Keywords

1 Introduction

In order to improve any firm’s sustainability performance, the role of “Reverse Logistics” has been regarded to be significant in different aspects, such as for cost-savings [7], higher sales’ revenue from products that are recovered and/or remanufactured [17], enhanced satisfactions of customers [14] with their loyalty [2], and by considerable reduction in carbon footprints, providing positive impacts on climate-change as well as global-warming [3], respectively. Moreover, higher competitive advantages are achievable through well-organized and sustainable reverse logistics practices [9]. Thus, for sustainable development, reverse logistics always have positive implications [5, 6, 21].

Although the reverse logistics concepts have been recognized to be very important in developing countries, however, the companies’ progress has been hampered owing to certain prevailing variables responsible for their sustainable developments. Thus, this study focused on identifying the associated variables with reverse logistics practices in the bottle manufacturing companies in Odisha (India), and to rank those variables by using suitable “multi-criteria decision-making (MCDM)” method.

1.1 Literature

A wide variety of tools and techniques have been utilized in order to evaluate sustainability in different cases. For instance, on account of weighted sum of product’s sustainability aspects, Jaffar et al. [8] represented a model by considering economical, environmental as well as social aspects for product’s sustainability assessments. Both environment as well as ecological factors were considered for a “desalination plant” to evaluate sustainability [1]. An “environmental impact assessment” was performed by Vinodh et al. [20] for an automotive sector by means of “eco-indicator.” Ticehurst et al. [19] have utilized “Bayesian-network approach” for the evaluation of coastal-lakes’ sustainability in New South Wales, Australia. Similarly, different researchers have made use of fuzzy-logic-based techniques for evaluating sustainability in a range of areas, such as in “petroleum corporation” [22], nation’s sustainability judgments [11], in chemical-industry [4], in mining as well as mineral segments [10], and in the pandemic situations with the use of Grey-TOPSIS [15], respectively.

2 Methodology

In this work, five bottle manufacturing companies from Odisha (India) were considered to analyze their reverse logistics practices for long-term sustainable development. Different associated variables with reverse logistics practices were identified using the literature and subsequent consultation with industry-based experts for further analysis. Furthermore, when a number of variables/criteria are involved in any problem, then the application of ‘multi-criteria decision-making (MCDM)’ methods becomes more useful. For instance, the ‘Grey-theory’ superiority has been reported in situations dealing with uncertain information that help in the study of judgments by human with uncertainties as well as ambiguities [12, 13]. In different areas the “technique for order of preference by similarity to ideal solution (TOPSIS)” method has been successfully utilized [16]. Thus, the ranking of the associated variables with reverse logistics practices in the bottle manufacturing companies/units was made based on the TOPSIS method.

2.1 TOPSIS Method

The linguistic variables, i.e., criteria weights as well as the criteria ratings (\(\otimes\) GN) in terms of grey numbers by using “1–7 scale” were illustrated in Table 1.

Table 1 Scale of criteria weights (\(\otimes w\)) and criteria ratings (\(\otimes {\text{GN}}\))
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The sequence of steps in the “Grey-TOPSIS” method included the following:

Step 1: With the formation of a decision-makers’ committee, the criteria weights were identified for alternatives (variables). By assuming “P” number of persons in the decision group, the criteria weight can be determined as:

$$\otimes w_{j} = \frac{1}{P}\left( { \otimes w_{j}^{1} + \otimes w_{j}^{2} + \cdots + \otimes w_{j}^{P} } \right)$$
(1)

where, \(\otimes w_{j}^{P} \left( {{\text{j}}\, = \,{1},{ 2}, \ldots ,{\text{ n}}} \right)\) denoted the criteria weight of Pth decision-makers’.

Step 2: By using the linguistic-variables, the rating values were obtained as:

$$\otimes GN_{ij} = \frac{1}{K}\left( { \otimes GN_{ij}^{1} + \otimes GN_{ij}^{2} + \cdots + \otimes GN_{ij}^{P} } \right)$$
(2)

where, \(\otimes GN_{ij}^{P}\) (i = 1, 2, …, m; j = 1, 2, …, n) denoted ‘criteria rating-value of Pth decision-makers’.

Step 3: The grey decision-matrix with \(\otimes GN_{ij}\) as linguistic-variables on the basis of grey numbers was established as:

$$GDM = \left[ {\begin{array}{*{20}c} { \otimes GN_{11} } & { \otimes GN_{12} } & \ldots & { \otimes GN_{1n} } \\ { \otimes GN_{21} } & { \otimes GN_{22} } & \cdots & { \otimes GN_{2n} } \\ \vdots & \vdots & \ddots & \vdots \\ { \otimes GN_{m1} } & { \otimes GN_{m2} } & \cdots & { \otimes GN_{mn} } \\ \end{array} } \right]$$
(3)

Step 4: Normalizing the grey decision-matrix as:

$$GDM^{*} = \left[ {\begin{array}{*{20}c} { \otimes GN_{11}^{*} } & { \otimes GN_{12}^{*} } & \ldots & { \otimes GN_{1n}^{*} } \\ { \otimes GN_{21}^{*} } & { \otimes GN_{21}^{*} } & \cdots & { \otimes GN_{2n}^{*} } \\ \vdots & \vdots & \ddots & \vdots \\ { \otimes GN_{m1}^{*} } & { \otimes GN_{m2}^{*} } & \cdots & { \otimes GN_{mn}^{*} } \\ \end{array} } \right]$$
(4)

where, for a benefit-criterion, \(\otimes GN_{ij}^{*}\) was expressed as:

$$GN_{ij}^{*} \, = \,\frac{{{}_{ - }^{GN} ij}}{{GN_{j}^{\text{max}} }}, \frac{{{}_{GN}^{ - } ij}}{{GN_{j}^{\text{max}} }};\,GN_{j}^{\text{max}} \, = \,{\text{max}}_{1 \le i \le m} \left( {\overline{GN}_{ij} } \right)$$
(5)

where, for a cost-criterion, \(\otimes GN_{ij}^{*}\) was expressed as:

$$GN_{ij}^{*} \, = \,\frac{{GN_{j}^{{{\text{min}}}} }}{{{}_{GN}^{ - } ij}},\frac{{GN_{j}^{{{\text{min}}}} }}{{{}_{ - }^{GN} ij}};GN_{j}^{{{\text{min}}}} \, = \,{\text{min}}_{1 \le i \le m} \left( {{}_{ - }^{GN} ij} \right)$$
(6)

Step 5: By considering each criterion with different importance, the “weighted normalized grey decision-matrix” was formulated as:

$$GDM^{*} = \left[ {\begin{array}{*{20}c} { \otimes VN_{11} } & { \otimes VN_{12} } & \ldots & { \otimes VN_{1n} } \\ { \otimes VN_{21} } & { \otimes VN_{22} } & \cdots & { \otimes VN_{2n} } \\ \vdots & \vdots & \ddots & \vdots \\ { \otimes VN_{m1} } & { \otimes VN_{m2} } & \cdots & { \otimes VN_{mn} } \\ \end{array} } \right]$$
(7)

Where, \(\otimes VN_{ij} = \left[ { \otimes GN_{ij}^{*} \times \otimes w_{j} } \right]\)

Step 6: For “m” possible alternative-sets, i.e. \({\text{S}}\, = \,\left\{ {S_{1} ,\,S_{2} ,\, \ldots ,S_{m} } \right\}\), the ideal referential-alternative was obtained as

$$S_{\text{max}} = \,\left[ { \otimes GN_{1}^{{{\text{max}}}} , \otimes GN_{2}^{{{\text{max}}}} ,{ } \ldots ., \otimes GN_{n}^{{{\text{max}}}} } \right]{ }$$
(8)

Step 7: The ‘grey possibility-degree’ was obtained between the compared alternative sets \({\text{S}}\, = \,\left[ {S_{1} ,\,S_{2} ,\, \ldots ,S_{m} } \right]\), and ideal referential-alternative \(S^{\text{max}}\) as:

$$P\,\left[ {S_{i} \le S^{\text{max}} } \right]\, = \,\frac{1}{n}\mathop \sum \limits_{j = 1}^{n} P\left[ { \otimes VN_{ij} \le \otimes GN_{j}^{\text{max}} } \right]$$
(9)

Step 8: The final ranking of the alternative sets was done by considering the following conditions: (a) For smaller P \(\left[ {S_{i} \le S^{\text{max}} } \right]\), the better was the ranking order of \(S_{i}\). (b) If not, the worse will be the ranking order.

2.2 Selection of Variables for Performance-Based Sustainable Manufacturing

Table 2 illustrates the performance-based sustainable manufacturing for the bottle manufacturing units with effective reverse logistics practices, where the sustainability assessment indices were as suggested by Singh et al. [18], literature, and the suggestions of experts involved in this work.

Table 2 Performance-based sustainable manufacturing
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3 Results and Discussion

The associated variable(s) with reverse logistics were assigned with different weight values (W) and the corresponding integrated matrix was obtained (Table 3). This was further followed by formation of the “normalized-matrix” and “weighted normalized-matrix,” respectively (Tables 4 and 5).

Table 3 Formation of “integrated-matrix”
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Table 4 Formation of “normalized-matrix”
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Table 5 Formation of “weighted normalized-matrix”
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On the basis of the values of “grey possibility-degree” between the associated variable(s) with reverse logistics, their ranking was done that were based on the minimum values of the “Grey possibility-degree” at first place and so on (Table 6).

Table 6 Determination of P \(\left[ {{\text{S}}_{{\text{i}}} \le {\text{S}}^{{{\text{max}}}} } \right]\) and the final ranking of associated variable(s) with reverse logistics
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It was found from Table 6 that, the associated variable(s) with reverse logistics that required of major attentions included “Member of staffs’ Consumers’ and Communities welfare” that ranked in the first-level followed by “Wastages’ and Emissions’ reductions; Water and Energy utilizations; Stuff handling; Sensitivity; and Quality,” respectively (Fig. 1).

Fig. 1
A chart ranks the order of the associated variables with reverse logistics that require major attention. 1. Member of the staff, consumers, and communities welfare. 2. Wastages and emissions reductions. 3. Water and energy utilization. 4. Stuff handling. 5. Sensitivity. 6. Quality.

Rank-order of the associated variable(s) with reverse logistics requiring major attention

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4 Conclusion

As the supply-chain management of any company gets more influenced by the reverse logistics practices, which has attracted many professionals and manufacturers to connect all the firm-related activities together. In this study, the associated variable(s) with reverse logistics that required of major attention for sustainable developments of the bottle manufacturing units included “Member of staffs’ Consumers’ and Communities welfare” which ranked in the first-level followed by “Wastages’ and Emissions’ reductions; Water and Energy utilizations; Stuff handling; Sensitivity; and Quality,” respectively.