Applied mathematics in Engineering, Management and Technology 2014 The special issue in Management and Technology (Sep. 2014):303-309 www.amiemt-journal.com 303 Abstract In this paper we have introduced a zero-one nonlinear programming model in order to optimize a specific cost in cellular manufacturing systems in a controlled manufacturing condition whose parameters are determined by continuous probability distributions. The purpose of this model is to optimize total costs of subcontractor by determining how to allocate machinery and parts to each of the cells when the decision maker controls over the employment rate of each machine in the system. a genetic algorithm approach to produce legitimate children of different sizes of the system after they optimizing operator rates was then used to solve the model. Keywords: Cellular Manufacturing System, Subcontractor Policy, Queue Theory, Genetic Algorithm 1. Introduction Group Technology (GT) is a manufacturing philosophy that tries to increase production efficiency by grouping similar parts and products according to the design and/or production process. It has many advantages such as reducing the transition time and material costs, reducing inventories in the making, shortening the production time and increasing productivity of machines, etc[1]. Cellular manufacturing system (CMS) is one of the main applications of the philosophy of group technology. Some limitations of this system in the real world are: the capacity of the machines is limited, a limited number of machines can be placed in a cell, the number of cells should not exceed their upper limit, the material costs should be minimized, and the machine should be used more effectively[2]. To evaluate the realistic production systems typical cellular parameters such as the time between two interval arrival of the parts, components processing time, setup time, and system demands in different cycles have been taken into consideration[3]. In cases that parameter are defined as non-deterministic models other methods such as queuing theory and stochastic programming are used[4]. In real-world situations there are always parts that require more than one cell in order to complete their production process. These parts are called exceptional elements. These elements require moving between cells but since in most hypothesis elements transition between cells is not allowed, contractors are used instead[5,6,7]. Expenses that normally occur in these systems are as the cost of assigning machines to cells, cost of exceptional elements, waste costs, costs due to defections of the machines, etc. Penalty fee of the subcontractor is one of the costs that are imposed on the system. When one part needs to be processed by a special machine but that part has not been assigned to the machine, the subcontractors will process the said part[8,9]. Extensive studies have been done in a variety of cellular manufacturing systems so far, all of which trying to optimally design the system. Many models regarding solving t cellular manufacturing problems which used random parameters and considered the probable existence of exceptional elements were developed in 1970. Some of them are provided in the table1.1. As defined in this article, we will identify the exceptional elements and apply the subcontractor policy which forces the subcontractor costs to the system. We also tried to create a real life atmosphere by taking into account some non-deterministic circumstances for some parameters such as interval time for each element and Using Genetic Algorithm to optimize total costs of subcontractor in cellular manufacturing problem Mohsen Yaghoubizadeh, M.S. of Industrial engineering, Qazvin Islamic Azad University, Iran, M.Yaghoobi@qiau.ac.ir Mani Sharifi, Assistant professor of Industrial engineering, Qazvin Islamic Azad University, Iran, M.sharifi@qiau.ac.ir Reza Derakhshani, M.S. of Industrial engineering, Qazvin Islamic Azad University, Iran, Derakhshani.reza@gmail.com Arash Zaretalab, M.S. of Industrial engineering, Qazvin Islamic Azad University, Iran, Arash_zaretalab@yahoo.com