Journal of the Operational Research Society (2008) 59, 443--454  2008 Operational Research Society Ltd. All rights reserved. 0160-5682/08 $30.00 www.palgrave-journals.com/jors A new solution for a dynamic cell formation problem with alternative routing and machine costs using simulated annealing R Tavakkoli-Moghaddam 1,3 ∗ , N Safaei 2,3 and F Sassani 3 1 University of Tehran, Tehran, Iran; 2 Iran University of Science and Technology, Tehran, Iran; and 3 The University of British Columbia, Vancouver, Canada This paper presents an integer-linear programming approach for a cell formation problem (CFP) in a dynamic environment with a multi-period planning horizon. The objectives are to minimize the inter-cell movement and machine costs simultaneously. In dynamic environments, the product mix and demand are different but deterministic in each period. As a consequence, the formed cells in the current period may not be optimal for the next period. Thus, the reconfiguration of cells is required. Reconfiguration consists of re-forming part families, machine groups, and machine relocation. The CFP belongs to the category of NP-hard problems, thus we develop an efficient simulated annealing (SA) method to solve such a problem. The proposed mathematical model is optimally solved and the associated results are compared with the results obtained by the SA run. The results show that the gap between optimal and SA solutions is less than 4%, which indicates the efficiency of the developed SA scheme. Journal of the Operational Research Society (2008) 59, 443 – 454. doi:10.1057/palgrave.jors.2602436 Published online 20 June 2007 Keywords: dynamic cell formation problem; mixed-integer programming; simulated annealing Introduction The implementation of cellular manufacturing systems (CMSs) means to group machines into a number of cells, in which each cell is dedicated to process a distinct family of part types and to operate on them as independently as possible. Benefits such as reduced material handling, setup times and work-in-process, and shorter lead times, improved productivity, simplified scheduling, and better overall control of operations have been reported (Wemmerlov and Johnson, 1997). In most industries, the production process is dynamic in such a way that the planning horizon can be divided into periods, in which each period has different product mix and demand requirements. In such cases, we face a dynamic envi- ronment. It is noted that in the dynamic condition, product mix and demand in each period are different from other periods but are deterministic (ie known as a priori). Also, in the dynamic production condition, the best cell design for one period may not be an efficient design for the subsequent periods. By rearranging the manufacturing cells, the CMS can continue operating efficiently as the product mix and part demand change. However, it may require some of the ∗ Correspondence: R. Tavakkoli-Moghaddam, Department of Industrial Engineering, Faculty of Engineering, University of Tehran, P.O. Box: 11365/4563, Tehran, Iran. E-mail: tavakoli@ut.ac.ir machines to be moved from one cell to another (ie machine relocation) and the number of cells be changed (Wemmerlov and Hyer, 1989; Shafer and Rogers, 1991; Chen, 1998; Schaller et al, 2000; Foulds and Neumann, 2003; Balakr- ishnan and Cheng, 2005). The cell formation model belongs to the category of NP-hard problems, in which real-world instances cannot be optimality solved within reasonable time. Thus, the use of meta-heuristic algorithms is unavoidable. One of the most efficient meta-heuristics to solve the facility planning prob- lems is simulated annealing (SA) (Kirkpatrick et al, 1983). SA is a stochastic neighbourhood search method that is developed for the combinatorial optimization problems. It has the capability to jump out of local optima and search for the global optimum. This capability is achieved by accepting worse solutions than the current solution. The probability of acceptance is determined by a control parameter called ‘temperature’ which decreases during the SA procedure. Many investigations have been conducted in the context of modelling and solution methodology for the dynamic cell formation problem (CFP) (Chen, 1998; Wilhelm et al, 1998; Balakrishnan and Cheng, 2005). Also, numerous schemes in similar research areas such as the dynamic plant layouts (Montreuil and Laforge, 1992; Rogers and Bottaci, 1997), flexible plant layouts (Black, 1991), and dynamic layout prob- lems (Lacksonen, 1994, 1997; Baykaso˘ glu and Gindy, 2001) have been proposed to deal with the dynamic condition. In