Extended version of EATWOS concerning satisficing levels for input quantities

Transcription

1 Extended version of EATWOS concerning satisficing levels for input quantities Dipl.-Kff. Adina Silvia Bruns Dr. Malte L. Peters Univ.-Prof. Dr. Stephan Zelewski HICL 2012, Hamburg, September 2012

2 Agenda (1) Introduction (2) EATWOS and its extension (3) Numerical Example (4) Future research directions 2

3 1 Introduction Data Envelopment Analysis (DEA) is limited: knowledge of linear programming required for DEA models low discriminating power in the case of a small number of Decision Making Units (DMUs) no DEA models available to consider satisficing levels for inputs or output EATWOS and its extension EATWIOS can overcome these limitations EATWIOS with satisficing levels for inputs will be presented at the first time 3

4 Input data preparation it has to be decided which inputs and which outputs should be considered the inputs and outputs have to be cardinally measured EATWOS offers the opportunity to consider a satisficing level for each output EATWIOS enlarges EATWOS with help of the consideration of a satisficing level for each input exogenous assessment of the relative importance weights of the inputs and outputs are required 4

5 Application of EATWIOS without consideration of satisficing levels normalization of the output quantities: output distance measure: 5

6 Application of EATWIOS without consideration of satisficing levels normalization of the input quantities: input distance measure: 6

7 Application of EATWIOS without consideration of satisficing levels efficiency score for each DMU: 7

8 Application of EATWIOS with consideration of satisficing levels for inputs constraints 8

9 Application of EATWIOS with consideration of satisficing levels for inputs constraints 9

10 Application of EATWIOS with consideration of satisficing levels for inputs not for each input k a satisficing level SL k has to be specified: 10

11 Application of EATWIOS with consideration of satisficing levels for inputs depending on the input quantitiy values and the satisficing level the following value combinations are possible: 11

12 Application of EATWIOS with consideration of satisficing levels for inputs 12

13 Application of EATWIOS with consideration of satisficing levels for inputs 13

14 Application of EATWIOS with consideration of satisficing levels for inputs 14

15 Application of EATWIOS with consideration of satisficing levels for inputs 15

16 Application of EATWIOS with consideration of satisficing levels for inputs 16

17 Application of EATWIOS with consideration of satisficing levels for inputs modified input quantities c ik are normalized: input distance measures are calculated: 17

18 Application of EATWIOS with consideration of satisficing levels for inputs efficiency scores are calculated: 18

19 3 Numerical Example Measuring Supply Chain Efficiency input and output quantities as well as relative importance weights: 19

20 3 Numerical Example Measuring Supply Chain Efficiency normalized input quantities and normalized output quantities: 20

21 3 Numerical Example Measuring Supply Chain Efficiency distance measured without consideration of satisficing levels: 21

22 3 Numerical Example Measuring Supply Chain Efficiency calculating of the efficiency scores without consideration of satisficing levels: the rank order R is as follows: 1. Supply Chain 2 2. Supply Chain 1 3. Supply Chain 3 22

23 3 Numerical Example Measuring Supply Chain Efficiency modified input quantities for input 2 considering the satisficing level: input distance measures for input 2 considering satisficing level : 23

24 3 Numerical Example Measuring Supply Chain Efficiency calculating the efficiency scores with consideration of the satisficing level for input 2: the rank order R SLk is as follows: 1. Supply Chain 2 rank reversal: with respect to rank order R 2. Supply Chain 3 without consideration of satisficing levels! 3. Supply Chain 1 24

25 4 Future research directions endogenous relative weights for input and output quantities extended version of DEA concerning the satiscifing levels for input and output quantities 25

26 Authors Dipl.-Kff. Adina Silvia Bruns Dr. Malte L. Peters Univ.-Prof. Dr. Stephan Zelewski University of Duisburg-Essen Institute of Production and Industrial Information Management (PIM) Faculty of Economic Sciences Universitätsstraße Essen Germany adina.bruns@pim.uni-due.de post@malte-peters.de stephan.zelewski@pim.uni-due.de 26