Abstract
The multi-floor facility layout problem (MFLP) is one of the most important and complex facility layout problems that has many applications in designing the facilities of manufacturing and service sectors. In this study, a hybrid version of the Dantzig-Wolfe decomposition algorithm is proposed to solve the MFLP for the first time. The proposed solution approach is performed in two steps. In the first step, a mathematical formulation is applied to assign the departments to the floors in a way that the departments with higher material flow between them be located on the same or closer floors. In the second step, the output of the first step is considered and the MFLP is decomposed into a master problem and some sub-problems to form the Dantzig-Wolfe decomposition algorithm and find the optimal layout of each floor separately. Then the integrated layout of multiple floors is formed easily. The proposed algorithm is evaluated using some sample problems from the literature and some newly generated test problems. The obtained results show the superiority of the proposed algorithm compared to the approaches of the literature.
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