A bi-objective MIP model for facility layout problem in uncertain environment

Facility layout problem (FLP) is one of the classical and important problems in real-world problems in the field of industrial engineering where efficiency and effectiveness are very important factors. To have an effective and practical layout, the deterministic assumptions of data should be changed. In this study, it is assumed that we have dynamic and uncertain values for departments’ dimensions. Accordingly, each dimension changes in a predetermined interval. Due to this assumption, two new parameters are introduced which are called length and width deviation coefficients. According to these parameters, a definition for layout in uncertain environment is presented and a mixed integer programming (MIP) model is developed. Moreover, two new objective functions are presented and their lower and upper bounds are calculated with four different approaches. It is worth noting that one of the objective functions is used to minimize the total areas, which is an appropriate criterion to appraise layouts in uncertain conditions. Finally, we solve some benchmarks in the literature to test the proposed model and, based on their results, present a sensitivity analysis.

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