This study considers a supply chain master planning problem in an uncertain environment where operating costs, customer demand, production capacity, manufacturer’s acceptable defective rate, and manufacturer’s acceptable service level are uncertain. Our supply chain consists of one manufacturer, multiple suppliers, and multiple distribution centers. While one objective is to minimize the total costs of logistics that consists of purchasing cost, production cost, and distribution cost, the other objective is to maximize total value of purchasing. These objectives are in conflict with each other. In this paper, the fuzzy multi-objective linear model is applied with α-Cut analysis to achieve the optimal supply chain master planning in an uncertain environment by balancing these two conflicting objectives. The α-Cut analysis is introduced to ensure decision-makers that the outcome satisfies their preferences based on a specified minimum allowed satisfaction value (α).

This paper presents an alternate technique based on fuzzy goal programming (FGP) approach to solve multi-objective programming problem with fuzzy relational equations (FREs) as constraints. The proposed technique is more efficient and requires less computational work than that of algorithm suggested by Jain and Lachhwani (2009) [Jain, & Lachhwani (2009). Multiobjective programming problem with fuzzy relational equations. International Journal of Operations Research, 6(2), 55?63.]. In FGP formulation, objectives are transformed into the fuzzy goals using maximum and minimal solutions elements of FREs feasible solution set. A pseudo code computer algorithm is developed for computation of maximum solution of FREs. Suitable linear membership function is defined for each objective function. Then achievement of the highest membership value of each of the fuzzy goals is formulated by minimizing the sum of negative deviational variables. The aim of this paper is to present a simple and efficient solution procedure to obtain compromise optimal solution of multiobjective optimization problem with FREs as constraints. A comparative analysis is also carried out between two methodologies based on numerical examples.

Having an efficient budget normally has different advantages such as measuring the performance of various organizations, setting appropriate targets and promoting managers based on their achievements. However, any budgeting planning requires prediction of different cost components. There are various methods for budgeting planning such as incremental budgeting, program budgeting, zero based budgeting and performance budgeting. In this paper, we present a fuzzy goal programming to estimate operational budget. The proposed model uses fuzzy triangular as well as interval number to estimate budgeting expenses. The proposed study of this paper is implemented for a real-world case study in province of Qom, Iran and the results are analyzed.

The aim of this research is to present a hybrid model to select auto part suppliers. The proposed method of this paper uses factor analysis to find the most influencing factors on part maker selection and the results are validated using different statistical tests such as Cronbach & apos; s Alpha and Kaiser-Meyer. The hybrid model uses analytical network process to rank different part maker suppliers and fuzzy goal programming to choose the appropriate alternative among various choices. The implementation of the proposed model of this paper is used for a case study of real-world problem and the results are discussed.