Solving the sustainable supply chain network design problem by the multi-neighborhoods descent traversal algorithm
Introduction
Many companies are facing serious sustainability challenges due to pollution, climate change, and a scarcity of natural resources such as fossil fuels (Chen et al., 2014, Chen et al., 2017). In general, sustainability management seeks to balance economic, social, and environmental performance indicators, which is known as the “triple-bottom-line”: (3BL) of sustainability. Traditionally, supply chain network design was primarily driven by measures such as cost (or profit) and service levels. However, recently, the sustainability challenge has conducted companies to incorporate sustainability concerns in their supply chain management. As a result, the field of Sustainable Supply Chain Management (SSCM) is receiving increasing attention from both industry and the research community. Typically, most proposed models are multi-objective models that incorporate the trade-off between economic and environmental performance metrics (Bouchery et al., 2017, Seuring and Muller, 2008). Solving these models by jointly optimizing economic and environmental measures in supply chains is not straightforward due to their complexity. Thus, given the increased demand for efficient solution methods (Gunasekaran and Irani, 2014, Gunasekaran et al., 2014, Gunasekaran et al., 2015), further SSCM research is essential to provide decision support to enterprises seeking to make their supply chains more sustainable and competitive (Bryceson & Smith, 2008).
Fahimnia, Sarkis, and Davarzani (2015) identified more than 1000 published SSCM studies. They found that conceptual and empirical studies have established a sound research foundation and have been the most influential. Fahimnia, Bell, Hensher, and Sarkis (2015) also found few studies have employed Operations Research (OR) models and methods to optimize sustainable supply chain networks. Eskandarpour et al., 2015, Govindan and Cheng, 2015 and Barbosa-Póvoa, Silva, and Carvalho (2018) have also published relevant literature studies. Eskandarpour et al. (2015) reviewed more than 80 relevant papers that focused on supply chain network design. The review covered mathematical models that include economic factors as well as environmental and/or social dimensions. In addition to the traditional cost minimization or profit maximization dimension, Eskandarpour et al. (2015) found that most studies focus only on greenhouse gas indicators to cover the environmental dimension. Moreover, few solution approaches that ensure a trade-off between solution quality and computational time have been developed for large-scale (i.e., real-world) SSCM problems. This scarcity is primarily due to the increased complexity involved in solving multi-objective models that include multiple criteria.
A recent literature review (Barbosa-Póvoa et al., 2018) examines more than 200 papers to identify the OR methods being used. The review identifies five potential research ideas. One of the identified research areas is the objective of this study, i.e., exploring and developing generic solution methods to solve sustainable supply chain models efficiently.
Optimization models become more complex when social and environmental criteria are added to the traditional cost or profit criterion. Considering sustainability criteria in supply chain optimization problems requires the inclusion of many additional variables and constraints, as well as additional objective functions, which makes solving these models efficiently difficult. This study addresses that challenge by presenting an algorithm that can efficiently solve multi-objective optimization models that consider sustainability criteria in the decision-making process.
With regard to the sustainability indicators and criteria, most studies consider carbon dioxide (CO2) emissions, which are primarily generated through production and transportation activities. However, in many production environments, the production of various commodities, such as paper, food, refined petroleum, chemicals, and metals, consumes large amounts of water. The water is usually withdrawn from lakes, rivers, and underground reservoirs, and reducing withdrawals from these sources is crucial for environmental protection. Therefore, in addition to considering CO2 emissions, we also explicitly consider water consumption, which is an important criterion and metric in the SSCM problem. The water footprint is defined as the total amount of water consumed across the entire supply chain process and the importance of the water at each selected location (e.g., region, country) using the water stress indicator determined by the World Resources Institute (2013).
The general sustainable supply chain design problem is already NP-hard. Addressing environmental and social indicators increases the complexity, preventing large-scale instances from being solvable via precise algorithms within acceptable computation time (Validi et al., 2015). To provide a favorable trade-off between solution quality and computational time, we develop the Multi-Neighborhood Descent Traversal Algorithm (MNDTA). The MNDTA uses a multi-neighborhood search structure and, during the search process, neighborhoods are explored in a deterministic order. Several specifically designed neighborhood structures are predefined according to the characteristics of the sustainable supply chain network design (SSCND) problem. Initially, MNDTA provides a structured solution and then improves the incumbent solution by traversing the neighborhoods sequentially over generations. The algorithm terminates when no further improvements can be made or the maximum number of iterations is reached. Finally, an evaluation method that calculates the lower bounds of solutions is introduced to avoid the time-consuming process of solving the integer linear programming (ILP) problem.
We also conduct an extensive numerical study to verify the efficiency and effectiveness of the proposed solution method. The experimental results demonstrate that the proposed algorithm performs very well. Indeed, the computational time for large-scale instances is very short, and the solution quality is very close to the optimum. For all tested instances, the maximum relative gap was less than 4%. The numerical study also reveals that, by addressing environmental and social indicators in the supply chain network design, our approach can improve the environmental impact by up to 14.80% and social responsibility by up to 6.91% at an average cost increase of only 1.32%.
Through this study, we make two important contributions to the literature. First, we develop and test an efficient and effective solution method for the multi-objective SSCND problem. Second, our numerical study demonstrates the added value of including environmental impact and social responsibility factors in supply chain network design problems. The inclusion of such factors can reduce negative environmental impacts and improve social responsibility performance at a negligible cost increase.
The remainder of this paper is organized as follows. In Section 2, we provide an exhaustive review of related work. In Section 3, we present the mixed-integer linear programming (MILP) model formulation of the SSCND problem. In Section 4, we introduce MNDTA, and, in Section 5, we present the experimental results and discuss them. Finally, in Section 6, the main conclusions and suggestions for future work are presented.
Section snippets
Literature review
Sustainable Supply Chain Design (SSCND) refers to the practices, policies, and methods to design supply chains that may be elaborated in the context of taking simultaneously the 3BL indicators into consideration. It involves different multiple objectives of financial, social, and environmental. Several 3BL frameworks exist in the literature classifying these objectives according to the three dimensions. Relevant reviews could be found in Chardine-Baumann and Botta-Genoulaz, 2014, Martins and
Problem formulation
In Section 3.1, we outline the preliminaries and in Section 3.2, we formally define the SSCND problem.
The multi-neighborhood descent traversal algorithm
The SSCND problem can be considered a combination of a binary linear programming problem and an integer linear programming (ILP) problem. The selection of vertexes at each level of the supply chain network is described by a set of binary variables, and the amounts of products and raw materials are represented by a set of integer variables. Due to the complexity of the proposed model, obtaining the optimal solution using exact approaches, such as the CPLEX solver, is very time consuming,
Numerical experiment
In this section, we apply the proposed MNDTA to a large case study of a global manufacturer of electronic components. The production can occur in 100 possible plants (including owned, potential and subcontracted sites) located in Europe and Asia. The supply chain network comprises 350 suppliers and 350 customers globally. We conduct several numerical experiments to evaluate the performance of the proposed MNDTA. First, a set of instances of different scales is generated in Section 5.1. Then, in
Conclusions and future work
Since many firms are facing growing sustainability issues in their SCND, the need for an efficient and effective approach is becoming increasingly urgent. This study addresses that need by introducing an MILP model that considers the three pillars of sustainability (economic, environmental, and social) to optimize the design of a multi-echelon, multi-product, multi-modal SSCND problem. Since traditional methods are not effective in solving large instances of the SSCND, we develop the MNDTA that
CRediT authorship contribution statement
Yuhan Guo: Conceptualization, Methodology, Writing - original draft, Supervision, Formal analysis, Resources, Project administration. Junyu Yu: Investigation, Visualization, Software. Youssef Boulaksil: Conceptualization, Validation, Writing - review & editing, Project administration. Hamid Allaoui: Conceptualization, Writing - review & editing, Resources. Fangxia Hu: Data curation, Validation, Software.
References (79)
- et al.
Sustainable agro-food supply chain design using two-stage hybrid multi-objective decision-making approach
Computers & Operations Research
(2018) - et al.
Decision support for collaboration planning in sustainable supply chains
Journal of Cleaner Production
(2019) - et al.
A new model for designing sustainable supply chain networks and its application to a global manufacturer
Journal of Cleaner Production
(2017) - et al.
Optimisation of transportation service network using K-node large neighbourhood search
Computers & Operations Research
(2018) - et al.
Closing loops in agricultural supply chains using multi-objective optimization: A case study of an industrial mushroom supply chain
International Journal of Production Economics
(2017) - et al.
Opportunities and challenges in sustainable supply chain: An operations research perspective
European Journal of Operational Research
(2018) - et al.
Quantitative models for sustainable supply chain management: Developments and directions
European Journal of Operational Research
(2014) - et al.
A multi-objective optimization model for the design of an effective decarbonized supply chain in mining
International Journal of Production Economics
(2017) - et al.
Multi-objective optimization of a nearly zero-energy building based on thermal and visual discomfort minimization using a non-dominated sorting genetic algorithm (NSGA-II)
Energy and Buildings
(2015) - et al.
A framework for sustainable performance assessment of supply chain management practices
Computers & Industrial Engineering
(2014)
Manufacturing facility location and sustainability: A literature review and research agenda
International Journal of Production Economics
Supply chain collaboration for sustainability: A literature review and future research agenda
International Journal of Production Economics
An integrated supply chain problem with environmental considerations
International Journal of Production Economics
Sustainable supply chain network design: An optimization-oriented review
Omega
Green supply chain management: A review and bibliometric analysis
International Journal of Production Economics
Supply chain design for efficient and effective blood supply in disasters
International Journal of Production Economics
Sustainable supply chain management: Advances in operations research perspective
Computers & Operations Research
Green supply chain collaboration and incentives: Current trends and future directions
Transportation Research Part E
Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax
International Journal of Production Economics
An integrated green supplier selection approach with analytic network process and improved Grey relational analysis
International Journal of Production Economics
A two-stage supply chain problem with fixed costs: An ant colony optimization approach
International Journal of Production Economics
Multi-objective Green Supply Chain Optimization with a New Hybrid Memetic Algorithm Using the Taguchi Method
Scientia Iranica
Closed-loop supply chain network design under uncertain quality status: Case of durable products
International Journal of Production Economics
Closed loop supply chain networks: Designs for energy and time value efficiency
International Journal of Production Economics
A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling
Applied Mathematical Modelling
The design of sustainable logistics network under uncertainty
International Journal of Production Economics
Supply chain models with greenhouse gases emissions, energy usage, imperfect process under different coordination decisions
International Journal of Production Economics
Carbon footprint and responsiveness trade-offs in supply chain network design
International Journal of Production Economics
A novel network data envelopment analysis model for evaluating green supply chain management
International Journal of Production Economics
Investigating structure of a two-echelon closed-loop supply chain using social work donation as a Corporate Social Responsibility practice
International Journal of Production Economics
The fuzzy multi-objective distribution planner for a green meat supply chain
International Journal of Production Economics
An accelerated Benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain
Transportation Research Part E: Logistics and Transportation Review
A conceptual framework for measuring sustainability performance of supply chains
Journal of Cleaner Production
A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method
Journal of Cleaner Production
An optimization model for reverse logistics network under stochastic environment by using genetic algorithm
Journal of Manufacturing Systems
From a literature review to a conceptual framework for sustainable supply chain management
Journal of Cleaner Production
A proactive model in sustainable food supply chain: Insight from a case study
International Journal of Production Economics
Supplier selection using fuzzy ahp and fuzzy multi-objective linear programming for developing low carbon supply chain
Expert Systems with Applications
Green supply chain network optimization and the trade-off between environmental and economic objectives
International Journal of Production Economics
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2022, Cleaner Logistics and Supply ChainCitation Excerpt :Mohammed et al., (2021) and Ortiz-Barrios et al., (2020) suggested that the supply chain should include a full range of purchasing, production, marketing, packaging, and logistics activities from a sustainable perspective. Various theories and evolving practices are suggested by various researchers (Carvalho et al., 2017; Dey et al., 2019; Digalwar et al., 2020; Guo et al., 2021; Lucía Sabogal-De La Pava et al., 2021; Vafaeenezhad et al., 2019) for restructuring the traditional management philosophies by the integration of lean, agile, resilient, and green supply chain for sustainable development in this highly competitive environment. It has been noticed that purchasing managers consider conventional criteria for supplier selection (Lamba and Singh, 2019).