A DEA‐based method of allocating the fixed cost as a complement to the original input

Abstract

This paper focuses on the problem of how to divide a fixed cost as a complement to an original input among decision‐making units (DMUs) equitably. Using the data envelopment analysis (DEA) technique, this paper concerns the problem from the perspective of efficiency analysis. It is found that not all DMUs can become efficient under common weights if a low enough fixed cost is assigned. Therefore, the global modified additive DEA (MAD) model is introduced. By optimizing the global MAD‐efficiency, a new allocation method and the corresponding algorithm to ensure the uniqueness of the allocation result is designed. The proposed method can be used under both constant returns to scale and variable returns to scale for nonnegative data; it is suitable for the situation where the costs play a great role in the production of DMUs. Numerical results show the validity and advantages of our method.

Firm capability assessment via the BSC and DEA

“…A data envelopment analysis (DEAs) is a data-oriented technique proposed by Charnes et al (1978). It was developed for measuring the relative efficiencies within a group of decisionmaking units (DMUs) that utilize some inputs to generate a set of outputs (Dobos and V€ or€ osmarty, 2019;Hilmola et al, 2015;Khodakarami et al, 2016;Lin and Chen, 2017;Yu and Hsiao, 2018;Seydel, 2006). A data envelopment analysis can identify the strengths and weaknesses of each industrial unit based on industry criteria.…”

Information sharing under different warranty policies with cost sharing in supply chains

“…() also discuss the cost sharing contract as applied to channel coordination and performance improvement in the green supply chain. More recently, Lin and Chen () investigate a problem of how to divide a fixed cost as a complement to an original input equitably by using a data envelopment analysis (DEA) technique. None of these papers consider the warranty policy with cost sharing and the issue of information sharing in a supply chain context.…”

Fixed cost allocation based on the principle of efficiency invariance in two-stage systems

“…Khodabakhshi and Aryavash (2014) proposed that the allocation must be directly proportional or inversely proportional to the inputs and the outputs. Lin and Chen (2017) introduced a global modified additive DEA (MAD) model to allocate fixed cost by optimizing the global MAD-efficiency. Li, Zhu, and Liang (2019) suggested that each DMU should propose an allocation plan to punish itself so as to guarantee the acceptability of the allocation plan.…”

“…However, Ding, Chen, Wu, and Wei (2018) thought the achievement of a common technological level by all DMUs is impractical and thus presented a new approach that accounts for technological heterogeneity. Most of studies mentioned above regarded the fixed cost as a new input for the DMUs, but Li, Yang, Liang, and Hua (2009), Lin and Chen (2017) allocated fixed cost as a complement of other cost inputs on the basis of DEA approach, and this method was extended to two-stage systems by Zhu, Zhang, and Wang (2019). Zhang, Wang, Qi, and Wu (2018) combined game theory and DEA approach to solve the problem of transmission cost allocation.…”