Integrating Triple-Bottom-Line Goals and Uncertainty in Aggregate Production Planning Using Fuzzy Goal Programming

Abstract

This study develops a Sustainable Aggregate Production Planning (SAPP) model based on Fuzzy Goal Programming (FGP) that integrates economic, environmental, and social objectives under uncertainty. Conventional aggregate production planning primarily focuses on cost minimization, often resulting in excessive overtime, high emissions, and workforce instability. To address these limitations, the proposed model simultaneously considers total cost, carbon emissions, energy consumption, waste generation, workforce stability, and worker satisfaction within a unified fuzzy optimization framework. From a mathematical perspective, the main contribution of this study lies in the explicit formulation of a max–min FGP structure using aspiration-based linear membership functions for all sustainability objectives, enabling a balanced compromise solution without relying on deviation-variable-based goal programming commonly adopted in existing SAPP models. The resulting formulation is a linear mixed-integer optimization model that preserves tractability while accommodating conflicting sustainability goals. Numerical experiments are conducted using illustrative demand and operational data adapted from a reference study, solely for mathematical calibration and validation of the proposed model rather than empirical inference. The results indicate a global satisfaction level of λ = 0.67, representing a balanced max–min compromise among economic, environmental, and social objectives. Compared to the baseline scenario, the optimized plan achieves notable improvements in cost efficiency and waste reduction while keeping emissions, energy consumption, and workforce-related indicators within predefined fuzzy tolerance limits. Overall, the proposed SAPP–FGP model provides a transparent and flexible decision-support framework for sustainability-oriented production planning, offering clear insights into trade-offs among competing objectives and contributing to the applied mathematical literature on multi-objective production planning under uncertainty.