Optimization of facility layout design with ambiguity by an efficient fuzzy multivariate approach

This paper presents an integrated fuzzy simulation-fuzzy data envelopment analysis (FDEA)-analytic hierarchy process (AHP) approach to deal with a flow shop facility layout design (FSFLD) problem with ambiguous inputs and outputs. Ambiguous inputs and outputs are defined as noncrisp operational, qualitative, and dependent indicators. At first, feasible layout alternatives are generated by a software package. Then, fuzzy AHP is used for weighting noncrisp qualitative data (maintainability, accessibility, and flexibility). Fuzzy simulation is then used to incorporate the ambiguity associated with processing times in the flow shop by considering all generated layout alternatives with uncertain inputs. The outputs of fuzzy simulation or noncrisp operational indicators are average waiting time-in queue, average time-in system, and average machine utilization. Finally, FDEA is used for finding the optimum layout alternative among all feasible generated alternatives with respect to operational, qualitative, and layout-dependent indicators (distance, adjacency, and shape ratio). The integrated approach of this study is more precise and efficient than previous studies with ambiguous inputs. It also provides a comprehensive analysis on the FSFLD problems by using operational and subjective and fuzzy indicators. The results have been verified and validated by DEA, principal component analysis, and numerical taxonomy. The unique features of this study are the ability of dealing with multiple noncrisp inputs and outputs. It also uses fuzzy mathematical programming for optimum layout alternatives. Moreover, it is a practical tool and may be applied in real cases by considering uncertain and ambiguous aspects of the manufacturing process within FSFLD problems.