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In this paper, value stream mapping (VSM) is integrated with fuzzy set theory to incorporate variability and uncertainty in the lean production system. VSM is one of the primary analytical tools for identifying waste and optimizing a production line. However, the standard VSM fails to consider the variability in manufacturing environments, which is, in fact, one of the root causes of waste. Therefore, this article proposes fuzzy VSM to overcome this weakness. Two alternative forms of fuzzy numbers, triangular fuzzy numbers (TFNs) and normal fuzzy numbers (NFNs), are applied, respectively, to depict time intervals, inventories, and other operating variables in VSM. An industrial case for assessing the validity of the proposed approaches is presented. Both approaches make it possible to incorporate and analyze variability in VSM and can be easily applied to industrial cases, as they only require basic algebraic operations. The obtained results are compared and the choice between TFNs and NFNs is discussed accordingly. A triangular fuzzy VSM tends to overestimate the variability of the process in complex production environment with complicated operational processes. However, it permits a more accurate description of variation in the environment where the optimistic and pessimistic values have very different variations from the core.

Incorporating Variability in Lean Manufacturing: A Fuzzy Value Stream Mapping Approach