New Approach in Fixed Resource Allocation and Target Setting Using Data Envelopment Analysis with Common Set of Weights

Marzieh Ghasemi,Mohsen Rostamy Malkhalifeh,Mohammad Hasan Behzadi,Mohammad Reza Mozaffari,Farhad Hosseinzadeh Lotfi,Jorge-Antonio Lopez-Renteria

doi:10.1155/2022/2149093

Marzieh Ghasemi, Mohsen Rostamy Malkhalifeh + Show 4 more

Open Access

https://doi.org/10.1155/2022/2149093

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Abstract

One of the mathematical programming techniques is data envelopment analysis (DEA), which is used for evaluating the efficiency of a set of similar decision-making units (DMUs). Fixed resource allocation and target setting with the help of DEA is a subject that has gained much attention from researchers. A new model was proposed by determining a common set of weights (CSW). All DMUs were involved with the aim of achieving higher efficiency in every DMU after the procedure. The minimum resources and targets allocated to each DMU were commensurate to the efficiency of that DMU and the share of DMU in the input resources and the output productions. To examine the proposed method, other methods in the DEA literature were examined as well, and then, the efficiency of the method was demonstrated through a numerical example.

Highlights

Introduction e original concepts related todata envelopment analysis (DEA) were first introduced in 1978 by Charnes et al [1] and rapidly gained popularity among researchers
We consider the fixed resources as an additional input and the target setting as an output, and using a common set of weights (CSW), we present a model that, while including all decision-making units (DMUs) in the resource allocation and target setting, ensures that, after the procedure, the efficiency of all DMUs would be the same as before or higher
The minimum target set for each DMU is equal to its outputs and the efficiency that it has had before fixed resource allocation. erefore, any DMU that has a larger share in the inputs and can achieve higher efficiency with those inputs needs to receive more resources

Summary

Proposed Model

J 1 e efficiency score of DMUj when the resources are not allocated and the target is not set is represented by θ∗j , which is calculated using the multiplier CCR model. Erefore, for each DMU, we consider the least share in the allocated resources and the set targets. The minimum target set for each DMU is equal to its outputs and the efficiency that it has had before fixed resource allocation. Erefore, any DMU that has a larger share in the inputs and can achieve higher efficiency with those inputs needs to receive more resources. By setting vm+1fj fj′ and us+1gj gj′ , model (10) would change as follows:. Using model (17) for allocation or resource and setting target improve the efficiency.

Examples

Conclusion