Sustainable Inventory Management in Supply Chains: Trends and Further Research

Abstract

This article presents an overview of the models applied to sustainable inventory management in supply chains and a roadmap for new research. It aims to address the lack of understanding of how sustainability is being incorporated into quantitative inventory management models in the supply chain context. The study is based on a classification of the reviewed literature according to the following criteria: supply chain structure, environmental approach, problem type, modeling, and solution approach. As a result, 36 articles were analyzed and classified. The main findings show that studies that incorporate social sustainability into inventory management along supply chains are lacking, while environmental studies are a growing research area. Uncertainty issues also need to be incorporated into sustainable inventory management models. Another important result of this study is the definition of a roadmap with trends and future research guidelines. The identified future research guidelines include incorporating decisions that can help to improve economic, environmental, and social sustainability. Thus, future studies should focus on both following quantitative models that incorporate inventory decisions integrally with transportation and location decisions, and more complex models, and employing new algorithms and heuristics to solve them.

1. Introduction

The economic growth process based on process technology began after the first industrial revolution in the second half of the 18th century. The industrial revolution unleashed not only an economic, scientific, and technical boom but also an intensive, extensive and irrational use of natural resources to search for accelerated economic growth models that occurred when it began. Environmental aspects are very important for reducing the global warming effect associated with increasing CO₂ emission rates as a result of globalized industrialization, goods storage, and transportation. According to Arikan et al. [1], the storage and transport of goods are considered the most important causes of environmental hazards in the logistics chain and are the main reasons for CO₂ emissions.

Sustainable inventory management (SIM) relates to decisions on inventory, warehousing, and material handling by focusing on reducing environmental and social impacts without affecting profitability [2]. Incorporating location and transportation issues into modeling could lead to sustainable supply chains (SCs). Recent research has highlighted the need to include factors other than traditional inventory models to design sustainable inventory systems by integrating the factors affecting the environmental impact into the traditional economic order quantity (EOQ) model [3]. It is crucial to develop a SIM model that takes into account income increase and waste prevention and reduces energy costs [4]. Decisions on lead times, replenishment quantities, and storage facilities influence emissions and costs [5].

Very few review articles have focused on the collection and analysis of inventory models that include sustainability, which is the main motivation of this paper. Pattnaik et al. [6] present a systematic literature review about integrating sustainability issues into inventory management models, specifically those topics that consider environmental criteria such as greenhouse gas (GHG) emissions, ecological quality controls, unsold inventory, and fixed carbon costs. Hence these authors mainly contribute decision-makers to identify the environmental and social factors that could be included in inventory models to encourage sustainable development. A comprehensive literature review of studies on inventory routing problems that incorporate sustainability aspects is provided by Malladi and Sowlati [7]. Chan et al. [8] classify the mathematical problems that deal with the management of sustainable manufacturing systems by classifying selected articles into three categories according to the main manufacturing system elements: production planning and control; inventory management and control; and manufacturing network design. Finally, a more extensive review that focuses on green SC quantitative models for SIM is found in Becerra et al. [9]. They identify and classify specific criteria related to modeling sustainable inventory problems in terms of purpose, application context, SC structure, decision level, shared information, inventory policies, inventory modeling, sustainability, circular economy and green modeling approaches, modeling approach, solution approaches, and software tools. Yadav et al. [10] identify the research gaps and advantages of waste management, preservation technology, and setup cost reduction from an SC perspective with a smart manufacturing system for products with cross-price elasticity of demand.

In addition, the present study attempts to bridge the research gap of how sustainability should be integrated into quantitative SC inventory management models. Therefore, this article contributes to identifying research trends related to quantitative SIM models in SCs and, by doing so, to proposing a roadmap for future studies. These trends and further research works are based on the following classification criteria: environmental approach, problem type, SC structure, model approach, and solution approach. The literature review by [6] focuses on SIM models approached by quantitative methods (the modeling and solution approach) exclusively and in a supply-chain context by also considering the inventory problem, location, and routing problems.

Therefore, the aim of this study is twofold: (1) to offer an overview of the literature on SIM in SCs from an environmental perspective by identifying the type of problem, SC structure, model, and solution approach; (2) to propose a roadmap for future research lines based on the trends identified in this work according to the classification criteria. The posed research question is: what is the roadmap of trends and further research lines for SIM models in an SC?

The remainder of the paper is structured as follows. Section 2 describes the review methodology. Section 3 offers an overview of the literature on SIM in SCs. Section 4 presents the discussion and proposes a roadmap for further research. Finally, Section 5 includes the conclusions and further research from the study.

2. Review Methodology

In order to fulfill this overview objective, relevant literature was compiled after considering the scientific articles published in the journals indexed in Scopus and Web of Science (WoS). In order to answer the research question, the following keywords were used in combination: supply chain, supply network, sustainable, green, circular economy, environment, social, inventory management, quantitative method, mathematical programming, optimization, analytic models, simulation, and artificial intelligence. No time window is defined. According to these search criteria, WoS and Scopus, respectively, indicated 142 and 183 related scientific articles published from 2004 to 2021. These articles were selected based mainly on the defined exclusion criteria: papers not related to the principal research field, i.e., that do not include environmental aspects, case studies on specific sectors not related to SCs, nonquantitative models, among others; duplicated studies; conference reviews; articles that neither present potential future lines nor develop a model (see

Table 1. Search methodology and paper selection process.

Keyword Used	(Supply Chain or Supply Network) and (Sustainab* or Green or Circular Economy or Environment or Social) and (Inventory Management) and (Quantitative Method or Mathematical Programming or Optimization or Analytic Models or Simulation or Artificial Intelligence)
Scopus database	183 articles
Wos database	142 articles
Total papers in the two databases excluding duplication, conference reviews, not considering environmental aspects, case studies on specific sectors not related to SCs or nonquantitative models	47 articles
Articles that present potential future lines or develop a quantitative model	36 articles

). The remaining 36 articles were analyzed and classified to learn trends and future research areas. The followed review methodology is found in Figure 1.

Of the 36 selected papers, 25% of the articles about SIM in SCs are published in three journals: International Journal of Production Economics, Computer Aided Chemical Engineering, and Journal of Cleaner Production. Appendix A.1. Distribution of Reviewed Publications per Journal presents the distribution of the reviewed publications per journal.

The number of publications per year (see Figure 2) reveals that researchers have recently paid attention to this research topic. Most of the research (86.11%) has been conducted in the last 10 years, and over half the research papers (61.11%) were published in the past 5 years.

3. Literature Review

The literature review focuses mostly on the main objective of the reviewed articles, and on the proposals of future research lines, by distinguishing the three sustainability aspects: economic (EC), environmental (EN), and social (S). The research methodologies addressed in the reviewed papers are classified according to (Dangayach and Deshmukh [11] and Malhotra and Grover [12]): (i) conceptual, basic or fundamental concepts; (ii) descriptive, an explanation or description and questions related to the addressed problem; (iii) empirical, where the study data are taken from existing databases, and from literature reviews, case studies and taxonomy or typology approaches; (iv) cross-sectional exploratory, with surveys at a given time; (v) longitudinal exploratory, also based on surveys in which data are collected at two different time points, or more, in the same organizations. Here, empirical proposals stand out; that is, those referring to mathematical programming and simulation models. Very few studies include a statistical analysis by exploratory cross-sectional research, and only two studies select the proposed conceptual research, specifically by literature reviews. The details of the findings of this literature review are provided in Appendix A.2. Sustainability Aspects, Research Methodology, Objectives and Proposed Further Research per Article.

Table 2 presents an overview of how SIM in SCs has been studied. It includes the following classification criteria: SC structure: D (dyadic), SE (serial), C (convergent), DV (divergent), CJ (cojoined), N (network), CL (closed-loop), RL (reverse logistic); environmental approach: R1 (recycling), R2 (reusing), R3 (remanufacturing), R4 (renewable), R5 (repair), R6 (reduce); problem type: L (location), I (inventory), R (routing); model approach: MP (mathematical programming), S (simulation), R (regression), C (conceptual); solution approach: E (exact), H (heuristic), M (metaheuristic), ST (statistical) and SS (simulation software).

The SC structures proposed by [13] are extended in this work to include reverse logistics and closed-loop approaches because both correspond to 30% of the reviewed articles. These structures include product returns, which imply reusing, repairing, reconditioning, remanufacturing, and recycling materials, an efficacious reverse logistics network design that offers not only environmental benefits but also economic benefits in terms of reduced raw material acquisition, inventory management, and waste disposal [14].

When developing inventory models to consider sustainability by incorporating its three pillars, the S aspect appears to be poorly studied because only nine of the reviewed articles incorporate it. For example, Battini et al. [3] apply “external costs” to jointly include the EN and S dimensions in delivery operations, warehousing, and waste disposal. Nativi et al. [15] propose a model that involves an S approach for patients to gain equitable access to essential medicines. Ivanov [16] and Ganev et al. [17] agree about using the offer of jobs in the local economy to estimate the S impact. Dekker et al. [18] developed a simulation model to study the effect of changing order size on the selected performance measures by addressing the S issue; for instance, it addressed the service level, amount of wasted food, and a product’s average remaining life. By also taking social welfare as an objective in sustainability [19], Halat et al. [20] specifically develop a model to guarantee access to food and healthcare.

Table 2. Overview of SIM in SCs.

Reference	SC Structure	Environmental Approach	Problem Type	Model Approach	Solution Approach
Arikan et al. [1]	SE	R6	I	S	SS
Battini et al. [3]	N	R6	I	EOQ	H
Chen et al. [4]	CJ	R6	I	MP	M
Fichtinger et al. [5]	U	R6	I	S	SS
Ali et al. [14]	RL	R1, R2, R3	I	MP	E
Nativi and Lee [15]	RL	R1	I	R	ST
Ivanov [16]	N	R6	L	MP	E
Ganev et al. [17]	N	R4	L-I-R	MP	E
Dekker et al. [18]	D	R6	I-R	S-C	SS
Tsolakis and Srai [19]	U	R4	I	S	SS
Halat and Hafezalkotob [20]	CJ	R6	I	MP	E
Al-Haidous et al. [21]	N	R6	I-R	MP	M
Žic and Žic [22]	SE	R6	I	S	SS
Amer et al. [23]	N	R6	I-R	S	SS
Mohammadnazari and Ghannadpour [24]	C	R6	I-R	MP	E
Zhang et al. [25]	C	R6	L-I-R	MP	E
Sun et al. [26]	N	R6	L-I-R	MP	E
Ching et al. [27]	D	R6	I	S	SS
Paam et al. [28]	D	R6	I	MP	E
Wang et al. [29]	CJ	R6	I-R	MP	M
Nikolopoulou and Ierapetritou [30]	U	R1, R2, R3, R4, R6	L-I-R	MP-C	E-H
Bostel et al. [31]	RL	R1, R2, R3, R5	L-I-R	MP-S	E-H-SS
Kuo [32]	CL	R3	I	S	SS
Calmon and Graves [33]	CL	R3, R5	I	MP-S	M
Guo et al. [34]	CL	R2, R3	L-I	MP	M
Tighazoui et al. [35]	RL	R3	I-R	S	M
Ross et al. [36]	CL	R2	I	S-R	ST
Yang et al. [37]	CL	R2	I	MP	M
Zhang et al. [38]	C	R4	L-I-R	S	SS
Yılmaz Balaman and Selim [39]	CJ	R4	L-I-R	MP	E
Pati et al. [40]	RL	R1	I-R	MP	E
Ahmadini et al. [41]	SE	R6	I	MP	E-H
Rout et al. [42]	D	R6	I-R	MP	H
Tavana et al. [43]	N	R6	L-I-R	MP	E
Ugarte et al. [44]	D	R6	I-R	S	SS
Takeda et al. [45]	D	R6	I	S	SS

Table 2. Overview of SIM in SCs.

Reference	SC Structure	Environmental Approach	Problem Type	Model Approach	Solution Approach
Arikan et al. [1]	SE	R6	I	S	SS
Battini et al. [3]	N	R6	I	EOQ	H
Chen et al. [4]	CJ	R6	I	MP	M
Fichtinger et al. [5]	U	R6	I	S	SS
Ali et al. [14]	RL	R1, R2, R3	I	MP	E
Nativi and Lee [15]	RL	R1	I	R	ST
Ivanov [16]	N	R6	L	MP	E
Ganev et al. [17]	N	R4	L-I-R	MP	E
Dekker et al. [18]	D	R6	I-R	S-C	SS
Tsolakis and Srai [19]	U	R4	I	S	SS
Halat and Hafezalkotob [20]	CJ	R6	I	MP	E
Al-Haidous et al. [21]	N	R6	I-R	MP	M
Žic and Žic [22]	SE	R6	I	S	SS
Amer et al. [23]	N	R6	I-R	S	SS
Mohammadnazari and Ghannadpour [24]	C	R6	I-R	MP	E
Zhang et al. [25]	C	R6	L-I-R	MP	E
Sun et al. [26]	N	R6	L-I-R	MP	E
Ching et al. [27]	D	R6	I	S	SS
Paam et al. [28]	D	R6	I	MP	E
Wang et al. [29]	CJ	R6	I-R	MP	M
Nikolopoulou and Ierapetritou [30]	U	R1, R2, R3, R4, R6	L-I-R	MP-C	E-H
Bostel et al. [31]	RL	R1, R2, R3, R5	L-I-R	MP-S	E-H-SS
Kuo [32]	CL	R3	I	S	SS
Calmon and Graves [33]	CL	R3, R5	I	MP-S	M
Guo et al. [34]	CL	R2, R3	L-I	MP	M
Tighazoui et al. [35]	RL	R3	I-R	S	M
Ross et al. [36]	CL	R2	I	S-R	ST
Yang et al. [37]	CL	R2	I	MP	M
Zhang et al. [38]	C	R4	L-I-R	S	SS
Yılmaz Balaman and Selim [39]	CJ	R4	L-I-R	MP	E
Pati et al. [40]	RL	R1	I-R	MP	E
Ahmadini et al. [41]	SE	R6	I	MP	E-H
Rout et al. [42]	D	R6	I-R	MP	H
Tavana et al. [43]	N	R6	L-I-R	MP	E
Ugarte et al. [44]	D	R6	I-R	S	SS
Takeda et al. [45]	D	R6	I	S	SS

Environmental approaches have been widely studied. Here from the circular economy perspective, extending the options for value retention from the well-known reduce, reuse, and recycle policies to the 10R policies is suggested [46] by including the criteria proposed in this article. The most studied concept is “reduce” (R6) because it appears in 22 of the reviewed articles (see Figure 3) and is described to minimize GHG emissions [1,5,18,20,21,22,23,24,42,43,44,47] and to reduce waste production rather than disposing of created waste [3,4,25,26,27,28,29,30,45]. Ahmadini et al. [41] incorporate both GHG emissions and waste disposal minimization. Another studied environmental aspect is “remanufacture”, which involves products at the end of their life or them needing maintenance and being returned. Parts or components are refurbished to be used as new products [14,30,31,32,33,34,35]. The “Reuse” (R2) aspect is less studied than the others. However, it comes over as a relevant aspect because it is often studied along with remanufacturing processes by considering return items that can be directly reused without them having to undergo major operations [14,30,31,34,36,37].

The reviewed literature identified three problem types; location, inventory, and routing. They appear as individual problems or as combinations of two or three. Only one article includes the location problem in a review, that of Ivanov [16], who determines the optimum location of a bioethanol plant. In Guo et al. [24], an optimal solution to the location-inventory problem is developed to define the location and number of orders placed annually in a CL SC by considering sales on the primary and secondary markets for new and used products, respectively. Only one article presents a model that solves an inventory-production problem; Ahmadini et al. [41] consider that the production process contributes immensely to global warming. Eight articles solve the location-inventory-routing problem. This problem type addresses the relevance of coordinating location decisions, inventory management, and vehicle routing, such as selecting the distribution center’s location, allocating customers for distribution, transportation routing of vehicles, and inventory strategy formulation [17,25,26,30,31,38,39,43].

Of all the available model approaches, mathematical programming models are the most widely used to solve the aforementioned problems (66.67%). Figure 4 particularly depicts: mixed-integer linear programming with six single objective cases [16,17,20,24,26,28]; multi-objective models [21,42]; multi-objective with fuzzy goal programming [39,43]; fuzzy multi-objective linear programming [14]; a multi-objective fractional programming model by Ahmadini et al. [41]; linear programming with one case [40]; sustainable EOQ developed by Battini et al. [3]; a constrained programming model overcome by Zhang et al. [25]; a stochastic optimization problem [33]; a Markov decision process [37]; mixed-integer nonlinear programming [34]; two integer programming models [4,29]. Simulation models are also widespread (33.33%). Bostel et al. [31] and Nikolopoulou et al. [30] examine both simulation and mathematical programming models. Simulation models offer two main approaches: discrete-event simulation [1,5,18,22,23,32,35,36,38,44,45] and system dynamics models [19,27]. Dekker et al. [18] and Nikolopoulou and Ierapetritou [30] apply a conceptual model to supplement their studies. Two regression models appear: one by Ross et al. [36] that describes a hybrid simulation-regression model and a regression model for the insight generation of managerial decisions by [15].

Solution approaches are closely related to the modeling approach. Thus, mathematical programming problems are solved by exact methods (58.33%), heuristics (16.67%), and metaheuristics (25%). Otherwise, simulation models are modeled and solved mostly by simulation software (91.67%). Tighazoui et al. [35] use metaheuristics to overcome their simulation problem. Ross et al. [36] and Nativi and Lee [15] apply a statistical approach to develop their multilinear regression models.

Finally, regarding the distribution of the articles reviewed in the different industrial sectors, 25% do not define a specific sector, but 22% focus on consumer goods, 14% on the energy sector, 8% on transport, and 8% on electrical and electronic devices. The rest are distributed in the different sectors, as shown in more detail in Figure 5.

4. Discussion

Researchers show an interest in these designs thanks to their contributions to economic, social, and sustainable competitiveness, as indicated by [19]. The SC analysis can be reinforced in a closed network model that involves the integration of customized direct and reverse logistics for several problems. These structures need to include the amount and quality of return products, sources, and constraints [6,7,34]. Complexity in SC designs considers more levels with multiple products, and by including potential variability in different echelons [1,4,14,25,26,28,35].

The main purpose is to reduce or minimize carbon emissions and to reduce waste production (see Figure 4). Green SC management is being increasingly contemplated by some countries and industries to develop SIM approaches that consider increased revenue while reducing waste and minimizing energy costs [4,19,20,44]. The impact of environmental government regulations on inventory costs should be studied [20,40]. The S aspect of sustainability is poorly studied, which makes it a future research opportunity.

There is a growing need for models to integrate all relevant factors, such as inventory, production, disassembly activities, and transport for collection or distribution. Incorporating location, vehicle routing problems, and transport modes, and considering the variability of delivery times, loading and unloading times, and truck capacity may better reflect reality [17,19,26,44,47]. Extending inventory problems by contemplating location and transport issues is an opportunity to help to develop new models for SIM models in SCs; for instance, inventory costs, fixed and variable warehouse operating costs, the total cost at the destination, including production and delivery costs [5,31].

Models should deal with a more complex system that considers uncertainty by developing stochastic methods to contemplate demand and supply uncertainty, vehicle breakdowns, return products supply, or capacities [14,28,30,31,35]. For further research purposes, the development of integrated sustainable SC models should be enhanced to incorporate the whole sustainability dimension, including social aspects such as job satisfaction, worker welfare, and occupational safety [5,21]. The inclusion of multi-objective models is fundamental for practitioners and researchers, and the most widely applied approach to model such problems is mathematical programming, mainly with a single objective and solved by exact methods. So, developing multi-objective models that simultaneously incorporate the three sustainability pillars is essential [16,29,34]. A promising way to solve these problems is to develop and apply new algorithms and heuristics [26].

Finally, a roadmap (Figure 6) to identify trends and future directions in relation to each classification criterion is proposed.

First, regarding environmental aspects, the trend of studies focuses on reducing or minimizing GHG emissions and on minimizing waste generation in production activities. For future studies, we identify that SIM models should incorporate environmental government regulations about inventory costs and also incorporate the S sustainability issue. Second, inventory problems are considered in isolation regardless of facility location and transportation routing decisions. Therefore, we propose integrating inventory, production, disassembly activities, and location decisions into SIM models, as well as transport for the collection and distribution of returned products. It would also be desirable to consider the uncertainty about the amount and quality of returned products, sources, and constraints. Third, sustainability is introduced by designing the supply network mainly through reverse logistics and closed-loop SCs (CLSC). With this criterion, future research should consider more complexity levels in SC designs using multiproducts and the potential variability in different SC echelons. Fourth, the development of MP models, specifically single-objective models, is a trend in SIM modeling approaches. For further research, it is advisable to develop multi-objective models to simultaneously deal with the three sustainability pillars; EC, EN, and S. Finally, on MP models, the most widely used solution approaches are exact methods. For future models, we propose developing and applying new algorithms and heuristics to solve multi-objective SIM problems.

5. Conclusions

This article provides an overview of the scientific literature on SIM models in the SC context. It is specifically oriented to identify, select and analyze the main studies addressing how sustainability is being managed by SCs through quantitative inventory management models. The 36 reviewed articles are categorized according to the subsequent classification criteria: SC structure, environmental approach, problem type, modeling approach, and solution approach.

From the reviewed literature and the five classification criteria, the main findings reveal that almost one-third of the studies introduce sustainability aspects into designs by incorporating reverse and closed-loop logistics, whereas the environmental approach is widely studied in the reviewed articles. Uncertainty considerations should also be included in stochastic and fuzzy inventory management models [48]. Additionally, the new results from this study can be proposed on a roadmap that contemplates the main trends and future research guidelines, based on the main limitations and future research proposals of the reviewed articles, to be addressed by SIM quantitative models (Figure 6).

The managerial insights of this roadmap are oriented to serve as an initial conceptual framework to support practitioners and researchers in articulating strategies and practices that develop and implement SIM quantitative models in SCs by, for instance, repairing and reworking defective items in local stores to maximize profits in a global SC [49].

It is worth noting that there are some limitations to this review. The consulted scientific databases were Scopus and WoS, which are constantly updated. The provided data are those collected at the time when this research was carried out. Here we review the literature published until January 2022. Despite following a systematic search process, some valuable papers may have been overlooked for this review. Models are considered in an SC context, which leaves out single-stage sustainable inventory models.

Finally, new forthcoming works are about building a high-level conceptual SIM framework based on this study and considering SC structures, sustainable inputs, quantitative models, inventory policies, and sustainability objectives, among other dimensions and elements. This conceptual framework should be the basis for novel quantitative models, such as multi-objective mathematical implementations to optimize these SIM models in an SC context in terms of EN, EC, and S factors. These new conceptual and quantitative SIM models should be applied to several real-world applications. Indeed, the authors are working to do so in the copper mining industry.