J Intell Manuf (2012) 23:1849–1860 DOI 10.1007/s10845-010-0499-8 Intelligent design of a dynamic machine layout in uncertain environment of flexible manufacturing systems Ghorbanali Moslemipour · T. S. Lee Received: 28 September 2010 / Accepted: 14 December 2010 / Published online: 23 January 2011 © Springer Science+Business Media, LLC 2011 Abstract Since Facility Layout Problem (FLP) affects the total manufacturing cost significantly, it can be considered as a critical issue in the early stages of designing Flexible Man- ufacturing Systems (FMSs), particularly in volatile environ- ments where uncertainty in product demands is inevitable. This paper proposes a new mathematical model by using the Quadratic Assignment Problem formulation for design- ing an optimal machine layout for each period of a dynamic machine layout problem in FMSs. The product demands are considered as independent normally distributed random vari- ables with known Probability Density Function (PDF), which changes from period to period at random. In this model, the decision maker’s defined confidence level is also considered. The confidence level represents the decision maker’s atti- tude about uncertainty in product demands in such a way that it affects the results of the problem significantly. To val- idate the proposed model, two different size test problems are generated at random. Since the FLP, especially in multi- period case is a hard Combinatorial Optimization Problem (COP), Simulated Annealing (SA) meta-heuristic resolution approach programmed in Matlab is used to solve the math- ematical model in a reasonable computational time. Finally, the computational results are evaluated statistically. Keywords Dynamic facility layout problem · Uncertain environment · Flexible manufacturing system · Simulated annealing G. Moslemipour · T. S. Lee (B ) Faculty of Engineering and Technology, Multimedia University, 75450 Melaka, Malaysia e-mail: tslee@mmu.edu.my Introduction A Flexible Manufacturing System (FMS) consists of at least four automated and multifunctional machine centres such as Computer Numerical Control (CNC) machine tools, which are linked together mechanically by an automated material handling system and electronically by a distributed computer control system. The problems in the FMS can be catego- rized into designing, programming, scheduling and control- ling. One of the most important steps in the design of the FMS is the arrangement of facilities (machines) called FLP. The Material Handling Cost (MHC) is one of the most appropri- ate measures to evaluate the efficiency of a facility layout so that an efficient layout has the minimum MHC. According to Tompkins et al. (2003), the MHC forms 20–50% of the total manufacturing costs and it can be decreased at least 10–30% by an efficient layout design. The MHC is calculated as the product of the flow of materials between facilities and travel distance between locations. Considering the known facility locations leads to the known and fixed travel distance. In this case, the MHC can be regarded as a function of the flow of materials. According to the nature of the flow of materials, the FLP can be static or dynamic. In the Static Facility Layout Problem (SFLP), the flow of materials is deterministic and constant over the entire time planning horizon. In this problem, the optimum rela- tive location of each facility is determined so that the total MHC is minimized. It is very difficult to forecast the product demands in a long period of time. Therefore, in the SFLP, the single time planning horizon is divided into several time periods so that each period has different and fixed product demand requirements. By doing so, the SFLP is become a multi-period layout problem named Dynamic Facility Lay- out Problem (DFLP). Actually, in the DFLP, the demand for products is deterministic and constant for each period, but 123