A study into the sustainability efficiency of supply chain network based on economic, social, and environmental trade-offs

Abstract

Assessing the sustainability efficiency of a supply chain network (SCN) is a complex issue due to the inherent conflict of interest among components. In these systems, there are two levels of conflict of interest: on the one hand, network players, including suppliers, manufacturers, retailers, etc., have conflicting interests. On the other hand, the three sustainability goals, namely economic, social and environmental, are not in line with each other. Improvement in one of these goals is not possible while keeping the others constant. Using hybrid models of game network data envelopment analysis (GNDEA), this study presented a new framework to measure an Iranian pharmaceutical company’s supply chain network sustainability efficiency (SCNSE). This was done considering two levels of conflict of interest simultaneously, which is the main contribution of this study. The proposed model also measures the performance of components and the entire network in all three dimensions of sustainability. It enables managers to gain a better insight into the sustainability efficiency of an SCN and its individual components. Acquiring this knowledge allows managers to identify system weaknesses and design more effective improvement plans. Future studies can develop models for appraising the sustainability efficiency of an SCN under uncertain conditions considering different players.

Appendices

Appendix A

Lemma 1

The feasible set S is compact and convex.

Proof 1

Since feasible set S is defined in a Euclidean space, the compactness condition has been met. To prove that the solution space is convex, assume:

$$ \begin{aligned} & \left( {w_{1}^{1\prime } , \ldots ,w_{D1}^{1\prime } ,w_{1}^{2\prime } , \ldots ,w_{D2}^{2\prime } ,w_{1}^{3\prime } , \ldots ,w_{D3}^{3\prime } ,w_{1}^{4\prime } , \ldots ,w_{D4}^{4\prime } ,v_{1}^{1\prime } , \ldots ,v_{m}^{1\prime } } \right) \in S \\ & \left( {w_{1}^{1\prime \prime } , \ldots ,w_{D1}^{1\prime \prime } ,w_{1}^{2\prime \prime } , \ldots ,w_{D2}^{2\prime \prime } ,w_{1}^{3\prime \prime } , \ldots ,w_{D3}^{3\prime \prime } ,w_{1}^{4\prime \prime } , \ldots ,w_{D4}^{4\prime \prime } ,v_{1}^{\prime \prime } , \ldots ,v_{m}^{\prime \prime } } \right) \in S \\ \end{aligned} $$

According to this assumption and for each $\lambda \in \left[ {0,1} \right]$ there is:

$$ \begin{aligned} & \lambda w_{d1}^{1\prime } + (1 - \lambda )w_{d1}^{1\prime \prime } > 0,\quad \forall d1 = 1, \ldots ,D1 \\ & \lambda w_{d2}^{2\prime } + (1 - \lambda )w_{d2}^{2\prime \prime } > 0,\quad \forall d2 = 1, \ldots ,D2 \\ & \lambda w_{d3}^{3\prime } + (1 - \lambda )w_{d3}^{3\prime \prime } > 0,\quad \forall d3 = 1, \ldots ,D3 \\ & \lambda w_{d4}^{4\prime } + (1 - \lambda )w_{d4}^{4\prime \prime } > 0,\quad \forall d4 = 1, \ldots ,D4 \\ & \lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } > 0,\quad \forall i = 1, \ldots ,m \\ \end{aligned} $$

Therefore, based on the above assumptions, the feasible set is compact. Thus, in model (2) for the first constraint, there is:

$$ \frac{{\sum\nolimits_{d2 = 1}^{D2} {w_{d2}^{2} z_{d2j}^{2} } }}{{\sum\nolimits_{i = 1}^{m} {v_{i} x_{ij} } }} \le 1{ ; }\;\forall {\text{j}} = {1}, \ldots ,{\text{n}} \Rightarrow \sum\limits_{d2 = 1}^{D2} {w_{d2}^{2} z_{d2j}^{2} } \le \sum\limits_{i = 1}^{m} {v_{i} x_{ij} } \Rightarrow $$

$$ \begin{aligned} \sum\limits_{d2 = 1}^{D2} {w_{d2}^{2} z_{d2j}^{2} } & = \sum\limits_{{d2 = 1}}^{{D2 }} {\left( {\lambda w_{d2}^{2\prime } + (1 - \lambda )w_{d2}^{2\prime \prime } } \right)z_{d2j}^{2} } \\ & { = }\lambda \sum\limits_{d2 = 1}^{D2} {w_{d2}^{2\prime } z_{d2j}^{2} } + (1 - \lambda )\sum\limits_{d2 = 1}^{D2} {w_{d2}^{2\prime \prime } z_{d2j}^{2} } \le \lambda \sum\limits_{i = 1}^{m} {v_{i}^{\prime } x_{ij} } + (1 - \lambda )\sum\limits_{i = 1}^{m} {v_{i}^{\prime \prime } x_{ij} } \\ & = \sum\limits_{i = 1}^{m} {\left( {\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right)} x_{ij} \\ \end{aligned} $$

Similarly, for the second and third constraints, there is:

$$ \begin{aligned} \sum\limits_{d3 = 1}^{D3} {w_{d3}^{3} z_{d3j}^{3} } & = \sum\limits_{d3 = 1}^{D3} {\left( {\lambda w_{d3}^{3\prime } + (1 - \lambda )w_{d3}^{3\prime \prime } } \right)z_{d3j}^{3} } \\ & = \lambda \sum\limits_{d3 = 1}^{D3} {w_{d3}^{3\prime } z_{d3j}^{3} } + (1 - \lambda )\sum\limits_{d3 = 1}^{D3} {w_{d3}^{3\prime \prime } z_{d3j}^{3} } \le \lambda \sum\limits_{i = 1}^{m} {v_{i}^{\prime } x_{ij} } + (1 - \lambda )\sum\limits_{i = 1}^{m} {v_{i}^{\prime \prime } x_{ij} } \\ & = \sum\limits_{i = 1}^{m} {\left( {\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right)} x_{ij} \\ \end{aligned} $$

$$ \begin{aligned} \sum\limits_{d4 = 1}^{D4} {w_{d4}^{4} z_{d4j}^{4} } & = \sum\limits_{d4 = 1}^{D4} {\left( {\lambda w_{d4}^{4\prime } + (1 - \lambda )w_{d4}^{4\prime \prime } } \right)z_{d4j}^{4} } \\ & = \lambda \sum\limits_{{d4 = 1}}^{D4} {w_{d4}^{4\prime } z_{d4j}^{4} } + (1 - \lambda )\sum\limits_{{d4 = 1}}^{{D4 }} {w_{d4}^{4\prime \prime } z_{d4j}^{4} } \le \lambda \sum\limits_{i = 1}^{m} {v_{i}^{\prime } x_{ij} } + (1 - \lambda )\sum\limits_{i = 1}^{m} {v_{i}^{\prime \prime } x_{ij} } \\ & = \sum\limits_{i = 1}^{m} {\left( {\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right)} x_{ij} \\ \end{aligned} $$

For the fourth, fifth, and sixth constraints, there are:

$$ \begin{aligned} \sum\limits_{d2 = 1}^{D2} {w_{d2}^{2} z_{d2o}^{2} } & \ge \theta_{\min ,o}^{Ec1} \sum\limits_{i = 1}^{m} {v_{i} x_{io} } \Rightarrow \\ & \quad \sum\limits_{{d2 = 1}}^{{D2 }} {\left[ {\lambda w_{d2}^{2\prime } + (1 - \lambda )w_{d2}^{2\prime \prime } } \right]z_{d2o}^{2} } \ge \theta_{\min ,o}^{Ec1} \sum\limits_{{i = 1}}^{m} {\left[ {\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right]x_{io} } \, \\ \end{aligned} $$

$$ \begin{aligned} \sum\limits_{d3 = 1}^{D3} {w_{d3}^{3} z_{d3o}^{3} } & \ge \theta_{\min ,o}^{En1} \sum\limits_{i = 1}^{m} {v_{i} x_{io} } \Rightarrow \\ & \quad \sum\limits_{d3 = 1}^{D3} {\left[ {\lambda w_{d3}^{3\prime } + (1 - \lambda )w_{d3}^{3\prime \prime } } \right]z_{d3o}^{3} } \ge \theta_{\min ,o}^{En1} \sum\limits_{i = 1}^{m} {\left[ {\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right]x_{io} } \\ \end{aligned} $$

$$ \begin{aligned} \sum\limits_{d4 = 1}^{D4} {w_{d4}^{4} z_{d4o}^{4} } & \ge \theta_{\min ,o}^{So1} \sum\limits_{i = 1}^{m} {v_{i} x_{io} } \Rightarrow \\ & \quad \sum\limits_{{d4 = 1}}^{{D4 }} {\left[ {\lambda w_{d4}^{4\prime } + (1 - \lambda )w_{d4}^{4\prime \prime } } \right]z_{d4o}^{4} } \ge \theta_{\min ,o}^{So1} \sum\limits_{i = 1}^{m} {\left[ {\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right]x_{io} } \\ \end{aligned} $$

And for the last constraint, there is:

$$ \begin{aligned} & \sum\limits_{d2 = 1}^{{D2 }} {\left[ {\lambda w_{d2}^{2\prime } + (1 - \lambda )w_{d2}^{2\prime \prime } } \right]z_{d2o}^{2} } + \sum\limits_{{d3 = 1}}^{{D3 }} {\left[ {\lambda w_{d3}^{3\prime } + (1 - \lambda )w_{{d3 }}^{3\prime \prime } } \right]z_{d3o}^{3} } \\ & \quad + \sum\limits_{{d4 = 1}}^{{D4 }} {\left[ {\lambda w_{d4}^{4\prime } + (1 - \lambda )w_{d4}^{4\prime \prime } } \right]z_{d4o}^{4} } = \theta_{o}^{Sup*} \sum\limits_{i = 1}^{m} {\left[ {\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right]x_{io} } \\ \end{aligned} $$

Therefore, for every $(d2 = 1,\ldots ,D2 )$, $(d3 = 1,\ldots ,D3 )$, $(d4 = 1,\ldots ,D4 )$,$(i = 1,\ldots ,m)$, there is:

$$ \begin{aligned} & \left( {\lambda w_{d2}^{2\prime } + (1 - \lambda )w_{d2}^{2\prime \prime } ,\lambda w_{d3}^{3\prime } + (1 - \lambda )w_{d3}^{3\prime \prime } } \right., \\ & \left. {\lambda w_{d4}^{4\prime } + (1 - \lambda )w_{d4}^{4\prime \prime } ,\lambda v_{i}^{\prime } + (1 - \lambda )v_{i}^{\prime \prime } } \right) \in S \\ \end{aligned} $$

which is equal to:

$$ \begin{aligned} & \lambda \left( {w_{1}^{2\prime } , \ldots ,w_{D2}^{2\prime } ,w_{1}^{3\prime } , \ldots ,w_{D3}^{3\prime } ,w_{1}^{4\prime } , \ldots ,w_{D4}^{4\prime } ,v_{1}^{\prime } , \ldots ,v_{i}^{\prime } } \right) \\ & \quad + (1 - \lambda )\left( {w_{1}^{2\prime \prime } , \ldots ,w_{D2}^{2\prime \prime } ,w_{1}^{3\prime \prime } , \ldots ,w_{D3}^{3\prime \prime } ,w_{1}^{4\prime \prime } , \ldots ,w_{D4}^{4\prime \prime } ,v_{1}^{\prime \prime } , \ldots ,v_{i}^{\prime \prime } } \right) \in S \\ \end{aligned} $$

Hence, the feasible set S is convex.

Appendix B Indicator selection survey questionnaire

2.1 Introduction

Thank you for agreeing to help us use your experience to select proper measures for the supply chain sustainability of the company. As you know, we are evaluating the sustainability efficiency of your company’s supply chain with a focus on supplier and manufacturer stages to determine the current status and see if we can Identify improvement initiatives. For this purpose, we have provided an attachment, which is the list of measures that have been collected through the literature review.

Please answer the following questions by writing your answer in your own words in the box provided. If you have any questions about this questionnaire, don’t hesitate to contact us.

Name:
Department:	Job position:
Date of employment:	Total work experience:
Highest education certification:	Field of Study:

2.2 Directions

• 1. Please indicate four questions as below:

  • Q1: Is the indicator aligned with goals and strategies?

  • Q2: Does the indicator have computational complexity?

  • Q3: Is the indicator actionable?

  • Q4: Is there reliable data to calculate the indicator?

• 2. Please select at least ten measures in each stage of the supply chain

• 3. Please sort them by priority and Note in the table below:

  

Appendix C Table of the results

3.1 Results of SCN sustainability efficiency

DMU	The first scenario (cooperative model)									The second scenario (non-cooperative model)
	$\theta_{o}^{OC}$	$\theta_{o}^{{Sup* }}$	$\theta_{o}^{{Man* }}$	$\theta_{o}^{{Ec1 }}$	$\theta_{o}^{{En1 }}$	$\theta_{o}^{{So1 }}$	$\theta_{o}^{{Ec2 }}$	$\theta_{o}^{{En2 }}$	$\theta_{o}^{{So2 }}$	$\theta_{o}^{ON}$	$\theta_{o}^{{Sup* }}$	$\theta_{o}^{{Man* }}$	$\theta_{o}^{{En1 }}$	$\theta_{o}^{{So1 }}$	$\theta_{o}^{{Ec2 }}$	$\theta_{o}^{{En2 }}$	$\theta_{o}^{{So2 }}$	$\theta_{o}^{{En1 }}$
1	0.89	0.42	1.00	0.46	0.40	0.40	0.60	0.51	1.00	1.0	1.0	1.0	1.00	1.00	0.64	0.24	0.47	0.99
2	1.00	0.53	1.00	0.56	0.52	0.52	0.79	0.54	0.99	0.9	0.8	1.0	0.72	0.71	0.82	0.87	0.50	0.98
3	0.83	0.70	0.86	0.71	0.69	0.69	0.45	0.50	0.84	0.9	0.8	1.0	0.65	0.65	0.75	0.57	0.46	1.00
4	0.79	0.87	0.71	0.86	0.87	0.87	0.00	0.68	0.58	1.0	1.0	1.0	0.84	0.86	0.99	0.77	0.68	0.89
5	0.82	0.81	0.78	0.80	0.81	0.81	0.19	0.79	0.55	1.0	0.9	1.0	0.77	0.79	0.91	0.00	0.91	0.61
6	0.85	0.74	0.88	0.74	0.74	0.74	0.00	0.84	0.71	0.9	0.8	1.0	0.64	0.65	0.75	0.00	0.81	0.82
7	0.85	0.52	0.96	0.54	0.51	0.52	0.00	0.92	0.78	0.9	0.8	1.0	0.69	0.69	0.80	0.00	0.81	0.82
8	0.86	0.83	0.73	0.83	0.83	0.83	0.01	0.70	0.59	0.9	0.9	1.0	0.72	0.73	0.85	0.37	0.67	0.82
9	0.91	0.86	0.85	0.85	0.86	0.86	0.00	0.82	0.69	1.0	1.0	1.0	0.83	0.86	0.99	0.98	0.78	0.82
10	0.88	0.86	0.85	0.86	0.85	0.85	0.41	0.91	0.53	1.0	1.0	1.0	0.84	0.86	0.99	0.55	0.93	0.58
11	0.86	0.62	0.97	0.63	0.61	0.62	0.00	1.00	0.66	0.9	0.8	1.0	0.71	0.72	0.83	0.00	0.86	0.72
12	1.00	0.75	1.00	0.75	0.75	0.75	0.00	0.96	0.81	1.0	1.0	1.0	0.82	0.84	0.97	0.29	0.81	0.82
13	1.00	0.89	0.83	0.87	0.89	0.89	0.00	0.72	0.54	1.0	1.0	1.0	0.83	0.87	1.00	0.37	0.66	0.59
14	1.00	0.74	0.95	0.73	0.74	0.74	0.00	0.60	0.83	1.0	0.9	1.0	0.79	0.82	0.94	0.00	0.55	0.91
15	0.94	0.98	0.81	0.97	0.98	0.98	0.50	0.78	0.66	1.0	1.0	1.0	0.84	0.86	0.99	0.81	0.85	0.74
16	1.00	1.00	0.82	0.99	1.00	1.00	0.00	0.78	0.66	1.0	1.0	1.0	0.84	0.86	0.99	0.47	0.81	0.82
17	0.95	0.72	0.97	0.73	0.72	0.72	1.00	0.49	0.72	1.0	1.0	1.0	0.84	0.86	0.99	1.00	0.45	0.79
18	0.94	0.71	0.92	0.71	0.70	0.71	0.70	0.65	0.68	1.0	1.0	1.0	0.84	0.86	0.99	0.71	0.60	0.75
19	0.78	0.56	0.78	0.57	0.56	0.56	0.07	0.73	0.64	0.9	0.9	1.0	0.72	0.74	0.85	0.88	0.67	0.77
20	0.94	0.77	0.82	0.76	0.77	0.77	0.21	0.84	0.57	1.0	1.0	1.0	0.83	0.86	1.00	0.02	0.87	0.62
21	1.00	0.68	1.00	0.69	0.67	0.67	0.72	0.96	0.81	1.0	1.0	1.0	0.84	0.86	0.99	0.00	0.81	0.82
22	0.96	0.81	0.94	0.81	0.80	0.80	0.00	0.71	0.84	1.0	1.0	1.0	0.85	0.86	0.99	0.27	0.66	0.90
23	1.00	0.70	1.00	0.71	0.70	0.70	0.00	0.67	0.87	0.9	0.8	1.0	0.71	0.72	0.83	0.00	0.61	0.92
24	0.96	0.71	0.96	0.72	0.70	0.70	0.00	0.92	0.77	1.0	0.9	1.0	0.78	0.79	0.91	0.00	0.81	0.82
25	0.99	0.71	0.99	0.72	0.70	0.70	0.67	0.98	0.75	1.0	0.9	1.0	0.80	0.81	0.93	0.29	0.81	0.82
26	0.96	0.61	1.00	0.61	0.60	0.61	0.10	0.96	0.81	1.0	1.0	1.0	0.81	0.84	0.97	0.55	0.81	0.82
27	0.90	0.51	1.00	0.51	0.50	0.50	0.00	0.95	0.81	1.0	1.0	1.0	0.84	0.86	0.99	0.00	0.81	0.82
28	0.96	0.85	0.80	0.85	0.84	0.84	0.00	0.77	0.65	1.0	1.0	1.0	0.85	0.86	0.99	0.00	0.81	0.82
29	1.00	0.70	0.91	0.72	0.69	0.69	0.00	0.94	0.63	1.0	1.0	1.0	0.85	0.85	0.98	0.24	0.87	0.68
30	1.00	0.71	0.87	0.73	0.70	0.70	0.07	0.85	0.69	1.0	1.0	1.0	0.85	0.86	0.99	0.06	0.84	0.76
31	1.00	0.29	0.95	0.32	0.27	0.28	0.57	0.91	0.77	1.0	1.0	1.0	0.85	0.86	0.99	0.59	0.81	0.82
32	1.00	0.70	0.86	0.70	0.69	0.69	0.14	0.86	0.63	1.0	0.9	1.0	0.79	0.80	0.93	0.72	0.87	0.69
33	1.00	0.65	0.93	0.65	0.64	0.64	0.01	0.89	0.75	1.0	0.9	1.0	0.79	0.81	0.93	0.00	0.81	0.82
34	0.99	0.62	0.90	0.64	0.61	0.61	0.13	0.79	0.76	1.0	1.0	1.0	0.85	0.86	0.99	0.37	0.72	0.86
35	1.00	1.00	0.64	1.00	0.99	1.00	0.02	0.68	0.40	1.0	1.0	1.0	0.85	0.85	0.99	0.21	1.00	0.44