Document Type : Research Paper

Authors

• Maryam Sharifi ¹
• Sohrab Kordrostami ²
• Leila Khoshandam ³

¹ PhD student, Department of Applied Mathematics, Faculty of Basic Sciences, Rasht Branch, Islamic Azad University, Rasht, Iran

² Professor, Department of Applied Mathematics, Faculty of Basic Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran

³ Assistant Professor, Department of Applied Mathematics, Faculty of Basic Sciences, Rasht Branch, Islamic Azad University, Rasht, Iran

Abstract

In production technology, studying the effect of an indicator on one or more other indicators while maintaining efficiency, named marginal rate, can provide valuable information to managers for better management of the system. In this paper, the aim is to study the effect of meaningful indicators on each other in a specific two-stage structure with undesirable outputs. In this study, production technology is divided into two sub-technologies in a two-stage structure, and then, focusing on the application issue, first, the effect of a specific input from the first stage on the intermediate indicator is measured, and then, by calculating the changes made in this indicator, its effect on the specific final output is measured as a transmission factor. In this paper, focusing on data collected from 21 provincial power plants consisting of interdependent "generation" and "transmission" sections, each unit has a similar structure to the stated structure. Considering the total technology distribution, the effect of increasing or decreasing the fuel type component is taken as the first-stage input on the electricity flow, and then the changes in electricity flow are measured on the total system revenue.
Introduction
In today’s world, one of the appropriate tools for measuring and evaluating productivity is data envelopment analysis (DEA). In classical DEA models, the main objective of the increase in output per unit cost is to increase the output, but in some processes with undesirable outputs, other outputs are produced as undesirable outputs. In DEA, different views have been expressed in addressing these outputs. The weak disposability of Kuosmanen (2005), one of the most common ways, is used in this study. In the traditional DEA approach, decision-making units were considered as black boxes. However, in the real world, we are faced with manufacturing processes that have two or more stages to produce final products with network structures. Therefore, network data envelopment analysis (NDEA) is introduced. The network models not only provide overall efficiency for the production processes but also provide the efficiency score for each individual stage. In production theory, calculating the effect of an index on another index can provide valuable information so that managers can access the desired performance by maintaining the efficiency and the exchange between the inputs and outputs. Due to inherent complexity in most of the manufacturing processes, a decision parameter cannot be changed without affecting one or more parameters. Exchanges between inputs and outputs are known as marginal rates and marginal productivity in economics and partial derivatives in mathematics. Although in DEA models, the ratio of optimal coefficients provides this information, due to the nature of the linear segmentation of the border and also due to the multiplicity of these coefficients, the marginal rates will not be unique. Researchers have provided solutions in this field, which are discussed in the following sections. In general, by knowing these rates, valuable suggestions can be made to the managers in order to improve the overall performance of the system. As far as we know, very little research has been done in the field of studying marginal rates and marginal productivity in two-stage production networks with the presence of unfavorable factors. Therefore, this topic is still seen as a research gap in the DEA literature. In this paper, a four-stage process is presented to obtain marginal productivity in a two-stage system in the presence of unfavorable factors. For this purpose, an efficiency measurement model has been proposed to evaluate the efficiency score of two-stage systems in the presence of undesirable outputs. Then, with the idea of Asmild’s method, which was used in 2006 to calculate the right and left marginal rates, the marginal productivity was calculated in the proposed network.
Methodology
To show the practical nature of the proposed method, the model and process were analyzed on the collected data related to 21 provincial power plants of the country. The electricity generation process in each power plant is a two-stage process, which includes the production and transmission sectors, respectively. The flow of electricity was used as an intermediate product in the production sector with an output nature and in the transmission sector with an input nature. Personnel costs and types of fuel, respectively, are defined as the first and second inputs, and pollutants as the undesirable output of the production sector. In the second stage, i.e., the transmission part, the expected outputs including the total income and the covered area have been considered. In the study of production processes, the effect of changing one indicator on one or more other indicators can provide managers with valuable information. Such exchanges between inputs or outputs are known as marginal rates and marginal productivity. Therefore, the estimation of such rates is a significant issue.
Results
Power plants of each country are considered as one of the most important pillars of growth and development of the country and have a significant impact on increasing the welfare of people. In this paper, 21 provincial power stations have been studied.
In this way, by considering a two-stage structure and with undesirable outputs, the effect of an index on the intermediate product and then the effect of this change on the final output of the system has been studied. For this purpose, during a four-step process, marginal productivity has been calculated for each component of the production process. As can be seen from the results, in a two-step process, any change in the first component can be transferred to the second component through the intermediate product. In this study, the aim is to measure the amount of personnel cost changes on the total income of power plants.
Conclusion
In production theory, studying the effect of one indicator on one or more other indicators is important as long as we are addressing multi-stage processes. Such exchanges in economics are known as marginal rate and marginal productivity. In this paper, focusing on 21 provincial power plants that have two-stage structures and undesirable outputs, for the first time, through a four-stage process, the effect of changes in the input indicators on the intermediate index and then its effect on the outputs is addressed. According to this study, any increase or decrease in the inputs of the first component of the two-stage network can be transferred to the final product through changes in the intermediate index, so it is possible to manage the final outputs of the entire system by changing the inputs of the first component and maintaining the efficiency. In order to provide suggestions for future studies, it is recommended to study networks with more components and a combination of series and parallel modes. Also, the studied network should be analyzed in other industries with a similar structure.

Keywords

• data envelopment analysis
• two-stage structure
• marginal productivity
• undesirable output

Main Subjects

• perfomance management