Supply chain performance evaluation in the presence of undesirable products: A case on power industry

1.   Introduction

An electricity supply chain is a network of suppliers, producers, transmitters and distributors in which raw materials are transformed into final products and delivered to the customers. Supply chain management includes a set of profit methods to the efficient and effective integration of supplier, manufacturer, transmitter, distribution, and customer to minimize of system costs and prompt and reliable delivery of high-quality products. The energy sector is considered one of the most important types of advanced infrastructures in any country. The oil and gas fields and refineries are considered as the energy basic sectors in Iran so they provide demand fuels to nonrenewable power plants. More than 150 billion cubic meters flare gas released in the world, annually. According to the World Bank statistics in the year 2017, this number is equivalent to one-third of Europe continent consumption that seventy-five percent of emitted gases belong to ten countries as Iran had a global third rank and first rank in the Middle East. Also, Energy and power plant sections besides to produce energy, consume a lot of energy in economic activities. For instance, the daily more than 45 million cubic meters associated gas (gas in oil) have been burned to avoid from the possible explosion in oil and gas fields that burning fossil fuels not only a big thread for human health and the other organisms but also cause decrease economic return in industrial activities. Therefore, the flare gas recovery and return of wasted energy to gas natural cycle are an immediately necessary to environmental efficiency enhancement and economic growth. Similarity, power plants from production to consumption produce various harmful substances in the environment. Power plants are the largest fossil fuel consumers such as coal, fuel oil and gasoline and natural gas. These fuels play most of the role in electricity production Therefore, the more usage of them and power production increases greenhouse gas emissions. In the global scale, the key greenhouse gases are carbon dioxide (CO₂), methane (CH₄), nitrogen oxides, and sulfur oxides. These gases have been released during the combustion of fossil fuels also Electricity production generates the largest share of greenhouse gas emissions. Approximately, 68 percent of consumption electricity comes from burning fossil fuels, mostly coal, fuel oil, gasoline and natural gas. Carbon dioxide (CO₂) has the most contributions to pollution emissions in power plants. This gas cause climate changes and global warming also it is a threat to human health and other organisms. Therefore, we must reduce an number of greenhouse gases (GHG) by enhancing systems efficiently, otherwise, we will confront sever events such as heat waves, droughts, floods and other harmful factors to social and economics. In this case, decision-makers should adapt to various regulations to reducing pollution emissions. Approximately, one percent of power plants’ nominal capacity is devoted to power losses in transmission and distribution lines. The one percent of power plant capacity is equivalent to 2.5 billion kilo watt-hour power that to produce this amount of electricity releases about 1.8 ton Carbon dioxide (CO₂) in air. Therefore, a profit solution to this problem is new ideas performance to investment opportunities and Technology innovation to harmful effects protection of environmental. In other word, if supply chain enterprises equipped with improved engineering capability and invest in improvement and repair of equipment in all of the divisions then undesirable outputs considerably decrease in production processes. Besides, the resulting investment in the energy industry, power plant sections and transmission and distribution lines usually depend on the especial span time for fulfillment and enterprise improvement. Therefore, supply chain management should can propose an appropriate approach to activity level control and wasted energy harness to environmental efficiency enhancement in the power industry. Data envelopment analysis (DEA) is a profitable method for performance of new ideas to the protection of environmental harmful effects in industrial activity. Let us now suppose that supply chain divisions apply inputs to produce desirable and undesirable outputs and the material flow is transferred from suppliers to manufacturers and from manufacturer to transmitters and from them to distributors and finally from distributors to customers in the production processes. Let us consider undesirable outputs such as emissions of harmful substances in the air, water and ground and other detrimental variables of production activities.

In this study, we are going to answer the following question: how a decision-making unit or a supply chain enables decrease pollution gases emissions in oil and gas fields and power plants by scale down of production level and power plants fuel consumptions regulation and nominal capacity handling as power losses dramatically decrease in transmission and distribution lines? In this case, decision-makers should be able to identify which inputs of supply chain divisions decline to wasted energy abatement in electricity supply chain sectors. Indeed, the supply chain management needs to the size and type of reduced inputs to activity level control as handling flare gas in energy sections and reducing harmful substance emissions and greenhouses gases in power plant sectors and harnessing power losses in transmission and distribution networks.

Therefore, supply chain management enables simultaneously minimize the negative environmental impacts whilst maximizing its operational performance Indeed, the main objective of supply chain management is minimizing operational and environmental costs while delivering value products to customers by production, transmission, and distribution inaccurate quantity, to suitable place, at the correct time and in a sustainability process. In other words, to achieve this goal we may compare cases in which firms are usually interested in decreasing inputs and undesirable outputs. Now we consider the week disposability of undesirable outputs. In addition, the weak disposability is accomplished by the activity level control to flare gas recovery and environmental protection into energy sections also the week disposability assumption is adapted to the inner electricity consumption control of power plants (technical and non-technical) and prevention of pollution gases emissions in power plants sectors. Similarity, the weak disposability is employed to the capacity and length control of transmission and distribution lines and power losses reduction in transmission and distribution networks.

To include the undesirable outputs in the technology and account for their negative impact on productivity Hailu et al. ^[1] introduced disposability conditions on their technology which they refer to as the "weakly disposable" and treated detrimental variables as inputs, Färe et al. ^[2,3] applied an alternative approach that models undesirable emissions as outputs and imposing an assumption that these undesirable outputs are weakly disposable. They implicitly assume that all firms in the sample application a uniform abatement factor. Kuosmanen ^[4] presented a simple formulation of weak disposability that allows for non-uniform abatement factors and preserves the linear structure of the model.

In this paper, we introduce a DEA approach to calculate environmental and operational efficiency in an electricity supply chain. Furthermore, DEA can conduct an industrial policy regarding how to increase the level of economic prosperity and how to decrease the amount of flare, GH gases and power losses, simultaneously. In the offered model the intensity weights of supply chain divisions separated into two categories of components as one of two category components related to the amount outputs are abated through scaling down of activity level and the other category contains components that remains active in the production process. In other word, this study focuses on environmental assessment of supply chain that minimizes the environmental impacts and maximizes economic returns and satisfies social requests. Besides, the supply chain sustainability assessment is measured by its divisions’ efficiency scores that the first priority is environmental performance and the second priority is operational performance.

The rest of the paper is organized as follows. In Section 2, we present a review of the appropriate literature in DEA and supply chain management that indicates weak disposability in nonparametric production analysis with undesirable outputs. In Section 3, we present a brief review of the DEA model namely the "weakly disposable" DEA model. We show how to correctly specify weak disposability in an activity analysis model of supply chain performance evaluation problems. Section 4 is devoted to introducing a procedure to calculate unified efficiency (operational and environmental) of the supply chain under weak disposability of undesirable outputs and free disposability of inputs and desirable outputs. In Sections 5 we present a case study to exhibit properties of the procedure and demonstrate the applicability of the proposed method to a supply chain performance evaluation problem to the power industry in Iran. In Section 6 we present our conclusions.

2.   Literature review

The undesirable factors may also need to be considered in real- life applications. In this section, various studies on undesirable outputs and green supply chain management GSCM are briefly summarized as follows.

Hailu et al. ^[1] extend the non-parametric analysis of Chavaz et al. ^[5] by incorporating undesirable outputs to provide a more complete representation of the production technology. Shephard ^[6] introduced the definition of weak disposability and proposed basic production axioms on that. They constructed Inner and outer non-parametric technology bounds. They also introduced disposability condition on their technology, which claimed as is preferable to what they referring to as the "weakly disposable" DEA model and developed a production model.

Färe et al. ^[4,5] showed that the monotonicity condition introduced by Hailu et al. ^[1] is inconsistent with physical laws and the standard axioms of production of weak disposability according to ^[3] and implicitly assume that, all firms in the sample application a uniform abatement factor. Kuosmanen ^[4] presented an alternative approach that models undesirable emissions as outputs imposing an assumption that these undesirable outputs are weakly disposable. He showed how weakly disposable technology can be modeled in a way such that non-uniform abatement factors can be applied as Kuosmanen technology is the correct minimum extrapolation technology under the stated axioms.

Data Envelopment Analysis (DEA) was developed by the CCR model ^[8] to evaluate the relative efficiency of decision-maker units (DMUs).To measure the efficiency of the complex network systems, Färe and Grosskopf ^[9] and Färe et al ^[10] built division production possibility set satisfying the standard available in ^[11].Tone and Tsutsui ^[12] proposed a method called Epsilon based measure (EBM). The EBM models simultaneously consider both the radial and non-radial measures of efficiency in DEA. Färe et al. ^[10] developed a sequence of network models. They presented three network models and formalized technologies by a series of linear in quality constraints.

Zhu ^[13] proposed a DEA approaches for airlines performance by two–stage network.

Kao et al. ^[14] built a relation network DEA model, taking into account the interrelationship of the processes within the system to measure the efficiency of the system and those of the processes at the same time.

Kao ^[15] modified the conventional DEA model by taking into account the series relationship of the two sub-processes within the whole process.

Tone and Tsutsi ^[16] proposed a slacks-based network DEA model called network SBM.

Chen and Yan ^[17] consider a general network structure in which modeling processes are based upon the concept of centralized, decentralized and mixed control organization mechanisms. They first build division production possibility set all satisfying the strong free disposability as it is common in conventional DEA models, then the production possibility set of the assumption supply chain is formed by combining its divisional production possibility sets. They calculated supply chain efficiency according to ^[18] projection on the efficient frontier of the supply chain.

Tavana et al. ^[19] extended the EBM model proposed by Tone and Tsutsi ^[16] and proposed a new Network EBM (NEMB).

Nevertheless, all of the above- mentioned approaches to determine efficiency score assume that the outputs are desirable.

Mirhedayatian et al. ^[20] presented a DEA-based model in the presence of undesirable outputs, dual-role factors, and fuzzy data. They indicated a method to improve environmental performance a green the supply chain management and incorporate dual-role factor and undesirable output into (NSBM) model proposed by Tone and Tsutsui ^[12].

Tajbakhsh et al. ^[21] proposed a multi-stage data envelopment analysis model to evaluate the sustainability of a chain of business partners. They assess supply chain sustainability in the banking sector and beverage case.

In summary, all of the abovementioned references for environmental performance assessment of supply chain do not consider network DEA model based on production level reduction to undesirable products. Also, the aforementioned models are not able to define parameters to the amount activity level abatement and undesirable products.

3.   The production technology set of overall supply chain and all of the divisions

In this Section is reported the production technology set and outputs set to the overall supply chain and its divisions under weak disposability of undesirable outputs.

3.1.   Modeling weak disposability in a supply chain

Definition: Outputs are weakly disposable if $(v, w) \in p\, (x)$ and $0 \leqslant \theta \leqslant 1$ implies $(\theta \, v, \theta \, w) \in p\, (x)$ (see^[3]).

Let us consider, ${h_s}$, ${h_m}, {h_t}, {h_d}, {h_c}$ the number of divisions in the supplier, manufacturer, transmitter, distributor and customer, respectively. Also, $x_{nk}^h, y_{rk}^h, w_{jk}^h$ represent the nth input $\left( {n = 1, ..., N} \right)$, the rth desirable output $(r = 1, ..., s)$ and the jth undesirable output $(j = 1, ..., J)$ of the $h$th division $h = (1, ..., H)$ in the kth supply chain $\left( {k = 1, ..., K} \right)$, respectively. $v_{m\, \, k}^{(h, h')}$ Represents the intermediate measure between the $h$th division to the $h'$th division of kth supply chain (DMU) with subscript (m, k) indicating mth intermediate measure $\left( {m = 1, ..., {M_h}} \right)$ in kth supply chain $\left( {k = 1, ..., K} \right)$. Furthermore, $\theta _k^h$ are defined as abatement factors that scale down both desirable and undesirable outputs of $h$th division in kth supply chain and $z_k^h$ indicate the intensity is divided into two parts as $z_k^h = \lambda _k^h + \mu _k^h$ where $\mu _k^h$ represents the part of output that is abated through scaling down of activity level and $\lambda _k^h$ denotes the part of output that remains active of $h$th division in kth supply chain ($\lambda _k^h = \theta _k^h\, z_k^h$). $s_{mk}^{({h_s}, {h_m})}s_{mk}^{({h_m}, {h_t})}, s_{mk}^{({h_t}, {h_d})}, s_{mk}^{({h_d}, {h_c})}$ represent slack variables of mth intermediate measure from supplier divisions to manufacturer divisions, and manufacturer divisions to transmitter divisions, and from transmitter divisions to distributor divisions and from them to customer divisions in kth supply chain (k = 1, …, K). ${\phi _{{h_s}}}, {\phi _{{h_m}}}, {\phi _{{h_t}}}, {\phi _{{h_d}}}, {\phi _{{h_c}}}$ Represent the reduction variables of all undesirable outputs in suppliers, manufacturers, transmitter, distributors and customers divisions, respectively Suppose we observe the production data of k supply chains; the data for supply chain $(k = 1, ..., K\, )$ and hth division $(h = 1, ..., H)$ are represented by the vector, $\left( {v_k^h, y_k^h, w_k^h, x_k^h} \right)$. The production technology set of hth division in the kth supply chain is defined as follows. $Y = \left\{ {\left( {v_k^h, y_k^h, w_k^h, x_k^h} \right)\left| {\;x_k^h\, can\, produce\, \left( {v_k^h, y_k^h, w_k^h} \right)} \right.} \right\}$ Thus, the outputs set of hth division in the kth supply chain can be indicated as follows: $P_{k}^{h}(x) = \left\{\left(v_{k}^{h}, y_{k}^{h}, w_{k}^{h}\right) |\left(v_{k}^{h}, y_{k}^{h}, w_{k}^{h}, x_{k}^{h}\right) \in Y\right\}$

3.2.   The production technology set of overall supply chain and all of the divisions

Let us consider the general structure of the supply chain depicts in Figure 1.

Figure 1.  The general structure of supply chain.

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We shall assume free disposability of inputs and good outputs, weak disposability of good and undesirable outputs, the convexity of Y and variable returns to scale. In this method, the parameters abovementioned and intermediate measures are incorporated into the network model to the performance evaluation of cooperative and non-cooperative network and slack variables of intermediate measures are unrestricted that they will recognize better activity level as the decline in desirable output. Furthermore, the experimental outputs set are considered to suppliers, manufacturers, transmitter distributions and division’s customer and they indicate as, ${P_s}(x), P_m^{}(x), P_t^{}(x), P_d^{}(x), P_c^{}(x)$, respectively.

Figure 2 shows an electricity supply chain structure in the power industry. The electricity supply chains are power suppliers in industry activity. They are comprised of fuel suppliers (oil and gas fields), power producers (power plants), electricity transmitters (transmission lines), power distributors (distribution lines) and final customers. These entities collaborate to power production and management in economic business. In this study, the supply chains have been built in northern, southern, eastern, western and central districts in Iran. In this conformation oil and gas fields and refineries provide demand fuels of power plants and district power plants transfer produced power by regional power companies to the area distribution companies to dispatching to consumers or residents of their area. Other words, each supply chain or DMU is built of five stages and partners of each stage connected by intermediate measures to the successor stage. Supply chains are comparable and compete in the power industry. In Figure 2 is depicted intermediated measures sent from oil and gas fields to power plants, from transmissions companies to distributions companies and finally from them to customers. These measures indicate entities’ relationship in the supply chain. However, each division of entities operates in depending on other divisions per stage of economic activities and supply chains compete to high efficiency earn in economic business. The whole goal examines the corporate sustainability of the Iranian power industry to environmental and operational efficiency increase to wasted energy reduction and environment protection of harmful gas emissions in production processes.

Figure 2.  The supply chain structure.

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The outputs set can be separately defined for the partners of the supply chain as follows.

Therefore, outputs set can be defined to a supply chain which comprises an arbitrary number of each division type and production indexes. In particular, we develop outputs set both non-cooperative and cooperative or centralize approaches to performance evaluation of a sustainable supply chain. In the result, outputs set of overall supply chain can be formed of all of its partners outputs set in production processes as follows.

4.   Proposed model

Now, we present our cooperative approach to evaluate the sustainability of a supply chain as:

One straightforward approach to calculate the effect of production factors is non-cooperative network method in which each member of each stage is evaluated separately as follows.

The above model measures the efficiency of supplier divisions in a supply chain. The performance evaluating efficiency of supply chain partners can be calculated by a model similar to (8). After measuring the optimal efficiency of each member of supply chain network by a model such as model (8) the efficiency of under consideration DMU (supply chain) calculate by weighted average of optimal efficiency of each division of the supply chain as follows.

In the above model is supposed a supply chain contains an arbitrary number of suppliers, manufacturers, transmitters, distributers and customers. The objective function of Model (7) indicates the weighted average of the efficiency of partners as weights could be obtained through an expert opinion processes. In this study we considered the different weights for partners of a particular stage of the network supply chain. ${W_h}\, , \, (h = 1, \, ...\, , \, H)$are weights for H divisions that are defined by decision makers. The right and left hand sight of the first constraints categories indicates the intermediate measures exit from th division and enter to division, respectively. The fifth until the fourteenth constraints are corresponded to desirable and undesirable outputs respectively. Moreover, the fifteenth constraint until nineteenth constraint related to inputs of every division. The last constrains categories indicate variable return to scale in production processes. In addition, five pair $(\phi _o^{{h_s}}, \lambda _k^{{h_s}}), \, (\phi _o^{{h_m}}, \lambda _k^{{h_m}}), (\phi _o^{{h_d}}, \lambda _k^{{h_d}}), (\phi _o^{hc}, \lambda _k^{{h_c}}),$ indicates the main decision variable analogous to suppliers, manufactures, transmitters, distributers and customers, respectively. In this model is CCR-efficient if. Model (10) propose a supply chain multistage network based on cooperative or centralized approach following the method of ^[6]. This model measures the level of unified efficiency (operational and environmental) where all slack variables of intermediate measures are considered unrestricted; this allows higher flexibility in material flow of intermediate measures.

Proposition1. Suppose $\theta _o^*, \, \, \gamma _o^*$ are the optimal objective function cooperative and non-cooperative models, respectively then $\gamma _o^* \leqslant \theta _o^*$ where $o \in \left\{ {k = 1, ..., K} \right\}$, See proof ^[21].

5.   A real case on power industry

In this section, we apply the proposed model to the analysis of the power industry in Iran. In Subsection 5.1 we will describe the dataset and we will specify the inputs and outputs we will consider in our analysis, in Subsection 5.2 we will present the main results.

5.1.   Dataset

The stylized supply chain in the power industry can be summarized in five main actors: gas and fuel suppliers, power generators, transmission networks, distribution facilities, and final users. Conventional power plants consume fuel oil, natural gas and diesel to produce electricity, while renewable ones are solar, wind and hydro plants. Conventional plants can be further divided depending on the kind of technology adopted, in thermal, gas and combined cycle plants. In general, thermal power plants operated by fossil fuels produce huge amounts of air pollutants. The pollutants which have been considered in the study are sulfur oxides (SO_X), nitrogen oxides (NOx) and carbon dioxide (CO₂).

Our purpose is to highlight the theoretical and practical quality of the model, therefore each of the DMUs or the supply chain is built of five stages and each stage includes a set of partners connected to the predecessor stages members by some sustainable intermediate measures. In our application, we consider 10 supply chains (DMUs) including oil and gas fields (suppliers) that provide different fuels to power stations, power plants (manufacturers), regional power companies (transmitters), distribution companies (distributors) and customers. The supply chains have been built in northern, southern, eastern, western and central districts of Iran. In this study, energy sectors or oil and gas fields and fineries supplying demand fuels of area power plants so that, the energy sections are considered as suppliers and the power plants of the districts are selected as manufactures (power producers) in supply chain construction. Likewise, the region power companies transmit produced power of the area power plants to dispatching to distributions companies that are placed in the area. Finally, the distributions companies dispatch power to consumers or the area residences. Per each supply chain, we consider two suppliers: oil and gas companies that satisfy the fuel demand of power plants (intermediate product) and that can also sell fuels as final output. Suppliers use two inputs (capital and labor) and produce one desirable (oil or gas) and one undesirable output (flaring gas). Each manufacturer includes at least three power plants with different technologies (thermal, combined cycle, gas, hydro, wind and solar). They use fuels, capital, and labor to produce electricity and they sell it to regional power companies. To update and enlarge their capacity, manufacturers can substitute existing plants with more efficient ones or they can construct new plants. Three undesirable outputs are considered for manufacturers: CO₂, NOx, and SO_X emissions.

Transmitters transfer electricity from manufacturers to distributing companies and the capacity and length of the lines are considered as inputs in lines. The loose in the transmission lines is considered as undesirable output while the construction of new lines is a desirable one. Distribution companies receive electricity from transmitters and dispatch it to the final consumers. They use two inputs as capacity of the distribution lines and length of the distribution lines, one final desirable output as the meter of electricity and one undesirable output that is losses in the distribution lines. Finally, customers are classified as residential, public, agriculture and industrial. Table 1 indicates the production factors used for supply chain evaluation.

Table 1.  Production factors in performance evaluation.

Division	Numerator	Factors	Definition
Supplier	${h_s}$	$x_{1k}^{{h_s}}$	Capacity of oil (103 Barrels) and gas(106 m3)
		$x_{2k}^{{h_s}}$	Number of employees
		$y_{1k}^{{h_s}}$	Oil (103 Barrels) and gas (106 m3) sold
		$w_{1k}^{{h_s}}$	Flaring gas of oil field (103 barrels)and gas field(106 m3)
Manufacturer	${h_m}$	$x_{1k}^{{h_m}}$	Power nominal of power plants
		$x_{2k}^{{h_m}}$	Labor
		$y_{1k}^{{h_m}}$	Percentage of new construction of power plant
		$w_{1k}^{{h_m}}$	Emissions of Nox harmful Substances(103 Kg/106 K wh)
		$w_{2k}^{{h_m}}$	Emissions of SOx harmful Substances(103 Kg/106 K wh)
		$w_{3k}^{{h_m}}$	Emission of CO2 harmful Substances(103 Kg/106 K wh)
Transmitter	${h_t}$	$x_{1k}^{{h_t}}$	Capacity of regional company (M wa)
		$x_{2k}^{{h_t}}$	Length transmission line (Km circuit)
		$y_{1k}^{{h_t}}$	New construction of transmission lines (Km circuit)
		$w_{1k}^{{h_t}}$	Loose of transmission line (%)
Distribution	${h_d}$	$x_{1k}^{{h_d}}$	Capacity of distribution lines (M wa)
		$x_{2k}^{{h_d}}$	Length transmission line (Km)
		$y_{1k}^{{h_d}}$	New construction of distribution lines (Km)
		$w_{1k}^{{h_d}}$	Percentage of losses of distribution line (%)
Customer		$x_{1k}^{{h_c}}$	Average cost with fuel subsidy (Rial)
		$y_{1k}^{{h_c}}$	Number of customers
		$y_{2k}^{{h_c}}$	Sales of electricit(106 K wh)
		$w_{1k}^{{h_c}}$	Cut of power
		$v_{mk}^{h, h'}$	Material flow from division $h$ to division $h'$(106 K wa)

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More in detail, the parameters used to characterize this supply chain are defined as follows:

${h_s}$: Numerator of division in the supplier level (h_s = 1, 2)

$\boldsymbol{x}_{1k}^{{h_s}}$: Capacity of oil (10³ Barrels) and gas (10⁶ m³) fields of h_s the supplier in kth supply chain.

$\boldsymbol{x}_{2k}^{{h_s}}$: Number of employees from h_sth supplier in kth supply chain.

$\boldsymbol{y}_{1k}^{{h_s}} :$ Oil (10³ Barrels) and gas (10⁶ m³) sold to other companies from the h_sth supplier in kth supply chain.

$\boldsymbol{w}_{1k}^{{h_s}}$: Flaring gas of oil field (10³ barrels) and gas field (10⁶m³) of the h_sth supplier in the kth supply chain.

${h_m}$: Numerator of division in the manufacturer level (h_m = 3, 4, 5)

$\boldsymbol{x}_{1k}^{{h_m}}$: Power nominal of h_m th manufacturer in the kth supply chain (10⁶ Kwh).

$\boldsymbol{x}_{2k}^{{h_m}}$: Number of employees of h_mth manufacturer in the kth supply chain.

$\boldsymbol{w}_{1k}^{{h_s}}$: Flaring gas of oil field (10³ barrels) and gas field (10⁶ m³) of the h_sth supplier in the kth supply chain.

${h_m}$: Numerator of division in the manufacturer level (h_m = 3, 4, 5)

$\boldsymbol{x}_{1k}^{{h_m}}$: Power nominal of h_m th manufacturer in the kth supply chain (10⁶ K wh).

$\boldsymbol{x}_{2k}^{{h_m}}$: Number of employees of h_mth manufacturer in the kth supply chain.

$\boldsymbol{y}_{1k}^{{h_m}}$: Percentage of new construction of power plant of the h_mth manufacturer in the kth supply chain

$\boldsymbol{w}_{1k}^{{h_m}}$: Emissions of NO_x harmful substances of the h_mth manufacturer in the kth supply chain (10³ Kg/10⁶ K wh).

$\boldsymbol{w}_{2k}^{{h_m}}$: Emissions of SO_x harmful substance of the h_mth manufacturer in the kth supply chain (10³ Kg/10⁶ Kwh).

$\boldsymbol{w}_{3k}^{{h_m}}$: Emission of CO₂ harmful substance of the h_mth manufacturer in the kth supply chain (10³ Kg/10⁶ K wh).

${h_t}$: Numerator of the divisions in the transmitters level (${h_t}$ = 6, 7)

$\boldsymbol{x}_{1k}^{{h_t}}$: Capacity of regional company of the h_tth transmitter in the kth supply chain (M wa).

$\boldsymbol{x}_{2k}^{{h_t}}$: Length transmission line of the h_t th transmitter in the kth supply chain (Km circuit).

$\boldsymbol{y}_{1k}^{{h_t}}$: New construction of transmission lines of the h_tth transmitter in the kth supply chain (Km circuit).

$\boldsymbol{w}_{1k}^{{h_d}}$: Loose of transmission line of h_t th transmitter in the kth supply chain (%).

${h_d}$: Numerator of division in the distributer level (h_d: 8, 9, 10, 11)

$\boldsymbol{x}_{1k}^{{h_d}}$: Capacity of distribution lines of h_dth distributer company in the kth supply chain (M wa).

$\boldsymbol{x}_{2k}^{{h_d}}$: Length distribution line of the h_dth distributer in the kth supply chain (Km).

$\boldsymbol{y}_{1k}^{{h_d}}$: Meter of electricity of h_dth distributer in kth supply chain

$\boldsymbol{w}_{1k}^{{h_d}}$: Percentage of losses of distribution line of h_dth distributer in the kth supply chain

${h_c}$: Numerator of division in the customer level (h_c: 12, 13, 14, 15)

$\boldsymbol{x}_{1k}^{{h_c}}$: Average cost with fuel subsidy of the h_cth customer in the kth supply chain (Rial).

$\boldsymbol{y}_{1k}^{{h_c}}$: Number of customers of h_cth customer in the kth supply chain.

$\boldsymbol{y}_{2k}^{{h_c}}$: Sales of electricity of the h_cth customer in the kth supply chain (10⁶ K wh).

$\boldsymbol{w}_{1k}^{{h_c}}$: Cut of power of the h_cth customer in the kth supply chain (minute/year).

$\rm{V_{mk}^{h, h'}}$: Material flow from division $h$ to division $h'$(10⁶ K wa).

The dataset has been collected from power industry company in Iran and the reference year is 2015 (see TAVANIR website for the detailed data). The total emissions due to electricity generation in Iran, the amount and type fuel used in all power plants have been considered in the computation of undesirable output. All the data of the two oil and gas fields (suppliers), power plants (manufacturers), regional power companies (transmitters), distribution companies (distributors) and customers (residential, public, agriculture, industrial) are available in the Tavanir website ^[22]. Supplier inputs are obtained from oil and gas fields statistics of energy industry in Iran. Desirable output is computed as the difference between the average annual production and the amount of oil and gas that are sent to power plants; undesirable output (flaring gas) is calculated with 0.03% rate of the annual production of oil and gas. Information related to the demand fuel of power plants is collected from TAVANIR Company ^[22] in power industry and they are considered as intermediate measure from oil and gas fields to power plants. The capacity of power plants is a proxy of the input capital (for a similar approach see ^[23]). Undesirable outputs for manufacturers are computed based on the amount of electricity produced by the different power plants using different technologies and fuels. Dataset of inputs and desirable output of regional power company are collected from transmission division of TAVANIR company in power industry and losses of transmission line (undesirable output) is estimated with a 3.02% factor based on amount of loose of transmission in Iran. All of data of distribution company are obtained from dispatch division of TAVANIR company in power industry likewise input of customer divisions are collected from TAVANIR company and desirable output of customers are computed as total sale of electricity to residential, public, agriculture and industry divisions but undesirable output is computed by time cut off of electricity in different divisions of consumers in 2015.

The data sets corresponding to the 10 supply chains (DMUs) under analysis are presented in Tables 2–16. Tables 2 and 3 show inputs and desirable and undesirable outputs for suppliers 1 and 2, respectively. In Tables 4–7, we present the data of manufacturer (level 2, 3, 4).Tables 8 and 9 show the data of transmitters with two inputs, one good output and one undesirable output, respectively. Tables 10–13 collect the data on distributors where two inputs, one desirable and one undesirable output are considered. Finally, in Tables 14–16 the data of customers are reported with one input, two desirable outputs and one undesirable output. The material flow or intermediate measure from suppliers to manufacturers, from manufacture’s division to the transmitters from transmitters to distributors and from distributors to the customers are presented in Tables 17-22.

Table 2.  The supplier level-inputs.

DMU	supplier 1 (division 1)		supplier 2 (division 2)
	Capacity(103barrels) $x_{1k}^1$	labor $x_{2k}^1$	Capacity(103barrels) $x_{1k}^2$	labor $x_{2k}^2$
1	2550	3200	7200	2500
2	61200	1300	21600	2500
3	21600	3200	10800	2400
4	32400	3110	6480	1400
5	12600	2800	19440	3000
6	43200	2200	10800	2400
7	46800	2400	10800	1380
8	39600	1600	21600	2250
9	9360	2150	19440	2180
10	64800	2500	6480	2900
Source: category: oil field of iran-wikipedia, https//en.wikipedia.org/wiki/category:oil fields of iran; https//en.wikipedia.org/wiki/category:ntural gas in iran

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Table 3.  The supplier level desirable and undesirable outputs.

DMU	Supplier 1 (Division 1)		Supplier 2 (Division 2)
	Oil sold (103barrels) $y_{1k}^1$	Gas flare(103barrels) $w_{1k}^1$	gas sold (103barrels) $y_{1k}^2$	Gas flare(103barrels) $w_{1k}^2$
1	1739.693	54	1186.216	151.2
2	40572.996	1296	7203.230	345.6
3	8995.883	432	3726.203	183.6
4	26527.191	972	1930.025	140.4
5	4552.857	216	10438.190	367.2
6	23324.391	756	3350.675	183.6
7	17080.471	756	2353.130	172.8
8	15872.914	648	9455.104	345.6
9	6062.772	194.4	9849.593	367.2
10	25603.400	1296	2208.415	140.4
Calculations flaring gas and sold oil and gas.

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Table 4.  Manufacturers level inputs.

DMU	Manufacturer 1 (Division3)		Manufacturer 2 (Divition4)		Manufacturer 3 (Division5)
	Power nominal(106kwh) $x_{1k}^3$	labor $x_{2k}^3$	Power nominal(106kwh) $x_{1k}^4$	labor $x_{2k}^4$	Power nominal(106kwh) $x_{1k}^5$	labor $x_{2k}^5$
1	63224	4070	15408	1600	11903	1200
2	16200	2263	10400	700	2626.952	2600
3	10448	1000	5701.12	3300	16760	2005
4	8022.4	1000	8622.4	3300	8344	2005
5	5184	890	1920.48	900	16417.760	2823
6	13672.88	2300	3312	2500	3936	800
7	966.32	1450	8352	2700	17844.8	890
8	1491.2	1520	10320	2260	16800	1300
9	3872	1500	10590	3600	7072	4100
10	11453.6	3180	6787.200	760	2053.28	1590
Source: http//amar.tavanir.org.ir//tolid and calculations million kilo watt hou.

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Table 5.  Manufacturers level desirable and undesirable outputs.

DMU	Manufacturer 1 (Division 3)
	Percentage of new power plant $y_{1k}^3$	Emissions of Nox (103Kg/106Kwh) $w_{1k}^3$	Emissions of Sox (103Kg/106Kwh) $w_{2k}^3$	Emissions of Sox (103Kg/106Kwh) $w_{3k}^3$
1	12.2	454610.278	23891876.280	288025420.100
2	12.2	302399.805	4207069.806	191952930.500
3	13	235104.740	195553.061	149621794
4	12.2	229464.218	12059407.75	145380628.200
5	73.6	43498.708	38755.471	27536231.770
6	100	256638.343	217529.667	163094448.800
7	85.5	6683.633	5954.829	4230977.926
8	85.5	15138.687	184259.151	9585079.623
9	13	92035.892	76552.691	58572086.910
10	86.6	236364.062	196600.528	150423232.700
Source: http//amar.tavanir.org.ir//tolid and calculations 1000kg/million kilo watt hour.

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Table 6.  Manufacturers level desirable and undesirable outputs.

DMU		Manufacturer 2 (Division 4)
	Percentage of new power plant $y_{1k}^4$	Emissions of Nox (103Kg/106Kwh) $w_{1k}^4$	Emissions of Sox (103Kg/106Kwh) $w_{2k}^4$	Emissions of Sox (103Kg/106Kwh) $w_{3k}^4$
1	85.5	5715.366	5092.145	3618030.390
2	0	283431.105	14895617.700	179572190
3	12.2	174773.192	9070013.802	110729096.200
4	25.2	182851.984	152090.788	116367887.400
5	12.2	49845.037	2619587.603	3158009.070
6	85.5	27420.014	24430.049	17357845.530
7	12.2	273496.466	14373506.370	173277944.500
8	12.2	311634.456	21776302.480	197440862.200
9	98.8	176752.534	147351.908	112467128.500
10	86.6	79593.197	66419.786	50641168.170
Source: http//amar.tavanir.org.ir//tolid and calculations 1000kg/million kilo watt hour.

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Table 7.  Manufacturers level desirable and undesirable outputs.

DMU		Manufacturer 3 (Division 5)
	Percentage of new power plant $y_{1k}^5$	Emissions of Nox (103 Kg/106 Kwh) $w_{1k}^5$	Emissions of Sox (103 Kg/106 Kwh) $w_{2k}^5$	Emissions of Sox (103 Kg/106 Kwh) $w_{3k}^5$
1	73.600	19603.894	17519.680	12447945.190
2	73.600	27423877.76	24433491.25	17360291475
3	98.800	212448.268	690393.877	135090771.800
4	13	140748.540	117070.408	89573051.780
5	87	300157.654	9178172.226	190308335.200
6	13	77463.980	64432.212	49298451.340
7	13	471751.939	21768344.370	299051808
8	13	510495.755	21776302.480	323709891.900
9	13	94829.614	78876.425	60350025.180
10	1.200	59895.401	3147780.793	37947663.670
Source: http//amar.tavanir.org.ir//tolid and calculations 1000kg/million kilo watt hour.

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Table 8.  The transmitter level inputs.

DMU	Transmitter 1 (division 6)		Transmitter 2 (division 7)
	Capacity of regional company (Mwa) $x_{1k}^6$	Length line (Km circuit) $x_{2k}^6$	Capacity of regional company (Mwa) $x_{1k}^7$	Length line (Km circuit) $x_{2k}^7$
1	27542	8704	25086	14697.700
2	41011	9127.800	4938	2244.500
3	13659	8643.400	41011	9127.800
4	16545	10367.900	41011	9127.800
5	6871	2850.700	13659	8643.400
6	14068	11166.400	4938	2244.500
7	14171	5780.500	8762	4480.400
8	10812	8273.300	15407	6095.800
9	25086	14697.700	7367	3776.100
10	10812	8273.300	7716.400	1453.800
Source: http//amar.tavanir.org.ir//entagha.

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Table 9.  Transmitter level desirable and undesirable outputs.

DMU	Transmitter 1 (division 6)		Transmitter 2 (division 7)
	New construction (Km circuit). $y_{1k}^6$	Loose of power (%) $w_{1k}^6$	New construction (Km circuit). $y_{1k}^7$	Loose of power (%) $w_{1k}^7$
1	990	508.845	1541.400	51.880
2	1302.300	200.566	110	301.829
3	1961.500	175.381	1302.300	357.789
4	1596	328.197	1302.300	117.468
5	324	67.759	1961.500	263.987
6	431.300	254.862	110	107.780
7	1576.200	447.605	747	61.919
8	601.200	373.774	386	202.020
9 10	1541.400 601.200	273.358 294.146	110 1453.800	84.462 38.828
Source: http//amar.tavanir.org.ir//entaghal and calculations loose of electricity.

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Table 10.  The distributor level inputs.

DMU	Distributor 1 (division 8)		Distributor 2 (division 9)
	Capacity of distribution line (Mva) $x_{1k}^8$	length distribution line (Km) $x_{2k}^8$	Capacity of distribution line (Mva) $x_{1k}^9$	length distribution line(Km) $x_{2k}^9$
1	7792	40437	4067	60332
2	11349	64702	2330	19739
3	11349	64702	3068	28043
4	8612	12406	1787	8942
5	900	13383	2480	26770
6	11349	64702	3175	15731
7	3639	37153	1444	13785
8	2084	51688	4221	24689
9	7792	40437	1894	18162
10	2690	35606	2084	51688
Source: http//amar.tavanir.org.ir//tozee.

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Table 11.  The distributor level inputs.

DMU	Distributor 3 (division 10)		Distributor 4 (division 11)
	Capacity of distribution line (Mva) $x_{1k}^{10}$	length distribution line (Km) $x_{2k}^{10}$	Capacity of distribution line (Mva) $x_{1k}^{11}$	length distribution line (Km) $x_{2k}^{11}$
1	3325	13761	4492	10052
2	1787	18122	1324	11101
3	3651	32533	900	13383
4	1874	12075	3175	56184
5	3965	32533	3068	28043
6	1324	11101	1894	18162
7	900	13383	11349	64702
8	4067	60332	5395	52340
9	3325	13761	4067	60332
10	4067	60332	5395	52340
Source: http//amar.tavanir.org.ir//tozee.

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Table 12.  Distributor level desirable and undesirable outputs.

DMU	Distributor 1 (Division8)		Distributor2 (Divitson9)
	Meter of electricity $y_{1k}^8$	Power losses (%) $w_{1k}^8$	Meter of electricity $y_{1k}^9$	Power losses (%) $w_{1k}^9$
1 2 3 4 5 6 7 8 9 10	576253 2046151 2046151 1288350 265678 2046151 497281 294579 576253 469733	14.210 7.200 15.570 15.570 13.250 15.57 13.600 11.230 14.210 12.540	576253 323920 631924 345484 662102 513660 429044 368658 513660 347768	8.030 10.400 11.390 10.730 12.670 11.510 11.050 13.330 7.250 11.230
Source: http//amar.tavanir.org.ir//tozee.

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Table 13.  Distributor level desirable and undesirable outputs.

DMU	Distributor 3 (Division10)		Distributor 4 (Divition11)
	Meter of electricity $y_{1k}^{10}$	Power losses (%) $w_{1k}^{10}$	Meter of electricity $y_{1k}^{11}$	Power losses (%) $w_{1k}^{11}$
1	248079	13.590	327034	14.200
2	345484	10.730	208346	7.990
3	429044	11.050	265678	13.250
4	329071	7.670	309704	12.030
5	429044	11.05	631924	11.390
6	208346	7.990	333449	7.250
7	265678	13.25	2046151	15.570
8	550244	8.030	691491	8.100
9	208346	13.590	631924	8.030
10	550244	8.030	691491	8.100
Source: http//amar.tavanir.org.ir//tozee.

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Table 14.  The customer level inputs.

DMU	Customer1 (Division 12)	Customer2 (Division 13)	Customer 3 (Division 14)	Customer 4 (Division15)
	Average cost(Rial) $x_{1k}^{12}$	Average cost(Rial) $x_{1k}^{13}$	Average cost(Rial) $x_{1k}^{14}$	Average cost(Rial) $x_{1k}^{15}$
1	1400	1094.800	1096.400	2802.500
2	1400	1094.800	1096.800	2802.500
3	1400	1094.800	1096.800	2802.500
4	1400	1094.800	1096.800	2802.500
5	1400	1094.800	1096.800	2802.500
6	1400	1094.800	1096.800	2802.500
7	1400	1094.800	1096.800	2802.500
8	1400	1094.800	1096.800	2802.500
9	1400	1094.800	1096.800	2802.500
10	1400	1094.800	1096.800	2802.500
Source: http//amar.tavanir.org.ir//tozee.

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Table 15.  The Customer level desirable and undesirable outputs.

DMU	Customer 1 (division 12)			Customer 2 (division 13)
	Number of customers $y_{1k}^{12}$	Sales of electricity $y_{2k}^{12}$	Cut of power $w_{1k}^{12}$	Number of customers $y_{1k}^{13}$	Sales of electricity $y_{2k}^{13}$	Cut of power $w_{2k}^{13}$
1	1830958	6122.147	778.277	347030	3241.136	147.510
2	6441756	5485.296	725.081	1778416	2903.980	200.178
3	7866277	5821.292	725.323	2168359	3081.860	199.937
4	6560395	4865.888	727.327	1791210	2576.059	198.585
5	3804176	3622.099	752.559	855850	1917.582	169.308
6	8009286	3996.064	734.466	2078242	2115.563	190.588
7	8271676	5563.775	693.427	2196721	2945.528	184.154
8	3602333	6217.991	718.110	962150	3291.877	191.801
9	3213868	3906.777	752.079	691239	2068.293	161.757
10	3683518	3635.504	722.771	953080	1924.679	187.011
Source: http//amar.tavanir.org.ir//tozee and calculations time cut off of electricity

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Table 16.  The Customer level desirable and undesirable outputs.

DMU	Customer 3 (division 14)			Customer 4 (division 15)
	Number of customers $y_{1k}^{14}$	Sales Of Electricity $y_{2k}^{14}$	Cut of power $w_{1k}^{14}$	Number Of customers $y_{1k}^{15}$	Sales Of electricity $y_{2k}^{15}$	Cut of power $w_{1k}^{15}$
1	16364	2700.947	6.956	7663	5942.083	3.257
2	37745	2419.983	4.249	57685	5323.964	6.492
3	51444	2568.217	4.743	65030	5650.077	5.996
4	37480	2146.715	4.155	53509	4722.774	5.932
5	42460	1597.985	8.400	28981	3515.567	5.733
6	45458	1762.970	4.169	73999	3878.533	6.786
7	624532	2454.607	52.355	72330	5400.135	6.064
8	106646	2743.231	21.259	24231	6035.109	4.830
9	54540	1723.578	15.103	30174	3791.871	7.061
10	110055	1603.899	21.595	23562	3528.578	4.623
Source: http//amar.tavanir.org.ir//tozee and calculations time cut off of electricity.

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Table 17.  The material flow (intermediate products desirable outputs) (106 Kwa).

DMU	$v_{{1_{(1, 3)}}j}^{(1, 3)}$	$v_{{1_{(1, 4)}}}^{(1, 4)}$	$v_{{1_{(1, 5)}}}^{(1, 5)}$	$v_{{1_{(2, 3)}}}^{(2, 3)}$	$v_{{1_{(2, 4)}}}^{(2, 4)}$	$v_{{1_{(2, 5)}}}^{(2, 5)}$
1	60.307	0	0	2875.091	220.4	758.293
2	2064.952	203.532	358.519	2336.167	1695.484	258.119
3	2548.744	1724.993	1130.38	129.687	801.96	1462.15
4	2860.549	1507.982	1504.277	932.017	1093.177	724.781
5	503.449	378.483	1765.210	467.063	286.531	1048.213
6	1839.757	35.852	0	1886.773	285.119	597.451
7	16.681	2028.841	6074.007	93.521	1421.775	1891.574
8	0	5307.55	419.537	206.169	1116.091	742.636
9	203.507	102.486	111.235	570.477	1230.004	589.926
10	142.515	15401.05	2053.038	1645.455	705.324	120.806
Source: http//amar.tavanir.org.ir//tolid and calculations million kilo watt hour.

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Table 18.  The material flow (intermediate products desirable outputs) (106 Kwa).

DMU	$v_{{1_{(2, 7)}}j}^{(3, 6)}$	$v_{{1_{(3, 7)}}}^{(3, 7)}$	$v_{{1_{(4, 6)}}}^{(4, 6)}$	$v_{{1_{(4, 7)}}}^{(4, 7)}$	$v_{{1_{(5, 6)}}}^{(5, 6)}$	$v_{{1_{(5, 7)}}}^{(5, 7)}$
1	16849.166	0	0	954.941	0	762.931
2	6641.271	2846.259	0	6081.337	0	1066.752
3	0	7144.31	3791.372	0	2015.572	4703.002
4	4923.416	0	1666.995	3889.655	4277.035	0
5	1174.200	503.228	1069.482	0	0	8238.071
6	8439.133	0	0	1214.901	0	2353.958
7	0	259.243	4179.104	1791.044	10644.237	0
8	550.870	0	0	6689.385	11825.766	0
9	0	2796.766	5426.567	0	3625.006	0
10	7291.361	0	2448.571	0	0	1285.702
Source: http//amar.tavanir.org.ir//tolid and calculations million kilo watt hour

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Table 19.  The material flow (intermediate products desirable outputs) (106 Kwa).

DMU	$v_{{1_{(6, 8)}}}^{(6, 8)}$	$v_{{1_{(6, 9)}}}^{(6, 9)}$	$v_{1_{(6,10)}}^{(6,10)}$	$v_{{1_{(6, 11)}}}^{(6, 11)}$	$v_{{1_{(7, 8)}}}^{(7, 8)}$	$v_{{1_{(7, 9)}}}^{(7, 9)}$
1	11438.225	0	0	4902.096	0	499.798
2	4508.493	1932.211	0	0	0	0
3	0	0	3942.347	1689.577	8042.661	3446.851
4	0	7377.474	3161.775	0	2640.531	0
5	652.777	0	0	1523.146	0	2543.194
6	0	8184.271	0	0	356.886	0
7	10062.973	0	0	4312.703	0	1391.858
8	8402.003	0	0	3600.858	0	4399.742
9	0	0	2633.465	6144.751	813.691	1898.613
10	0	6612.050	2833.736	0	827.812	0
Source: http//amar.tavanir.org.ir//tolid and calculations million kilo watt hour.

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Table 20.  The material flow (intermediate products desirable outputs) (106 Kwa).

DMU	${\cal v}_{{1_{(7,10)}}j}^{(7,10)}$	$v_{{1_{(7, 11)}}}^{(7, 11)}$	$v_{{1_{(8, 12)}}}^{(8, 12)}$	$v_{{1_{(8, 13)}}}^{(8, 13)}$	$v_{{1_{(8, 14)}}}^{(8, 14)}$	$v_{{1_{(8, 15)}}}^{(8, 15)}$
1	1166.195	0	3888.996	2058.880	1715.834	3774.614
2	2907.756	6784.863	1532.888	811.529	676.274	1487.803
3	0	0	2734.506	1447.680	1206.400	2654.080
4	574.437	377.219	897.781	475.297	396.080	871.375
5	5934.119	0	221.944	117.500	97.917	215.416
6	2498.201	713.772	121.341	64.239	53.533	117.772
7	596.511	0	3421.411	1811.335	1509.446	3320.781
8	1885.604	0	2856.681	1512.361	1260.300	2772.661
9	0	0	276.655	146.464	122.054	268.518
10	0	374.062	296.755	157.106	130.922	288.028
Source: http//amar.tavanir.org.ir//tolid and calculations million kilo watt hour.

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Table 21.  The material flow (intermediate products desirable outputs) (106 Kwa).

DMU	$v_{{1_{(9, 12)}}j}^{(9, 12)}$	$v_{{1_{(9, 13)}}}^{(9, 13)}$	$v_{{1_{(9, 14)}}}^{(9, 14)}$	$v_{{1_{(9, 15)}}}^{(9, 15)}$	$v_{{1_{(10, 12)}}}^{(10, 12)}$	$v_{{1_{(10, 13)}}}^{(10, 13)}$
1	169.931	89.964	74.970	164.933	396.506	209.915
2	656.952	347.798	289.832	637.630	988.637	523.396
3	1171.931	620.434	517.029	1137.463	1340.398	709.622
4	2508.341	1327.945	1106.621	2434.567	1331.512	704.918
5	864.686	457.775	381.490	839.254	2017.600	1068.141
6	2782.652	1473.169	1227.641	2700.809	849.388	449.376
7	473.232	250.534	208.779	459.311	202.814	107.372
8	1495.912	791.954	659.961	1451.915	641.105	339.409
9	645.528	341.750	284.792	626.542	895.378	474.024
10	2248.097	1190.169	991.808	2181.977	963.470	510.072
Source: http//amar.tavanir.org.ir//tolid and calculations million kilo watt hour.

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Table 22.  The material flow (intermediate products desirable outputs) (106 Kwa).

DMU	$v_{{1_{(10, 14)}}j}^{(10, 14)}$	$v_{{1_{(10, 15)}}}^{(10, 15)}$	$v_{{1_{(11, 12)}}}^{(11, 12)}$	$v_{{1_{(11, 13)}}}^{(11, 13)}$	$v_{{1_{(11, 14)}}}^{(11, 14)}$	$v_{{1_{(11, 15)}}}^{(11, 15)}$
1	174.922	384.844	1666.713	882.377	735.314	1617.692
2	436.163	959.559	2306.820	1221.257	1017.714	2238.972
3	591.352	1300.974	574.456	304.124	253.437	557.560
4	587.432	1292.350	128.254	67.899	56.583	124.482
5	890.118	1958.259	517.870	274.166	228.472	502.638
6	374.830	824.406	242.682	128.479	107.066	235.545
7	89.477	196.849	1466.319	776.276	646.905	1423.192
8	282.841	622.250	1224.292	648.155	540.129	1188.283
9	395.020	869.043	2089.215	1106.055	921.713	2027.768
10	425.060	935.133	127.181	67.331	56.109	123.441
Source: http//amar.tavanir.org.ir//tolid and calculations million kilo watt hour.

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According to fuzzy–weighted average definition, the fuzzy index has been calculated and the entity weights, division weights and the overall weights of the 15 divisions are presented in Table 23.

Table 23.  The weights of the divisions.

Supply chains	Importance	Division	Division	Overall
Entity	Weights		Weight	Weight
Suppliers	0.15	S1	0.45	0.0675
		S2	0.55	0.0825
Manufacturers	0.20	M1 M2 M3	0.35 0.30 0.35	0.07 0.06 0.07
Transmitters	0.20	T1 T2	0.65 0.35	0.13 0.07
Distributers	0.15	D1	0.25	0.0375
		D2	0.30	0.045
		D3 D4	0.20 0.25	0.03 0.0375
Customers	0.30	C1	0.27	0.081
		C2	0.24	0.072
		C3 C4	0.20 0.29	0.06 0.087

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5.2.   Results

We now describe the results obtained in the new proposed approach. First the model is applied to estimate the efficiency score of supply chain 10 (DMUS). All models are solved by a linear programming solver using the GAMS software on a 8 GB RAM, 2.0 GHz desktop computer, the runtime of the computation in this study is negligible in model. The results are listed in Table 24.

Table 24.  The cooperative efficiency scores of supply chains (DMUs).

DMU	$\, {\theta _o}\,$	$\varphi _o^{Sup1}$	$\varphi _o^{Sup2}\,$	$\varphi _o^{Man1}$	$\varphi _o^{Man2}\,$	$\varphi _o^{Man3}$	$\, \varphi _o^{Tra1}$	$\varphi _o^{Tra2}\,$	$\varphi _o^{Dis1}$	$\varphi _o^{Dis2}\,$	$\varphi _o^{Dis3}\,$	$\varphi _o^{Dis4}\,$	$\varphi _o^{Cus1}\,$	$\varphi _o^{Cus2}\,$	$\varphi _o^{Cus3}\,$	$\, \varphi _o^{Cus4}$
1	0.75	1	0.39	0.50	1	1	0.18	1	0.14	1	0.41	1	0.91	1	1	1
2	0.69	1	0.73	0.01	0	1	0.58	0.36	1	0.45	1	1	0.92	0.86	1	0.82
3	0.83	0.66	0.75	1	0.30	1	1	0.10	0.46	1	1	1	1	1	1	1
4	0.77	1	1	1	1	0.55	0.43	0.30	1	1	1	0.20	0.82	0.79	0.93	0.82
5	0.84	0.67	1	1	1	1	1	1	1	1	1	1	0.58	0.62	0.46	0.54
6	0.82	0.99	0.64	1	1	1	0.15	1	0.46	1	1	1	0.91	0.91	0.98	1
7	0.90	0.72	1	1	1	1	1	0.32	1.13	1	1	1	1	1	1	1
8	0.73	1	1	1	1	0.66	0.14	0.05	0.04	0.39	1	0.65	1	1	1	1
9	0.65	1	1	1	1	0.82	0.50	0.04	0.14	1	0.34	0.64	0.61	066	0.38	0.46
10	0.68	0.63	1	1	1	1	0.18	1	0.57	0.44	1	0.65	0.60	0.58	0.44	0.61

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The first column of Table 24 represents the global efficiency score of the supply chain. It can be easily seen that no DMU can reach efficiency equal to 1. This implies that all the 10 supply chains can improve their performance in some of the divisions. Supply chain number 7 is the one that reaches the highest score (0.90) while supply chain number 9 is the worst performing one. Columns from 2 to 15 report the efficiency scores of all the 15 divisions. In this way, we can exploit which divisions are more efficient in the various supply chains (looking at the data in columns) and, in parallel, per each DMU which are the divisions that are more efficient and which are the ones to be improved.

Looking vertically in the tables, the more efficient divisions are divisions 3, 10 and 4, with efficient values (80% and 90% of the total), respectively. This implies that Manufacturers 2 and 3 and Distributer 3 are the more efficient ones concerning to the other divisions. Just three efficient units (30%) are obtained in the case of divisions 6, 8 and 12 (Transmitter 1, Distributer 1 and Customer 1, respectively).

Looking horizontally at the same table, it is possible to see, for each supply chain, the number of efficient divisions. As expected, DMU 7 has the highest efficiency score and the highest number of efficient divisions (12/15) while DMU 9 has the worst efficiency score and the worst number of efficient divisions (5/15). As an illustration, we consider the seventh supply chain (DMU7).

As the second column of Table 24 shows, the efficiency score is θ = 0.90 and this DMU has 12 efficient divisions, while divisions 1, 7 and 8 are inefficient (0.72, 0.32, 0.13, respectively). It is possible to compute the values that will render efficient this DMU. In particular, the undesirable output of oil field (gas flaring) could be reduced to 0.72 (756) = 544.32, the undesirable output of the second transmitter could decrease from 61.92 to 61.92 (0.32) = 19.81 and the undesirable output of the first distributor could reduce from 13.6 to 0.13 (13.6) = 1.77.

Besides, we consider the results of slack variables in the intermediate measures, S (1, 3) = −836.28.

S (1, 4) = 1948.21, S (1, 5) = 5931.98. These values highlight that, for improving the efficiency score, the intermediate measures sent from the oil field of supply chain 7 (DMU7) to manufacturer 1 should decrease, while this measure should increase towards the second and third manufacturers. Looking at the slack variables S (3, 7) = 0, S (4, 7) = 1791.04 and S (5, 7) = 660.63, for DMU7 it can be observed that electricity flows from manufacturers 2 and 3 sent to the second transmitter can increase by 1791.04 and 660.63 106 kwh, respectively. As concerning slack variables related to the connection between transmitters and distribution companies, the only inefficiency is obtained from the first transmitter to the first distributer (S (6, 8) = −8967.26), the other slack variables are null.

Finally, looking at slack variables of intermediate measures between distributors and customers, all the quantities from distributer 1 to the different final consumers have to be increased (S (8, 12) = 3048.87, S (8, 13) = 1614.11, S (8, 14) = 1345.09, S (8, 15) = 2959.20).

A similar analysis can be put forward to the remaining supply chains. According to the results of the slack variable in the inputs constraints this value shows that for improving the efficiency score, the first input of the oil field in supply chain 7 (DMU7) should decrease from 46800 to 27244.737.

Looking at the slack variables for DMU7, S₁⁻ (8) = 199.54, S₂⁻ (8) = 11297.82. It can be seen that the first input of distributer 1 should decrease from 3639 to 3439.446 and the second input should decline from 37153 to 25855.180, the other slack variables in input constraints are null. Specially, we consider the results of variables λ and μ in supply chain 7(DMU7) as follows:

µ (1, 2) = 0.025, µ (7, 2) = 0.482, µ (8, 5) = 0.757, λ (1, 2) = 0.975, µ (7, 2) = 0.482, λ (8, 5) = 0.243.

These values shows that, for improving the efficiency score, the first supplier (oil field) and the second transmitter inputs of supply chain 2 (DMU2) are utilized for cleaning up flaring gas and decline loose of power in supply chain 7 (DMU7).As similar the first distributer active level of supply chain 5 (DMU5) scaling down to decrease undesirable outputs while the other undesirable outputs have remained active in the supply chain (DMU7).

Let us now try to detect the determinants of the success of supply chain 7 (DMU7) in terms of efficiency. DMU7 presents the higher penetration level of RES concerning the other DMUs.

Approximately, supply chain 7 comprises 43% power plants operated by renewable technology. In particular, this DMU contains 29% wind, solar and 14% hydropower plants that produce a considerably amount of electricity in production processes without pollution emission. The use of renewable plants limits the needs of fossil fuels like gas and diesel and limits greenhouse gas emissions.

It is worth mentioning that supply chain 7 as the best performing unit has the most renewable power plants, while supply chain number 5 belongs to the second-highest efficiency score contain 25% solar, and wind power plants, the other hand supply chain number 5 has the number conventional power plants consume fuel oil, natural gas and diesel more than DMU number 7, therefore supply chain number 5 produce huge amount of air pollutants such as sulfur oxides, nitrogen oxides and carbon dioxides. As illustration, we consider the ninth supply chain (DMU9). According to Table 24 supply chain number 9 is the worst performing unit with efficiency score θ = 0.65 and this supply chain has seven power plants: one of them utilizes hydro technology and one power plant operates with renewable technology while the other power plants consume fossil fuels to produce electricity. More in detail, supply chain 9 includes 14% of wind, solar and 14% of hydropower plants, but power plants produce minimal intermediate measures in different divisions while the rest is composed of nonrenewable plants with high emission levels.

Now we investigate what factors inspire the highest efficiency score in supply chain number 7 (DMU7). Indeed, it is important to know which factors effect on efficiency score specifically, we are interested in knowing which indexes play an important role in the most efficient of the supply chain. According to table 23 DMU7 comprise 80% efficient divisions.the second supplier (gas field), all of the manufacture (power plants), the first transmitter, the second, third and fourth distributer and customers of residential, public, agriculture and industry divisions are efficient in supply chain 7. Firstly, the gas field of supply 7 transfer approximately 60% average annual production of gas to power plants to electricity production and power plants transmit about 63% annual maximum capacity to regional power companies.

Secondly, undesirable outputs of manufacture number1 have the least amount of pollution emissions of NO_X, SO_X and CO₂ gases between 10 supply chains. As concerning distributers capacity, the least capacity of distribution line in 10 supply chains belongs to second and third distribution companies in supply chain 7 (DMU7) and desirable outputs in residential, public and Agriculture divisions contain the most amount in the whole of supply chains. Thirdly, amount of oil and gas transmit to the third power plant, the electricity sent to the first transmitter and electricity dispatch to the residential division has the most measure in all of the supply chains.

Finally, according to Table 24, the first column shows the weights of entities to supply chains. The most weights of entities have been assigned to customer, manufacture, transmitter and supplier divisions respectively, therefore customer divisions have a fundamental role to distinguish the most efficient supply chain. Accordingly, if the supply chain wants to obtain the highest efficiency, it should pay attention noticeable to customer and manufacture divisions.

According to the model proposed in Section 4, a further analysis has been conducted by considering a non-cooperative network in which each member of each stage is evaluated separately by model (8). After finding the efficiency scores of each division of the network, the efficiency of each DMU is computed as a weighted average of the efficiency scores of each division by (9) equation. It has been proved that this second methodology has lower efficiency scores than the previous one (for proof see ^[21]). In Table 25 the results of this second analysis have been reported.

Table 25.  The non-cooperative efficiency scores of the considered supply chains (DMUs).

D M U	$\phi _o^{{h_s}}$	$\phi _o^{Sup1}$	$\phi _o^{Sup2}\,$	$\phi _o^{Man1}$	$\phi _o^{Man2}\,$	$\phi _o^{Man3}$	$\, \varphi _o^{Tra1}$	$\phi _o^{Tra2}\,$	$\phi _o^{Dis1}$	$\phi _o^{Dis2}\,$	$\phi _o^{Dis3}\,$	$\phi _o^{Dis4}\,$	$\phi _o^{Cus1}\,$	$\phi _o^{Cus2}\,$	$\phi _o^{Cus3}\,$	$\, \phi _o^{Cus4}$
1	0.73	1	0.39	0.50	1	1	0.17	1	0.14	0.57	0.41	1	0.91	1	1	1
2	0.67	1	0.73	0.01	0	1	0.58	0.36	1	0.63	1	1	0.92	0.86	1	0.82
3	0.82	0.66	0.75	1	0.30	1	1	0.10	0.46	0.73	1	1	1	1	1	1
4	0.76	1	1	1	1	0.55	0.43	0.30	1	0.69	1	0.20	0.82	0.79	0.92	0.82
5	0.84	0.67	1	1	1	1	1	1	1	0.96	1	1	0.58	0.62	0.45	0.54
6	0.82	0.98	0.64	1	1	1	0.15	1	0.46	0.74	1	1	0.91	0.91	0.98	1
7	0.89	0.72	1	1	1	1	1	0.32	1.13	0.81	1	1	1	1	1	1
8	0.73	1	1	1	1	0.66	0.14	0.05	0.35	0.46	1	0.65	1	1	1	1
9	0.62	1	1	1	1	0.82	0.50	0.03	0.14	0.51	0.34	0.65	0.61	066	0.38	0.46
10	0.68	0.63	1	1	1	1	0.18	1	0.57	0.39	1	0.65	0.60	0.57	0.44	0.61

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Looking at Table 25, it can be easily checked that the ranking between the 10 supply chains remain unchanged, even if the efficiency scores are slightly lower. It can be noticed that DMU6 and DMU3 in the non-cooperative model have the same efficiency scores. Nevertheless, looking at the efficiency scores of the divisions, DMU6 has 7/15 efficient divisions while DMU3 has 9/15 efficient divisions. In comparison with the overall model, the non-cooperative model can have a more discriminative power concerning the single divisions but a less discriminative on concerning the overall efficiency score. Similar results can be observed by comparing DMU1 and DMU8. Figure 3, present the efficiency scores measured by the overall model of supply chains DMU 10.

Figure 3.  The overall efficiency scores for 10 supply chain.

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6.   Conclusions

An appropriate performance measurement system is an important requirement for the effective management of a supply chain. To achieve this, the performance evaluation of the entire supply chain is extremely important. This means utilizing the combined resource of the supply chain members in the most efficient way helps to provide competitive and cost-effective products and services. Recently several studies have employed DEA approaches for incorporating undesirable outputs into efficiency and productivity change analysis. This model presents both the overall efficiency score of a supply chain and individual efficiency score of its partners at the same time taking into account undesirable outputs under a week disposability assumption. The proposed multi-stage DEA approach could evaluate the efficiency of a sustainable supply chain when there is an arbitrary number of supplier, manufacturer, transmitter, distributor and customers as each stage have unequal weights. Also, the proposed model can enable decision- makers to simultaneously minimize environmental harmful impact and maximize operational performance while meeting customers’ satisfaction. In particular, this study proposed an approach to sustainability assessment of supply chain which the first priority was environmental performance and the second priority was operational performance. Meanwhile, the two issues of privatization and competition in power industry sectors play an important role in global markets. As an application, this study analyzes the behavior of the Iranian power industry by subdividing the industry into different regions (each region represents a supply chain or DMU) and measures the performance of these regions by considering their electricity utilization and environmental protections. Some insights can be obtained from the analysis to improve the performance and in particular new investments in clean technologies could reduce the undesirable outputs that affect the performance of the different supply chains.

The proposed approach has methodological limitations in leading environmental performance assessment. The source energy is different among districts. Each region has its essential structure and different conditions for business activity. For instance, southern regions in Iran have noticeable energy sources and the high capacity of power plants respect to other regions. Such regional difference effects on the number of efficiency measures in each regional.The problem considered in this study needs to the further researches in future. Similarity, this study can be conducted for green supply chain management evaluation in the presence of dual-role factors and non-discretionary factors.