A New MIP Approach on the Least Distance Problem in DEA

2020 ◽  
Vol 37 (06) ◽  
pp. 2050027
Author(s):  
Xu Wang ◽  
Kuan Lu ◽  
Jianming Shi ◽  
Takashi Hasuike
Keyword(s):  
State Of The Art ◽  
Efficient Frontier ◽  
Decision Makers ◽  
Mixed Integer ◽  
Data Envelopment ◽  
Output Level ◽  
Decision Making Unit ◽  
Dea Models ◽  
Distance Problem ◽  
User Friendly

In this paper, we deal with the least distance problem (LDP) in Data Envelopment Analysis (DEA), which is to find a closest efficient target over the whole efficient frontier. To this end, we define the efficient frontier by a linear complementarity system and propose a mixed integer programming (MIP) approach to solve the LDP. Our proposed MIP approach: (1) can solve the LDP based on [Formula: see text]-norm ([Formula: see text]) by using a state-of-the-art solver and obtain the closest efficient target over the whole efficient frontier instead of a subset of it; (2) can be applied for computing the least distance DEA models satisfying the monotonicity; (3) is more user-friendly, because it allows a decision maker to improve the efficiency of a decision making unit (DMU) by setting the affordable input/output level under his/her circumstance. Thus, the efficient target provided by our approach may be more appropriate from the perspective of the decision makers of DMUs.

scholarly journals A Range Adjusted Measure of Super-Efficiency in Integer-Valued Data Envelopment Analysis with Undesirable Outputs

2021 ◽  
Vol 9 (4) ◽  
pp. 378-398
Author(s):  
Chunhua Chen ◽  
Haohua Liu ◽  
Lijun Tang ◽  
Jianwei Ren
Keyword(s):  
Data Envelopment Analysis ◽  
Transportation Systems ◽  
Decision Makers ◽  
Data Envelopment ◽  
Undesirable Outputs ◽  
Super Efficiency ◽  
Dea Model ◽  
Dea Models ◽  
Analysis Models ◽  
Transport Accidents

Abstract DEA (data envelopment analysis) models can be divided into two groups: Radial DEA and non-radial DEA, and the latter has higher discriminatory power than the former. The range adjusted measure (RAM) is an effective and widely used non-radial DEA approach. However, to the best of our knowledge, there is no literature on the integer-valued super-efficiency RAM-DEA model, especially when undesirable outputs are included. We first propose an integer-valued RAM-DEA model with undesirable outputs and then extend this model to an integer-valued super-efficiency RAM-DEA model with undesirable outputs. Compared with other DEA models, the two novel models have many advantages: 1) They are non-oriented and non-radial DEA models, which enable decision makers to simultaneously and non-proportionally improve inputs and outputs; 2) They can handle integer-valued variables and undesirable outputs, so the results obtained are more reliable; 3) The results can be easily obtained as it is based on linear programming; 4) The integer-valued super-efficiency RAM-DEA model with undesirable outputs can be used to accurately rank efficient DMUs. The proposed models are applied to evaluate the efficiency of China’s regional transportation systems (RTSs) considering the number of transport accidents (an undesirable output). The results help decision makers improve the performance of inefficient RTSs and analyze the strengths of efficient RTSs.

NEW APPROACHES FOR RESOURCE ALLOCATION VIA DEA MODELS

2012 ◽  
Vol 11 (01) ◽  
pp. 103-117 ◽  
Author(s):  
JIE WU ◽  
QINGXIAN AN
Keyword(s):  
Resource Allocation ◽  
Linear Programming ◽  
Programming Model ◽  
Multiple Objective Linear Programming ◽  
Data Envelopment ◽  
Integrated Models ◽  
Decision Making Unit ◽  
Dea Models ◽  
Pareto Efficient ◽  
Single Objective

This paper focuses on the problem of resource allocation through data envelopment analysis. We propose three integrated models for allocating resources. The first model aims at minimizing the input consumption, the second one aims at maximizing the total outputs within the current resources, and the last one aims at maximizing the total outputs using the predicted resources in the next production season. Since the number of inputs or outputs is usually more than one, the abovementioned issue is often a multiple objective linear programming (MOLP) problem. Through the proportion of inputs (outputs) of new decision making unit (DMU) to the total inputs (outputs) of all old DMUs, we transform the MOLP problem into a single objective linear programming model. We assume that decision maker must ensure that the expected outputs of each DMU after allocation in the next production season are not less than this production season. All these proposed models have the same advantage that the results gained from the models are Pareto efficient. A numerical example of 25 supermarkets is used to illustrate our proposed approach.

scholarly journals Efficiency Bounds for Two-Stage Production Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao Shi
Keyword(s):  
Production Systems ◽  
Efficiency Score ◽  
Insurance Companies ◽  
Practical Case ◽  
Data Envelopment ◽  
Production Structure ◽  
Two Stage ◽  
Decision Making Unit ◽  
Real World Applications ◽  
Dea Models

Traditional data envelopment analysis (DEA) models find the most desirable weights for each decision-making unit (DMU) in order to estimate the highest efficiency score as possible. These efficiency scores are then used for ranking the DMUs. The main drawback is that the efficiency scores based on weights obtained from the standard DEA models ignore other feasible weights; this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black Box” and developed models to obtain the efficiency bounds for each DMU over sets of all its feasible weights. In many real world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka’s (2011) model to a more common and practical case considering the two-stage production structure. The proposed approach calculates each DMU’s efficiency bounds for the overall system as well as efficiency bounds for each subsystem/substage. An application for nonlife insurance companies has been discussed to illustrate the applicability of the proposed approach and show the usefulness of this method.

scholarly journals Forecasting the Confidence Interval of Efficiency in Fuzzy DEA

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Azarnoosh Kafi ◽  
Behrouz Daneshian ◽  
Mohsen Rostamy-Malkhalifeh
Keyword(s):  
Confidence Interval ◽  
Geometric Mean ◽  
Decision Makers ◽  
Data Sets ◽  
Data Envelopment ◽  
Future Time ◽  
Dea Models ◽  
Time Periods ◽  
Fuzzy Dea ◽  
Decision Making Units

Data Envelopment Analysis (DEA) is a well-known method that based on inputs and outputs calculates the efficiency of decision-making units (DMUs). Comparing the efficiency and ranking of DMUs in different time periods lets the decision makers to prevent any loss in the productivity of units and improve the production planning. Despite the merits of DEA models, they are not able to forecast the efficiency of future time periods with known input/output records of the DMUs. With this end in view, this study aims at proposing a forecasting algorithm with a 95% confidence interval to generate fuzzy data sets for future time periods. Moreover, managers’ opinions are inserted in the proposed forecasting model. Equipped with the forecasted data sets and with respect to the data sets from previous periods, this model can rightly forecast the efficiency of the future time periods. The proposed procedure also employs the simple geometric mean to discriminate between efficient units. Examples from a real case including 20 automobile firms show the applicability of the proposed algorithm.

scholarly journals An Integrated Slacks-Based Measure of Super-Efficiency with Input Saving and Output Surplus Scaling Factors and its Application in Paper Chemical Mills

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dong Guo ◽  
Zheng-Qun Cai
Keyword(s):  
Efficient Frontier ◽  
Efficiency Score ◽  
Programming Approach ◽  
Decision Variable ◽  
Data Envelopment ◽  
Scaling Factors ◽  
Super Efficiency ◽  
Sbm Model ◽  
Dea Models ◽  
Pareto Efficient

Data envelopment analysis (DEA) as a nonparametric programming approach has been widely extended and applied in many areas. Conventional DEA models can well measure the efficiency of inefficient decision-making units (DMUs) but cannot further discriminate the efficient DMUs. A lot of methods are proposed to address this problem. One of the most important methods is the slacks-based measure of super-efficiency model (S-SBM model) developed by Tone in 2002. However, the projection for a DMU on the efficient frontier identified by S-SBM model may not be strongly Pareto-efficient that makes the super-efficiency score misestimated. This paper revises the usual slacks-based measure of super-efficiency by incorporating input saving and output surplus scaling factors into the objection function for measuring DMUs. We integrate SBM model and S-SBM model effectively and yield input saving and output surplus scaling factors as well as input and output slacks under only one integrated model. According to the study, the projection reference point identified by our method is strongly Pareto-efficient. Meanwhile, how each decision variable influences the efficiency score for a specific DMU is revealed and illustrated through two numerical examples and an empirical study in paper chemical mills.

Comparing Data Envelopment Analysis and Human Decision Making Unit Rankings: A Survey Approach

2014 ◽  
Vol 29 (2) ◽  
Author(s):  
Stanko Dimitrov
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Decision Makers ◽  
Data Envelopment ◽  
Rank Ordering ◽  
Decision Making Unit ◽  
Human Decision ◽  
Survey Approach ◽  
Decision Making Units ◽  
Better Than

AbstractIn this paper we compare the ordinal rankings generated through Data Envelopment Analysis (DEA) methods to ordinal rankings generated by human decision makers. Through eliciting the total rank ordering for approximately 100 individuals on all of the four different datasets of Decision Making Units (DMUs), we compare the rankings generated by individuals to those generated by ten DEA methods. We observe that depending on the characteristics of the dataset one of the DEA methods performs better than the others in matching human decision makers.

Restricted variation in data envelopment analysis with undesirable factors in nature

2015 ◽  
Vol 08 (03) ◽  
pp. 1550034 ◽  
Author(s):  
Sohrab Kordrostami ◽  
Alireza Amirteimoori ◽  
Monireh Jahani Sayyad Noveiri
Keyword(s):  
Data Envelopment Analysis ◽  
Efficient Frontier ◽  
Data Envelopment ◽  
Standard Data ◽  
Weak Disposability ◽  
Dea Models ◽  
Restricted Environment ◽  
Restricted Variation ◽  
Decision Making Units ◽  
Inputs And Outputs

In standard data envelopment analysis (DEA) models, inefficient decision-making units (DMUs) should change their inputs and outputs arbitrarily to meet the efficient frontier. However, in many real applications of DEA, because of some limitations in resources and DMU's ability, these variations cannot be made arbitrarily. Moreover, in some situations, undesirable factors with different disposability, strong or weak disposability, are found. In this paper, a DEA-based model is proposed to determine the relative efficiency of DMUs in such a restricted environment and in presence of undesirable factors. Indeed, variation levels of inputs and outputs are pre-defined and are considered to evaluate the performance of DMUs. Numerical examples are utilized to demonstrate the approach.

DEA models for two decision makers with conflicts: the principal-agent problem

2019 ◽  
Vol 53 (3) ◽  
pp. 749-765
Author(s):  
Yuandong Gu ◽  
Linlin Zhao ◽  
Yong Zha ◽  
Liang Liang
Keyword(s):  
Data Envelopment Analysis ◽  
Electric Power ◽  
Incentive Contracts ◽  
Decision Makers ◽  
The Other ◽  
Principal Agent ◽  
Data Envelopment ◽  
Principal Agent Problem ◽  
Dea Models ◽  
The Impact

This paper studies the impact of two decision makers’ interaction with conflicts on the efficiencies of the system. We start with a general principal-agent framework where the principal and the agent make decisions independently and the principal has a contradictive objective to that of the agent. We develop data envelopment analysis (DEA) models in the principal’s and the agent’s perspectives respectively. Non-cooperation between the principal and the agent is discussed to illustrate how one decision maker affects the other and the corresponding efficiency and incentive contract of the system. In addition, cooperation of the two parties is also analyzed to better derive how the performance of the system is influenced by the parties and their interactions as well. Then, this study illustrates the proposed models and effective incentive contracts by applying them to the efficiency evaluations of 22 China listed electric power companies.

scholarly journals New inverse DEA models for budgeting and planning

2021 ◽  
Author(s):  
Tahere Sayar ◽  
Mojtaba Ghiyasi ◽  
Jafar Fathali
Keyword(s):  
Planning Process ◽  
Efficiency Score ◽  
Decision Makers ◽  
Data Envelopment ◽  
Input And Output ◽  
Proposed Model ◽  
Dea Models ◽  
Business Sectors ◽  
Input Level ◽  
Decision Making Units

Data envelopment analysis (DEA) measures the efficiency score of a set of homogeneous decision-making units (DMUs) based on observed input and output. Considering input-oriented, the inverse DEA models find the required input level for producing a given amount of production in the current efficiency level. This article proposes a new form of the inverse DEA model considering income (for planning) and budget (for finance and budgeting) constraints. In contrast with the classical inverse model, both input and output levels are variable in proposed models to meet income (or budget) constraints. Proposed models help decision-makers (DMs) to find the required value of each input and each output's income share to meet the income or budget constraint. We apply the proposed model in the efficiency analysis of 58 supermarkets belonging to the same chain. However, these methods are general and can be used in the budgeting and planning process of any production system, including business sectors and firms that provide services.

Sign in / Sign up

Export Citation Format

Share Document