Sustainable Production Planning Under Uncertainty: A Z-Number-Based Multi-Objective Optimization Approach for Furniture Manufacturing

Abstract

Sustainable production planning requires the simultaneous optimization of economic, environmental, and social objectives under conditions where key parameters are not only imprecise but also variably reliable. This study proposes a Z-number-based multi-objective linear programming (Z-MOLP) framework that addresses this dual uncertainty. The framework incorporates eight conflicting objectives-profit maximization alongside minimization of particle board consumption, energy use, carbon emissions, production time, water usage, metal usage, and edge-band consumption-spanning economic, environmental, and social sustainability dimensions. Objective weights are determined through a Z-number-based reciprocal pairwise comparison procedure, and optimal production plans are obtained via weighted aggregation and integer linear programming. The framework is validated using real monthly production data from three furniture manufacturing enterprises in Azerbaijan. A comparative analysis between the full eight-objective model and a reduced six-objective model-excluding carbon emissions and production time-reveals that sustainability-specific objectives consistently constrain production volumes and reduce profit (+17.45%, +4.67%, and +0.57% profit increases when excluded for each of the three enterprises) but that these economic gains are driven entirely by production-scale expansion rather than efficiency improvement, with resource consumption rising in near-exact proportion. These findings confirm the existence of a genuine trade-off between economic performance and sustainability in developing-economy manufacturing contexts and demonstrate that Z-number representations add practical value by propagating data reliability through both the optimization and the output-reporting stages of production planning.