Selection of the best supplier with the help of random data envelopment analysis (case study: Khatam Al-Anbia construction site)

Subject Areas : Applied Mathematics Modeling

Ali Izadikhah ¹ (Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran)
Mehrzad Navabakhsh ² (Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran)

Received: 2023-06-10 Accepted : 2023-07-20 Published : 2024-06-15

Keywords: supplier, Khatam headquarters, Stochastic Data envelopment analysis, DEMATEL, network analysis process,

Abstract :

Data envelopment analysis is a non-parametric method for evaluating the efficiency of decision-making units, which recognizes the relative efficiency of decision-making units based on mathematical programming. Although data envelopment analysis has many advantages, one of the weaknesses in the data envelopment analysis model is that, in fact, data envelopment analysis does not allow random changes in input and output. However, in many. Finally, the results of determining the weight of criteria and sub-criteria with the help of ANP and the results of ranking the suppliers with the help of stochastic DEA have been compared and to select the supplier The final decision will be taken by the appropriate provider. Using the random data envelopment analysis technique, to evaluate and rank 20 supplier companies of Khatam al-Anbia construction site during the period of 1389-1400. In this research, we introduced data envelopment analysis with random data, random planning, efficiency Randomness and random ranking have been discussed. In this research, random data were determined by using mean and variance estimates for different inputs and outputs, and finally, random models and random super-efficiency were converted into deterministic models. Using the software, we have determined the efficiency and ranking of the decision-making units. The results showed that in five levels α = 0.1, α = 0.2, α = 0.3, α = 0.4, α = 0.5, Amitis company has the highest efficiency rating and Madesa company has the lowest efficiency rating.

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Selection of the best supplier with the help of random data envelopment analysis (case study: Khatam Al-Anbia construction site)

 

Abstract

Data envelopment analysis (DEA) is a non-parametric method used to evaluate decision-making units' efficiency through mathematical programming. However, DEA's limitation lies in its inability to handle random fluctuations in input and output. To address this, a research study aims to develop an evaluation approach considering the inherent variability encountered in practical scenarios. By incorporating error levels, the results obtained from DEA become probabilistic, with higher error levels reducing confidence in efficiency metrics. The research focuses on identifying the optimal supplier for goods and services by determining criteria and sub-criteria, establishing their relationships using Dimtel's technique, and assigning weights through Analytic Network Process (ANP). The most critical criteria are selected using ANP to rank the suppliers using stochastic DEA. The study evaluates and ranks 20 supplier companies associated with the Khatam al-Anbia construction site during the period of 2010-2021. Randomness in data, planning, efficiency, and ranking is thoroughly discussed, with random data generated based on estimated means and variances for different inputs and outputs. Deterministic models are derived from the random models and random super-efficiency, allowing for the determination of efficiency and ranking using specialized software. The results reveal that Amitis company achieves the highest efficiency rating across five levels (α = 0.1, α = 0.2, α = 0.3, α = 0.4, α = 0.5), while Madesa company exhibits the lowest efficiency rating.

Keywords: Dematel, supplier, network analysis process, stochastic Data Envelopment Analysis, Khatam headquarters

 

1 Introduction

This collection is based on the mission of guarding the Islamic revolution, focusing on the jihadi spirit, self-health, and honesty. It aligns with the country's 20-year vision document and aims to achieve Iran's Horizon 2025 goals with a resistance economy approach. As an experienced, sophisticated, and capable specialized collection, it has successfully employed domestic contractors and trained qualified managers for implementing national projects in various sectors, including oil, gas, petrochemicals, industry, mining, gas transmission lines, roads, runways, ports, dams, and marine structures. Despite facing cruel and arrogant sanctions over three decades, this collection has achieved remarkable milestones in development, independence, self-sufficiency, and pride for the Islamic homeland. It has completed over 1800 important infrastructure projects using the latest technical and executive methods, adhering to standards and project management practices. It has successfully implemented numerous deprivation removal projects nationwide, contributing to the construction and prosperity of the beloved country. The Khatam Al-Anbiya construction camp is fully prepared to efficiently complete large and complex projects with a committed, experienced, and knowledgeable workforce, along with advanced facilities, equipment, and machines. It ensures compliance with all technical and engineering specifications, standards, and offers suitable implementation methods, including EPC. Furthermore, this capability is expandable, enabling support for Muslim, neighboring, and friendly countries through the provision of technical and engineering services.

 

2 Statement of the problem

The purpose of selecting the supplier(s) is to use the most capable suppliers with the lowest cost to achieve the goal and meet the needs. In this research, the goal is to provide a regular and step-by-step method for this work. The presented method is completely general and comprehensive and can be applied in any case. But the details of the supplier selection process may vary from case to case. Since Khatam Al-Anbiya construction site, during its more than three decades of activity, many construction projects in the fields of dams and water networks, bridge construction, rail and road infrastructure, water, oil and gas transmission lines and refinery construction, He has presented tunnels and subways to the people. Therefore, the discussion of choosing a supplier in Khatam camp is very important and vital in order to maintain the quality of the projects and comply with the schedule. The proper selection of suppliers has a great impact on the reduction of production costs and the competitiveness of the organization, and in order to use the best suppliers in the projects of the Khatam Al-Anbia construction camp, it is necessary that the suppliers are selected based on their work areas, capacity and capabilities be ranked. In this research, the DEMATEL - ANP - DEA and SDEA methods are used to evaluate and rank the supply companies of Khatam Al Anbia Construction Base. The main purpose of this research is to select the best supplier and rank 20 supplier companies of Khatam Al Anbia construction site using the Random Data Envelopment Analysis (SDEA) approach. It should be noted that the parameters of random inputs and outputs of this research using Non-random inputs and outputs of 20 companies have been estimated. Finally, the results of the non-random model will be compared with the random model.

 

3 Research conceptual model

 

 

 

 

 

 

 

 

The geographical scope of this research on 20 supplier companies of Khatam Al-Anbia Construction Base includes:

Table 1: The Companies

1- Iran Pichkar Garmsar company	6- Pars Gem Armor Company	11- Behin Folad Gostar Ati Company	16- Yazd Electrode Company
2- Iran Pitch Yazd Company	7-Merrick Galvanized Company	12- Pars Pamchal Company	17- Ama company
3- Iran Tawheed Saveh Company	8- Rakor company	13-Nili Fam Ray Company	18- Welding exploration company
4- Sahand Pulad Company of Tabriz	9- Polad Pichkar company	14-Amitis company	19-Zanjan Mefnoli Industries Company
5- Sepand Pich Company, Yazd	10-Madesa company	15-Bajak company	20-Meshbak Pardazan company

 

3 Review of research literature

In a competitive market, for companies that want to increase quality and reduce costs, what is important is choosing the best supplier. What was mentioned is the reason for many companies in the evaluation and selection of suppliers. Each supply chain can be managed in different ways, while choosing the best supplier is very important in each supply chain, transportation cost, production time, order cost, quality level, etc. played an important role in supplier selection. Ho et al. (2010) have presented a method to evaluate suppliers and select them in multi-criteria decision making. Zulqadri et al. (2011) have considered supplier selection in product development projects. The current developments in the DEA technique and its wide application have attracted the attention of many scientists in both theoretical and practical aspects. Therefore, it has been used in many fields to evaluate the performance of different organizations. This method, the DEA technique, was first discussed in the CCR article by Charnes et al. (1997) and has since been developed by various researchers. The DEA technique has been widely used in calculating the relative efficiency of a set of decision-making units (DMU) that produce multiple outputs using multiple inputs. Since the issue of supply chain is of special importance in the industry, this issue has been discussed, developed and investigated by researchers from different aspects.

Based on the assumed methodology, the fuzzy network analysis method is used to obtain the importance of supplier selection criteria. This method can easily adapt the existing internal relationships between basic activities (Abdini et al., 2011). Ghazizadeh et al., in an article entitled "Analysis of supply chain management using D-Mettel technique", first reviewed the four supply chain approaches of lean, agile, resilient, and green and then integrated the four approaches of supply chain management. The supply was done using the D-Mettel technique. In a research, Shahroudi presented a mathematical model for selecting suppliers using the integrated approach of data coverage analysis and total cost of ownership. In this research, the information related to auto parts companies has been investigated using a strategic approach that can reduce the total cost of ownership, and using the data coverage analysis approach, the most efficient supplier with the lowest total cost of ownership has been introduced has been. Rooh Bakhshi et al. in an article titled "Evaluation and ranking of the most suitable criteria for selecting logistics service providers with the approach of developing quality and fuzzy performance" by presenting a tangible and reliable framework to collect and rank appropriate criteria and sub-criteria for selecting suppliers The logistics service provider paid from among the available options. In this research, seven main criteria and eighteen sub-criteria of collection, evaluation, and ranking have been ranked. In 2014, Dej et al. conducted a research entitled "Ranking of suppliers based on selected indicators of the dairy industry in Zanzibar". Green supply (case study in Sobh Sefid company) have worked. In this article, using multi-criteria decision-making and considering product criteria including price, quality, packaging, production capacity, and environmental criteria, including the implementation of the waste system, the purchase of environmentally friendly materials, and the environmental management system framework. In order to evaluate the suppliers in Shiraz milk and dairy companies, it is presented. In this framework, first the effective criteria are identified by the experts, and then using the fuzzy AHP method, the weights of the criteria are determined and compared, and finally, using the TOPSIS technique. Fazi was used to rank the suppliers. In the end, the results showed that quality and price criteria have the highest weight and suppliers have the highest priority.

Mohghar, Afzalian (2013) evaluated and selected suppliers in the supply chain using fuzzy multi-criteria decision making techniques, Afsana Baha (2008) investigated the relationship between the elements of information sharing and competitive strategies and the performance of the supply chain in the organization. Ali Mohghar, Mehdi Afzalian (2013) "Evaluation and selection of suppliers in the supply chain using the fuzzy multi-criteria decision making technique" scientific articles of management. Ramzanzadeh and his colleagues (2014) discuss fuzzy random variables as inputs and outputs of data envelopment analysis in their research, these variables are considered as extended L-R fuzzy random numbers with a known distribution. Abedifar and Khataei (1379) in their research, using the random frontier method, estimates the technical efficiency of the banking industry in Iran and concludes that specialized banks are more efficient compared to commercial banks and the technical efficiency of the relationship It has a direct relationship with the type of bank and the ratio of branches located in Tehran, and it also has an inverse relationship with the ratio of facilities granted in the form of mudarabah and civil participation and the employment of labor with at least a bachelor's degree. Abbaszadeh et al. (2017) used TOPSIS and DEMATEL to evaluate and select suppliers. Fallahpour et al. (2017) developed an integrated FTOPSIS-FPP model for sustainable supplier selection.

Dixon's research can be mentioned as the first research in the field of supplier selection and its criteria. Shiver and Shi evaluated suppliers using a multi-criteria composite model. They obtained the criteria's dependence using the network analysis process (ANP) and the criteria's dependence, the weights of each of them, and in the second step, using the preference method based on similarity to the ideal solution (TOPSIS), they prioritized did the criteria,] 6 pp. [761-749] Zimmer et al. (2015) Sustainable supplier management - a review of models supporting sustainable supplier selection, monitoring and development. Zdach Chi (2016) An integrated method for supplier selection: the case of a manometer manufacturer in Taiwan Govindan et al. (2017) Application of data envelopment analysis models in supply chain management: a systematic review and Tianyu Liu et al. (2017) Supplier Selection Evidence Based on DEMATEL and Game Theory Dobbs and Verosmarty (2020) Supplier Selection and Comparison of DEA Modelsmeta-analysis.

In their study, Deshmukh and Sonapwar (2019) used the fuzzy hierarchical analysis method to rank green suppliers in Indian industries. Avasti and Kanan (2016) evaluate green supplier development programs in an Indian automobile company and criteria such as green design by the supplier, environmental capability of the supplier, compliance with environmental and social standards by the supplier, supplier programs for Green development and supplier participation in green development activities are introduced for supplier development. Ke Hoon Lee (2015) Measuring Technical, Environmental and Environmental Efficiency for Supplier Selection: Extension and Application of Data Envelopment Analysis. Akman (2015) identifies the suppliers who should be involved in green supplier development by evaluating and segmenting the suppliers of the Turkish automotive industry. Supplier development strengthens relationships between customers and suppliers and creates mutual trust, which in turn leads to better communication links and strategic information sharing. Supplier development provides a common understanding of innovation and planning, which in turn strengthens the technological capability of the supply network (Reid and Walsh, 2002).

Today, it is difficult for organizations to survive or gain competitive advantage without improving supplier performance and buyer-supplier relationships. But many of them fail to get the maximum benefit from supplier development due to the existence of obstacles (Dalloy and Kant, (2017b preferred). The concept of supplier development was first developed by Linders (1966) to describe the decision of manufacturers to increase the number of suppliers, with the aim of improving performance. The Dimtel method was used in order to investigate the internal relationships among the criteria, to build a network relationship map (Hu, Tsai, Tzeng et al., 2011). Dimtel's method, which is developed based on graph theory, enables the decision maker to plan and solve the problem graphically in such a way that the related factors are categorized based on cause and effect groups, in order to better understand the causal relationships. become (Pedro, Pola, Mbuler, et al., 2009). Using the subject literature, Wood determined 30 criteria for evaluating and selecting equipment suppliers and petrochemical industry development projects, and then using flexible entropy, fuzzy TOPSIS and intuitive fuzzy TOPSIS approaches, he weighted the thirty criteria and finally companies Rated the supplier.

In the field of supplier selection, Rao and Kasir classified a list of 60 topics into 6 groups, ease of communication, financial and economic criteria, capabilities and capacities, reliability, communication between the buyer and the supplier, and services. (Romelfanger and Hansech, (1989). Munzka, Trend and Handsfield (2005) consider supplier selection as the basic task of purchasing. According to Mendoza (2007), one of the essential (yet complex) tasks in the purchasing function, which plays a fundamental role in the success or failure of an organization, is the selection of suppliers who are able to provide the requested items, with the required specifications. Zhang et al. used distance intuitive fuzzy entropy approach to rank information technology service providers. As the literature review has shown (Giunipero et al., 2019), a significant stream of reviews focuses on supplier evaluation support. And a large number of methods are used to support purchasing decisions, the most common approaches being Analytic Hierarchy Process (AHP) and DEA.

 

4 Research implementation method

The basis of every science is its knowledge method, and the validity and value of the laws of every science is based on the knowledge method in which the science is used. (Ezzati, 2016). In fact, it can be said that the effectiveness of a research work depends on the right choice of the research method that is suitable for that specific type of research. The research being studied is an applied research in terms of its purpose and results, because when we do research with the aim of having the results of the research findings to solve the problems in the organization, that research is considered applied, on the other hand, the research method is a descriptive method. Because library studies have been used in it and it is placed in the applied research group in terms of type. The main purpose of this research is to evaluate the efficiency and ranking of 20 supplier companies of Khatam Al-Anbia construction site using random DEA for the years 2010-2021.

 

4.1 Selection of variables

Each unit (production, service, etc.) acquires inputs and creates outputs, therefore, in a general state, the set of variables affecting the performance of each company can be divided into two categories: input and output. considered output. In addition, the outputs may not always be positive and sometimes there are negative outputs as well. To evaluate electricity distribution companies, variables are needed that can show the correct result of the company's performance. In fact, the selection of input and output variables is one of the most important steps in the evaluation of electricity distribution companies. The lack of correct selection of variables The requirement invalidates the evaluation results between electricity distribution companies (Omrani and Qarizadeh, 2013). The selection of the variables of this research is based on the study of the set of research conducted in the supply companies of Khatam Al-Anbia Construction Base. We define inputs and outputs as follows:

Table 2: Input and output variables

Input variables (X_i)		Output variables (Y_r)
Variable name	variable description	Variable name	variable description
Time	Supply according to schedule	Quality	Providing products according to customer standards and demands
Cost	Product at a reasonable price	Production	The capacity to produce and develop new products
		Services	after sales service

 

4.2 Analysis of research data

The most important factor determining the method of analysis is the analytical model made by the researcher and the chosen method of analysis. The analysis model, according to which the method of analysis is selected, determines what information and how to analyze it. The research analysis method or methods are chosen according to its goals, hypotheses and analytical model. In addition, the use of different tools in the analysis can be effective in the accuracy of the analysis method. That is, while using the best method, it should be used along with the most appropriate tool, because the choice of method and tool is of particular importance and the results of the analysis depend entirely on the methods and tools. (Ezzati, 1386: 74) In the present study, the identified criteria and sub-criteria are presented in the form of a network analysis model. ANP analysis technique has been used to achieve the goal of the research. The results of this analysis are presented in this chapter. The Super Decision network analysis software was used to analyze the obtained data.

Effective and influential criteria in the selection of suppliers of Khatam al-Anbia construction site have been identified. In the first step, the main criteria have been identified, which are: quality, service, cost, reliability, production, strategic obstacles, delivery, technology, agility, flexibility. Adaptability, employees, responsiveness, geographical location, ISO, risk, time, capacity, experience, economic factors, materials and equipment. So that a total of 20 criteria have been selected. In this research, the technique of network analysis (ANP) has been used to determine the weight of the criteria. The network pattern of the model is designed using ANP technique in Superdesign software.

Calculation of direct correlation matrix (M): When the opinion of several experts is used, the simple arithmetic mean of the opinions is used and we form the direct correlation matrix or (M).

Table 3: Direct correlation matrix (M) of the main criteria

 

Calculation of normal direct correlation matrix: M = α*M ̂

First, the sum of all rows and columns is calculated. The inverse of the largest number of rows and columns forms k. According to Table 3-4, the largest number is 3.9, and all values in the table are multiplied by the inverse of this number to make the matrix normal.

 

ð M = 0.2564*

Calculation of the complete correlation matrix: To calculate the complete correlation matrix, the same matrix (I) is formed first. Then we subtract the same matrix from the normal matrix and invert the resulting matrix. Finally, we multiply the normal matrix by the inverse matrix:

T=  

Table 4: Complete correlation matrix (T) of the main criteria

 

 

4.3 Display the map of network relations

A threshold value must be calculated to determine the Network Relationship Map (NRM). With this method, partial relationships can be ignored and the network of significant relationships can be drawn. Only relations whose values in matrix T are greater than the threshold value will be displayed in NRM. To calculate the threshold value of relationships, it is enough to calculate the average values of the matrix T. After the intensity of the threshold is determined, all the values of the T matrix that are smaller than the threshold are zeroed, that is, the causal relationship is not considered. In this study, the threshold value equal to 0.1617 has been obtained. A causal diagram can be drawn by paying attention to the relationship pattern. Considering its role and importance in the selection of suppliers, the quality criterion affects many of the main criteria and does not have a direct effect on only a few criteria. The above pattern shows strong relationships between quality criteria and other criteria.

Table 5: The model of causal relationships, the main criteria of the model

 

- The sum of the elements of each row (Di) indicates the influence of that factor on other factors of the system. Therefore, the technology standard M8 has the most impact. The criterion of strategic barriers is in the second place, the criterion of production is in the third place, and the criterion of ISO is the least influential.

- The sum of column elements (Ri) for each factor indicates the degree of influence of that factor on other factors of the system. Therefore, the production standard M5 has a very high level of effectiveness. The criterion of geographical location is also the least effective than other criteria.

- The horizontal vector (D + R) is the degree of influence of the desired factor in the system. In other words, the higher the D + R value of an agent, the more interaction that agent has with other system agents. Therefore, the M5 criterion of production has the most interaction with other studied criteria, and the geographic location criterion has the least interaction with other variables.

The vertical vector (D - R) shows the influence of each factor. In general, if D - R is positive, the variable is considered a causal variable, and if it is negative, it is considered an effect. In this model, quality criteria, strategic barriers, technology, geographic location, ISO, experience, materials and equipment are causal variables and services, cost, reliability, production, delivery, agility, flexibility, employees, accountability, risk, time, capacity. And economic factors are disabled.

 

Fig. 1: Cartesian coordinate plot of DEMATEL output for main metrics

 

According to the results obtained from the final matrix, it is clear that, in the quality measure, company 7 (Merrick Galvanizing Company) and company 14 (Amitis Company) ranked first with an average of 46.8333, and company 16 (Yazd Electrode Company) ranked second with an average of 46.7500, and company 20 (Meshbak Pardazan Company) ranked second with an average of 46.6667 In the third place, company 6 (Nagin Zere Pars) is in the fourth place with an average of 46.5833, and company 8 (Racor Company) is in the fifth place with an average of 46.4167. And company 10 (Madesa company) is in the last place with an average of 32.2500. In the cost criterion, company 14 (Amitis Company) with an average of 11.5000 is in the first place, and company 13 (Nili Fam Ray Company) is in the second place with an average of 13.1667, and company 20 (Meshbak Pardazan Company) is in the third place with an average of 13.6667, and company 11 (Behin Folad Ati Gostar Company) ranks fourth with an average of 14.5833, and Company 19 (Zanjan Wire Industries Company) ranks fifth with an average of 14.8333. And company 4 (Sahand Poulad Company of Tabriz) ranks last with an average of 42.5833. In the time criterion, company 14 (Amitis Company) with an average of 11.5000 is in the first place, and company 13 (Nili Pham Ray Company) is in the second place with an average of 12.4167, and company 11 (Behin Folad Ati Gostar Company) is in the third place with an average of 12.8333. And Company 20 (Meshbak Pardazan Company) is in fourth place with an average of 13, and Company 7 (Merrick Galvanized Company) is in fifth place with an average of 15 and Company 8 (Racor Company) is in sixth place with an average of 15.6667. And company 12 (Pars Pamchal Company) is ranked last with an average of 40.5000.

In the production criterion, company 14 (Amitis Company) with an average of 47.5000 is in the first place, and company 13 (Nili Fam Ray Company) is in the second place with an average of 46.2500, and company 20 (Meshbak Pardazan Company) is in the third place with an average of 46, and company 11 (Behin Folad Ati Gostar Company) is in the fourth place with an average of 42.9167, and company 5 (Sepand Pich Yazd Company) is in the fifth place with an average of 41.9167, and company 8 (Racor Company) is in the sixth place with an average of 41.8333. And Company 9 (Polad Pichkar Company) is in the last place with an average of 20.6667. In the service criterion, company 14 (Amitis Company) ranks first with an average of 48, and company 13 (Nili Fam Ray Company) ranks second with an average of 47.1667, and company 11 (Behin Folad Ati Gostar Company) ranks third with an average of 46.5833, and the company 20 (Meshbak Pardazan Company) with an average of 45.8333 ranks fourth, and Company 5 (Sepand Pich Yazd Company) ranks fifth with an average of 44.9167, and Company 7 (Merik Galvanized Company) and Company 19 (Zanjan Wire Industries) ranks sixth with an average of 44.1667 has it. And Company 1 (Iranpichkar Company) ranks last with an average of 30.0833.

 

4.4 Stochastic CCR Model

To analyze the data in the tables, we use the random CCR model to evaluate the performance of the supply companies of the Khatam Al Anbia construction site, and considering that only one company was identified as efficient, therefore, the need to use ranking models It was not felt. Considering the error level, the possible limit form of the CCR model, which we call SCCR, is defined as the following model in the input oriented format.

(1)  

So that at that error level, it is specified by the manager that it is a number between zero and one. To evaluate a stochastic DMU with the help of model (1), this model can be converted into a deterministic form based on stochastic programming methods with probabilistic constraints. To solve the model, use EXCEL software as well as GAMS software, which is a powerful and comprehensive tool for solving mathematical models even in large dimensions, and it is very powerful for solving complex problems of data envelopment analysis optimization. Day by day, it plays a more colorful role in the fields of engineering, we use it, and thus, according to the obtained results, we offer suggestions for choosing the best supplier companies for Khatam Al-Anbia construction camp.

Now, by running the GAMS program using the random data of the above tables, for α = 0.1 = α 0.2 = α 0.3 = α 0.4 = α 0.5 = α the results of random efficiency and ranking of the decision-making units with data that follows the normal distribution are summarized in the following tables. It should be noted that we have and the results of the deterministic model will be completely the same as the random model.

Table 6: The results at the level of α = 0.1~0.5

 

As can be seen in the above table, in the five levels α 0.1 = α 0.2 = α 0.3 = α 0.4 = α 0.5 = α we had one efficient unit and the rest of the units became inefficient, in the mentioned five levels, According to the efficiency score, decision-making unit number 14 was recognized as the efficient unit, and unit number 10 was recognized as the most inefficient decision-making unit. Using EXCEL software, we depict the column charts of the decision-making units, or in other words, the supply companies of the Khatam al-Anbia construction camp.

 

Fig. 2: Efficiency of the supply companies of Khatam Al-Anbia construction camp in five levels. α =0.1,  α =0.2, α =0.3, α= 0.4, α =0.5

As it is clear from the bar chart above, the efficiency decreases with the increase of α. Only in company number 14 (Amitis company) with the increase of α, the efficiency has not changed and is constant.

 

5 Conclusion

 As it was said, we determine the distribution of random inputs and outputs by determining the unknown parameters (mean and variance) of the data, by choosing the random model suitable for the data, we convert this random model into a deterministic model and Then, by solving the deterministic model, we determine the random efficiency for different αs, and by choosing the random super-efficiency model, the ranking of the supply companies of Khatam Al-Anbia construction base is done using GAMS and EXCEL software. According to the results there is one decision making unit with an efficiency score of one, and nineteen DMUs with an efficiency score other than one in the five confidence levels mentioned. Inefficient units were ranked using the CCR model. Amitis company has the highest efficiency score in the five confidence levels mentioned, and Madesa company is considered one of the inefficient units with the lowest efficiency score in the five confidence levels. It is weak compared to other units. The random data coverage analysis technique can be used to analyze the efficiency of decision-making units, and the reason for using this technique is that it performs more realistic evaluations than other quantitative techniques and is able to identify efficient units and Determine the inefficient and prioritize accordingly. In this technique, output and input factors are evaluated together and it is not limited to one input and one output. In fact, stochastic DEA allows for random changes in input and output and is also able to predict the efficiency of decision-making units in order to plan better for their future.

As it was said before, the supply companies of Khatam al-Anbia Construction Base, which were rated efficient using the efficiency model, get a numerical value of one, this is significant, the higher the efficiency score, the decision making units In fact, the units whose efficiency score is more than one are 100% efficient, and their efficiency value is considered to be the same, and the units whose super-efficiency score is less than one are considered inefficient units. According to the observed table, we can see that one of the decision-making units, namely Amitis Company, has worked in five levels: 0.1 = α 0.2 = α 0.3 = α 0.4 = α 0.5 = α The efficiency score is one, it is 100% efficient, the lowest efficiency score in the five levels of confidence is related to Madsa company and it is known as the most inefficient decision making unit and therefore has the first inefficiency rating. , the second rank of inefficiency belongs to Poladpichkar in the mentioned five levels and the third rank of inefficiency belongs to Kavash Josh company, which these units show inappropriate performance compared to other units.

 

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