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This paper develops a fuzzy stochastic multi-objective linear programming model for a multi-level, capacitated lot-sizing problem (ML-CLSP) in a mixed assembly shop. The proposed model aims to minimize the total cost consisting of total variable production cost, inventory cost, backorder cost, and setup cost while maximizing the resource utilization rate simultaneously. To cope with inherent mixed fuzzy stochastic uncertainty associated with input data, e.g., the demand and process-related parameters, they are treated as fuzzy stochastic parameters. We conducted a numerical example from literature to illustrate the efficiency of the proposed method against other ones. To validate the expediency of the proposed ML-CLSP and solution method, a real case study was executed in a furniture company. The results demonstrate the usefulness of the proposed model and its solution approach.