Bi-Objective Production–Distribution Planning for Paper Manufacturing: A Credibility-Based Expected Value Approach

The paper manufacturing industry faces increasing challenges in balancing operational costs with service quality under uncertain market conditions. This research presents a bi-objective credibility-based expected value model for integrated production–distribution planning that simultaneously minimizes total costs and maximizes service-level performance. The model considers multiple paper grades, production facilities, warehouses, and customer zones while handling demand uncertainty through credibility theory. Three additional constraints are introduced: service time limitations, capacity expansion decisions, and quality assurance requirements. The Torabi–Hassini (TH) method is employed to solve the bi-objective optimization problem effectively. Computational experiments demonstrate the model’s capability to provide balanced trade-off solutions between cost efficiency and service quality, achieving service-level improvements of 8–13% with cost increases of 5–9% compared to cost-only optimization, and cost reductions of 10–15% compared to service-only optimization. The results show that the credibility-based expected value approach provides robust and practical solutions for paper manufacturing supply chain optimization.