Profit Malmquist Index and Its Global Form in the Presence of the Negative Data in DEA

This paper first introduces the allocative and profit efficiency in the presence of the negative data and then presents a new circular index to measure the productivity change of decision making units (DMUs) for the case that the dataset contains the inputs and/or outputs with the negative values in data envelopment analysis (DEA). The proposed index is decomposed into four components in the two stages. The range directional model (RDM) and the proposed efficiencies are used to compute the proposed index and its components. The interpretations of the components are presented. Finally, a numerical example is organized to illustrate the proposed index and its components at three successive periods of time

Undesirable Outputs’ Presence in Centralized Resource Allocation Model

Data envelopment analysis (DEA) is a common nonparametric technique to measure the relative efficiency scores of the individual homogenous decision making units (DMUs). One aspect of the DEA literature has recently been introduced as a centralized resource allocation (CRA) which aims at optimizing the combined resource consumption by all DMUs in an organization rather than considering the consumption individually through DMUs. Conventional DEA models and CRA model have been basically formulated on desirable inputs and outputs. The objective of this paper is to present new CRA models to assess the overall efficiency of a system consisting of DMUs by using directional distance function when DMUs produce desirable and undesirable outputs. This paper initially reviewed a couple of DEA approaches for measuring the efficiency scores of DMUs when some outputs are undesirable. Then, based upon these theoretical foundations, we develop the CRA model when undesirable outputs are considered in the evaluation. Finally, we apply a short numerical illustration to show how our proposed model can be applied

Efficiency evaluation of cement production companies using nonhomogeneous network DEA

Cement production in Iran takes place across various geographical locations, each characterized by distinct weather conditions. The technology employed in cement production varies depending on the availability of raw materials, fuel sources, and essential resources like water. Consequently, diverse inputs and outputs assume significance in each production technology, resulting in non-homogeneity among cement factories. Despite these differences, all these facilities are engaged in cement production, warranting a comparative analysis of their efficiency. This study examines the operational processes of five different cement production technologies—dry, semi-dry, humid, semi-humid, and wet slurry—across four companies comprising a total of nine factories. The study evaluates their efficiency between 2017 and 2020 using network data envelopment analysis under non-homogeneous conditions across three modeling stages. An important aspect of this study is its focus on the entire supply chain, from raw materials to the final product. Although the raw materials employed vary among different cement production technologies, the end product remains largely consistent.IntroductionIn certain real-world scenarios, even with similar production technologies, the assumption of homogeneous decision-making units may not hold true. Practical applications often involve supply chain structures that differ significantly from others. For instance, some supply chains may, at certain stages, eject intermediate products to meet specific needs, a phenomenon not universal to all supply chains, resulting in non-homogeneous chains. The cement industry, including Iran, constitutes one of the pivotal economic sectors. Therefore, mitigating shortcomings, including resource and material waste reduction, can have a substantial impact on this industry and consequently on the broader economy. Due to varying climatic conditions, cement production employs diverse technologies, primarily categorized as dry or wet processes. This study investigates the operational processes of five different cement production methods—dry, semi-dry, humid, semi-humid, and wet slurry—across four companies with a total of nine factories. Their performance between 2017 and 2020 is evaluated using network DEA under non-homogeneous conditions, encompassing three modeling stages.Materials and MethodsIn novel approaches, DEA is utilized to assess the performance of network decision-making units. The models typically assume homogeneity among decision-making units, which may not always align with real-world conditions. Practical situations often violate assumptions of unit homogeneity and uniformity in input and output parameters. Consequently, it is imperative to present and employ methods and models capable of accommodating non-homogeneous units. This study employs a scientific library research approach and practical purposive data collection to gather relevant information. This information informs specific adjustments to operational processes. Consequently, the development of a robust system for evaluating supply chain performance becomes essential. The study utilizes common models to evaluate efficiency under non-homogeneous conditions. Classification of operational processes and related data, followed by modeling using Lingo software, is employed in this research.Discussion and Result:This article consists of two parts. Initially, it introduces the fundamental performance evaluation model and subsequently delves into the three-stage model of data envelopment analysis (DEA) within the supply chain context. In the second part, the production processes of Portland cement are examined, covering dry, semi-dry, humid, semi-humid, and wet slurry processes. The proposed approach assesses the performance of four cement production companies over a four-year period. Efficiency calculations for nine factories are conducted in three stages:The first stage consists of three steps as follows:First step: Input and output parameters used across the entire production process are categorized based on the different production methods.Second step: Processes utilizing similar production steps, as determined in the first stage, are grouped into four categories.Third step: Efficiency assessments for factories sharing similar production stages from the previous step are conducted, resulting in the identification of nine categories.Second stage: The efficiency of each category, characterized by a common feature from the previous step, is calculated.Third stage: To determine the overall efficiency of each factory, the efficiencies of individual processes are multiplied.ConclusionsThe results indicate that the fourth cement production company exhibits the highest efficiency, while the first company has the lowest efficiency. Notably, the lowest efficiency for the years 2017 to 2020 was recorded by the first company in 2020, while the fourth company achieved the highest efficiency in the same year. Among the factories, the lowest efficiency was observed in 2017 for the first company's five semi-dry factories, the fourth company's four semi-humid factories in 2018, the fourth company's nine wet slurry factories in 2018, the third company's seven semi-humid factories in 2020, and the fourth company's four semi-humid factories in 2020, which recorded the highest efficiency. Further examination and identification of suitable solutions to enhance efficiency in cases with lower efficiency levels can follow this study