Title: A multi-objective robustness methodology for a closed cycle supply chain design considering volume discount and economic benefits by reducing CO₂ emissions of transportation modes

Authors: Nathalia Duque-Araujo; Luis Eduardo Muñoz-Pabón; John Willmer Escobar

Addresses: School of Industrial Engineering, Universidad del Valle, Cali, Cali 760001, Valle del Cauca, Colombia ' School of Industrial Engineering, Universidad del Valle, Cali, Cali 760001, Valle del Cauca, Colombia ' Department of Accounting and Finance, Universidad del Valle, Cali, Cali 760001, Valle del Cauca, Colombia

Abstract: This paper proposes a new methodology for designing a closed-loop chain based on multiple objectives and uncertainties in the parameters. First, a mixed-integer mathematical model for a closed supply chain is proposed considering volume discounts and economic benefits from CO₂ emissions reduction. The robustness measurement is then performed using a method adapted from electrical systems called features, perturbation, impact, and analysis (FePIA). The proposed multi-objective methodology considers three objectives such as minimising the cost of the environmental impact associated with CO₂ emissions (EC), maximising the net present value (NPV) of the supply chain investment, and minimising its financial risk (FR). The objectives are integrated using the weighted average sum methodology. The efficiency of the proposed methodology has been tested with real information from a multinational company operating in Colombia. The results show the effectiveness of the proposed methodology.

Keywords: closed supply chain; environmental impact; net present value; NPV; financial risk; weighted average sum; robustness; FePIA.

DOI: 10.1504/IJSTL.2025.146581

International Journal of Shipping and Transport Logistics, 2025 Vol.20 No.2, pp.190 - 223

Received: 09 May 2023
Accepted: 12 Sep 2023
Published online: 05 Jun 2025 *

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