Data envelopment analysis for bi-level systems with multiple followers

Xiaoyang Zhou, Rui Luo, Yan Tu, Benjamin Lev and Witold Pedrycz

Omega, 2018, vol. 77, issue C, 180-188

Abstract: This study aims to evaluate the performance of a bi-level system including two kinds of players: a leader positioned at the upper level and multiple followers located at the lower level. The overall system tries to use inputs to produce outputs in a cost-efficient way. However, each player in the bi-level system controls different decision variables and has varying objectives. Based on this, a novel bi-level data envelopment analysis model with multiple followers is developed, in order to evaluate the performance of overall bi-level system as well as each player in detail. Then the extended Kuhn–Tucker conditions are used to solve the proposed model. An illustrative example is presented to validate the proposed approach by evaluating supply chains with a single plant and two distribution centers. A comparative analysis is conducted to demonstrate that the developed model has stronger discriminating power and can provide more managerial insights. Several conclusions can be reached from this study: the lower level subsystem is cost-efficient if and only if every follower is cost-efficient, and the lower level cost efficiency lies between the smallest cost efficiency and the largest cost efficiency among all followers; being cost-efficient at both the upper level and the lower level results in an achievement of overall cost efficiency in a bi-level structure, and the overall cost efficiency falls in between the upper level and the lower level cost efficiencies.

Keywords: Multiple followers; Bi-level programming; Data envelopment analysis; Cost efficiency; Supply chain evaluation (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0305048317302918
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jomega:v:77:y:2018:i:c:p:180-188

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.omega.2017.06.007

Access Statistics for this article

Omega is currently edited by B. Lev

More articles in Omega from Elsevier
Bibliographic data for series maintained by Catherine Liu ().