Solving the sustainable supply chain network design problem by the multi-neighborhoods descent traversal algorithm

https://doi.org/10.1016/j.cie.2021.107098Get rights and content

Highlights

  • We study a network design problem taking sustainability explicitly into consideration.

  • We model the problem as a multi-objective MILP optimization model.

  • We develop a search algorithm that solves the problem very efficiently.

  • Our model provides solutions that are environmentally friendly.

Abstract

A multi-period, multi-echelon, multi-product, and multi-modal sustainable supply chain network design problem is considered. The problem is formulated as a multi-objective Mixed-Integer Linear Programming (MILP) model that explicitly considers the environmental footprint and social responsibilities. We introduce the Multi-Neighborhood Descent Traversal Algorithm (MNDTA), which can solve this problem efficiently. The MNDTA begins with a structured initial solution of the model and improves the incumbent solution by sequentially traversing several specifically designed neighborhoods over generations. A lower-bound-based evaluation method is introduced to reduce the computational complexity involved in solving the integer programming problem. Experimental results demonstrate that the proposed MNDTA can provide high-quality solutions that are close to the optimal solutions with a negligibly small (relative) gap and can solve large instances much more quickly than CPLEX can. In addition, the MNDTA outperforms existing solution algorithms. A numerical comparison of the results of the proposed model with those of a model that only considers financial aspects demonstrates that explicitly using our model when designing a supply chain network can substantially reduce the environmental impact and increase social responsibility at a negligible cost increase.

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.

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