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The multi-row facility layout problem (MRLP) is an important design problem often encountered in real life. Existing studies on MRLPs typically either ignore clearances between adjacent machines or consider only the minimum clearances. However, separating adjacent machines with clearances greater than the minimum ones may achieve lower material flow cost. In addition, current studies on MRLPs ignore the optimisation of layout area. In this paper, we study a  m ulti- r ow facility  l ayout  p roblem with  e xtra  c learances (MRLP-EC), with the objectives of minimising material flow cost and layout area. A mixed integer programming formulation is established for MRLP-EC. A hybrid approach combining an improved multi-objective greedy randomised adaptive search procedure (mGRASP) and linear programming (LP) is proposed for the problem. The mGRASP is used to optimise machine sequences to obtain a set of non-dominated machine sequences. A segments-based dominance method is suggested to measure the dominance relationship of any pair of machine sequences. LP is used to optimise extra clearances between adjacent machines (i.e. the exact location of each machine) for each non-dominated machine sequence. The proposed approach is compared against an exact method and two multi-objective heuristics. Experiments show that the approach is effective for MRLP-EC and outperforms comparative approaches.

A hybrid multiobjective GRASP for a multi-row facility layout problem with extra clearances