# Optimizing Green Supplier Selection and Order Allocation: A Fuzzy DNAP-Fuzzy TOPSIS-Bi Objective Mathematical Model Approach with Harmony Search Algorithm

Document Type : Research Paper

Authors

1 MSc., Department of Industrial Engineering, Faculty of Engineering, Khatam University, Tehran, Iran.

2 Assistant Prof., Department of Industrial Engineering, Faculty of Engineering, Khatam University, Tehran, Iran.

Abstract

Objective
In the realm of green supply chain management, the pivotal responsibilities of companies involve supplier selection and order allocation. These tasks were treated as independent challenges in prior studies. This issue holds significant importance within the context of green supply chain management, demanding the simultaneous consideration of both quantitative and qualitative criteria. These criteria, at times conflicting, necessitate an in-depth analysis of trade-offs. There is a pressing need for a comprehensive framework capable of concurrently addressing both aspects. In addition to accommodating green criteria, such a framework should enable the determination of order quantities allocated to suppliers.

Methods
The utilized approach in the present study included Fuzzy DNP, Fuzzy TOPSIS, and a Bi-objective optimization model. In the first stage, the criteria weights, encompassing both traditional and green criteria, were determined using the fuzzy DNP. Subsequently, the suppliers' scores were computed using the fuzzy TOPSIS. In the second stage, a non-linear bi-objective model was formulated, aiming to minimize the total cost and maximize the purchased value. The first objective function comprised the purchase price, suppliers' variable costs, ordering and setup costs, as well as buyer's and suppliers' inventory holding costs. Additionally, the second objective function ensured a higher allocation of orders to suppliers who had achieved a superior score in the supplier evaluation process. The model's constraints encompassed the suppliers' capacity, buyer's demand, and constraints associated with the suppliers' discounts. Acknowledging the bi-objective nature of the mathematical model, the Global Criterion method was employed to transform the bi-objective problem into a single-objective one. According to this method, the relative deviations of the objectives from their corresponding single-objective optimal values were minimized. Furthermore, due to the non-linearity of the mathematical model, a harmony search algorithm was developed for the problem, and a repair algorithm was proposed to handle constraints in the problem.

Results
The previous studies and expert opinions were utilized to identify the criteria, encompassing both traditional and green criteria. The results of fuzzy DANP indicated that the supplier's credit holds the utmost importance, followed by quality, green purchasing, green design, green transportation, green production, on-time delivery, and distance. Furthermore, all criteria exhibit an effect on the supplier's credit. Subsequently, six suppliers underwent evaluation based on the criteria using fuzzy TOPSIS, and their final scores were employed as the suppliers' weights in the second objective function of the mathematical model. To validate the proposed approach, a case study with real data in the field of the medical equipment supply chain was examined, and the optimal solution to the problem was presented. Subsequently, by adjusting the weights of the objective functions in the single-objective problem, the Pareto solutions were identified. The proposed approach facilitates the optimal allocation to the suppliers by considering the green criteria.

Conclusion
The results showed that a decision maker can choose the best solution according to the Pareto solutions in such a way that there is a correct trade-off between the supply chain costs and purchased value.

Keywords

Main Subjects

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