A Unified Optimization Model with Proportional Fairness and Robustness of Fuzzy Multi-Objective Aggregate Production Planning in Supply Chain under Uncertain Environments

Abstract

This study aims to provide Decision Makers (DMs) with a framework for achieving long-term development of Aggregate Production Planning (APP) in a Supply Chain (SC). The contribution of this study is to consider both Proportional Fairness (PF) and robustness in the APP optimization processes, recognizing that overlooking fairness among the multi-objectives in APP may result in inequitable considerations due to different priorities. Neglecting robustness may yield unreliable and non-resilient outcomes in APP, particularly in uncertain situations where uncertain and vague information poses a challenge. To address these concerns, a unified proportional fairness and robustness optimization model is proposed by applying the principles of PF and Robust Chance-Constrained Programming (RCCP) to the conventional weightless objective optimization approach. The effectiveness of this approach is demonstrated through a case study of an APP problem in a SC with the objectives of minimizing total costs, minimizing fluctuations in workforce levels, and maximizing total values of purchasing under uncertain environments. The comparative analysis indicates that the outcome derived from the proposed approach outperforms the results of both traditional weightless and fairness approaches, particularly in enhancing fairness and robustness in the APP.