Report and Opinion 2014;6(7) http://www.sciencepub.net/report 59 Determination of number of kanban in a cellular manufacturing system with considering rework process Mojtaba Aghajani 1* , Abbas Keramati 2 1, 2 Department of Industrial Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran * Full telephone:+98-21-82095510; Fax No: +98-21-88006076; m.aghajani@ymail.com Abstract: The main element of just-in-time production system is kanban and the number of kanban influences the product inventory level. This research studies the cellular manufacturing system (CMS) controlled by kanban mechanism which defective items are produced in any production run of each product and rework is carried out to transform them into serviceable items. In each cycle after the normal production of each product the machine is setup for the rework process. In this paper, an mixed-integer nonlinear programming (MINLP) model in order to minimize total cost was developed to determine number of kanban, batch size, and number of batches. A simulated annealing (SA) algorithm as a meta-heuristic method to avoid the large computational time in optimal solution is developed for solving a large MINLP. Some problems are solved by SA and it is shown that the SA algorithm is an efficient method for solving the proposed model. [Mojtaba Aghajani, Abbas Keramati. Determination of number of kanban in a cellular manufacturing system with considering rework process. Rep Opinion 2014;6(7):59-70]. (ISSN: 1553-9873). http://www.sciencepub.net/report . 9 Keywords: Kanban, Cellular manufacturing system, Mixed integer non-linear programming (MINLP), Meta- Heuristic, Simulated annealing 1. Introduction Most existing production–inventory models assumes that all items produced are of perfect quality, but in real world production systems due to various reasons including process deterioration, human mistakes and other factors generation of imperfect quality items is inevitable. In this paper, the above issues will be considered and is assumed that all imperfect quality items can be repaired through rework. Rework is the transformation of imperfect quality items generated during production period into serviceable ones. In recent years, the concepts of cellular manufacturing and just-in-time (JIT) production has received much attention and applied in many developed countries. A cellular manufacturing system (CMS) is a manufacturing philosophy that leads to achieving the JIT production system [Sridhar and Rajendran, 1996]. In this system, machines and similar parts are grouped into cells and part-families. Within each cell a particular part family with similar manufacturing characteristics such as process routing and tooling requirements are produced. JIT production system has been implemented widely in many factories to improve the productivity of the production and reduce production costs. The principle of JIT philosophy is a production of what is needed at the right time and in the right quantity [Hutchins, 1993]. Kanban system as information system is one of the major elements of JIT philosophy. Kanban is the Japanese word which means for a card. This system is the best-known pull systems in which production is triggered by the customer demand at the final stage. In a production environment that is controlled by kanban the material flow is from preceding stage to succeeding stage, but the information flow is downward and from succeeding stage to preceding stage. At each intermediate stage, production and delivery is triggered by succeeding stage order. This process is carried all the way from the last stage to the first stage. Goods are manufactured only when workstations receive a card. Empty containers show that more parts will be needed for production. Each workstation will only produce enough components to fill containers and then stops [Shahabudeen et al., 2002]. Since the number of kanban influences the product inventory level, it is very important for managers to determine the number of kanban used in the system introductory phase [Fukukawa and Hong, 1993]. In this paper, we study the CMS controlled by kanban under a JIT philosophy with rework policy through the development of mathematical models. The main objective of the mathematical model is determining of kanban numbers and lot sizes between two stages to minimize total relevant cost including material handling, holding and setup costs. Further, in this article we will see that the model of the problem is of MINLP type which takes a long time to achieve optimal solution. Thus, this paper presents a simulated annealing (SA) as a Meta- Heuristic algorithm to reduce computational time. The remainder of the paper is as follows: In Section 2, literature review about kanban is introduced. The problem is described in Section 3. In Section 4, problem assumptions are presented. Section