon in fuzzy forms to handle the uncertainties inherent in these factors. A possibilistic programming approach is proposed to solve the resulted multi-objective problem and a numerical example for three levels of possibility is conducted to analyze the model.