A MATHEMATICAL MODEL FOR DESIGNING OF PRODUCTION LINE USING RELIABILITY OPTIMIZATION APPROACH UNDER UNCERTAINTY

In related research about reliability optimization, often less attention has been paid to the practical aspects such as market demand for each product, space need for installation of facilities and work stations, financial resources and available capacity. The purpose of this paper is using of reliability optimization approach in designing of production line in order to increase the production of products through minimizing idle time due to breakdown of facilities. Most previous researches in reliability studies assumed that the parts of the system are known a priori and stochastic distributions are given. But in this research, we consider uncertain environment. In this paper, an integer non-linear multi-objective programming model with interval parameters is presented. We try to design the production line with addressing reliability optimization approach under uncertainty. The aim of this model is to determine the optimal number of production lines with regard to budget, space, capacity and demand for product limitations; so that reliability of whole system and total summation of holding cost and inventory shortage cost are respectively maximized and minimized. First, we discuss mathematical aspects of interval parameters: mean, variance and ordering the interval numbers. Then we present some notations and assumptions of our considered problem and build our proposed mathematical model. As we have considered two objectives; maximizing reliability and minimizing total cost, to solve the proposed model we apply a multi-criteria method. The proposed method is global criterion method. To test the model, three instances of the problem are generated randomly and solved by MATLAB software. The uniform and normal distributions are used to generate random data of each instances. The results showed the desirability of the proposed model. The dealed problem is NP-hard and to solve large instance of the problem it is necessary to develop heuristic or meta-heuristic methods.