Multi-Objective Optimization for Integrated Production and Distribution Planning Using Non-Linear Fuzzy Membership Functions

Efficient resource allocation for production and cost-effective dispatch under uncertainty is crucial for a streamlined supply chain. Traditional segregated and deterministic production–distribution models often fall short in providing robust solutions due to dynamic market demands, supplier reliability, and resource availability. In this context, this paper focuses on integrating production and distribution problems while managing conflicting goals and addressing uncertainties. A fuzzy multi-objective linear programming (FMOLP) model is developed to simultaneously minimize the total integrated production cost and delivery time amid uncertainties. This article aims to shed light on the practical implications and benefits of adopting integrated production and distribution models. Here, triangular fuzzy numbers and the concept of the minimum accepted level method are employed to formulate the problem. The minimum operator and weighted additive operator methods are employed to aggregate all fuzzy sets with non-linear exponential membership functions for a better representation of the FMOLP problem. A scenario-based analytical hierarchy process (AHP) is devised, integrating expert knowledge and experience to rank multiple objectives, thereby enhancing realism for the respective case. The experimental results reveal that the proposed integration increases the satisfaction level of decision makers from 0.684 to 0.747. Furthermore, the higher degree of closeness of the proposed model compared to the employed approach validates the final results. Impacts and interaction analysis also demonstrate the necessity of an integrated approach for production and distribution planning under uncertainty.