1. Desheng Dash Wu University of Toronto, Reykjavik University [with John R. Birge, Booth School of Business, University of Chicago] Accepted and to appear at POM DSJ, 43(1) 2012 0

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3. Introduction  Problem, Literature Background model Our model  Conceptual model, Math model  3 main contributions ▪ chain merger DEA model, leader-follower relations ▪ efficiency at both chain and sub-chain levels, incentive compatible ▪ banking intra-firm division mergers Case analysis Conclusion & Further study 2

4. o Introduction o Background model o Our model o Case Study o Conclusion 3

5. New York Times, March 11, 2013: “the dollar value of U.S. mergers and acquisitions so far this year is $233 billion, more than double last year. But there were almost 10 percent fewer deals than last year.“ “Today's mergers and acquisitions are more about building up than cashing in.” 4

6. IO: Salant (83), JOE; Deneckere and Davidson (85) RandJ;Perry and Porter (85), AER; Farrell, (90), AER; Rothschild (00) Reg Sci&E; Benjamin et al. (09)  merger paradox Finance: Sapienza (02), JOF; Guerard Jr. (89); Geppert and Kamerschen(08); Houston and Ryngaert (94) JBF; Duffie (07) JFE  stock OR: Sherman and Rupert (06), EJOR; Cummins et al.(08) JBF; Ray (04); Bogetoft (05), JPA  efficiency 5

7.  A model for gauging merger efficiency of supply chains  different structure  Supply chain view of banking operations  Link operations to finance  Apply the model to banking operations with DEA, considering M&A with multiple metrics  Link OR to IO/Finance 6

8.  Question: banks or subdivisions merged, how business performance is affected considering such a banking chain? How to achieve potential gains? 7

9. o Introduction o Background model o Our model o Case Study o Conclusion 8

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11.  The efficiency of merger can then be measured as  denotes the harmony effect.  represents the scale effect.  potential gains from the merger of the two firms positive if > 1. 10

12. What 1. a linear programming to measure the efficiency of multiple decision-making units (DMU) when the DMUs present a structure of multiple inputs and outputs.  Different versions: Constant return to scale (CRS), Variable return to scale (VRS) How 1. Define DMU, input/output variables 2. Define the efficiency frontier. 3. A numerical weight coefficient is given to each firm, computing its relative efficiency. 11

13. o Introduction o Background model o Our model o Case Study o Conclusion 12

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15. N : number of DMUs  : multiplier, to be solved, i=1,2…N; l=1,2  P, Q: price vector In the l th stage, to evaluate the efficiency of the I th DMU with 2- stage chain:  (2) Here, are the decision variables 14

16.  Step 1: solve the DEA model for each chain and sub- chain, and construct the efficient input-output combination for each supply chain.  Step 2: Compute the average input bundle, intermediate output/input bundle and output bundle for each supply chain and members.  Step 3: Solve the series-chain DEA problem for the average input-output supply chain 15

17.  Step 4: Compute the total input and output bundle of the N Series-chain models.  Step 5: Solve the merger chain DEA problem for the whole chain with input and output bundle  Step 6: Compute the sub-chain efficiency, merger efficiency for the whole chain, the harmony and scale components. 16

18.  Theorem 1. full two-stage chain is efficient if and only if the sub-chain members are both efficient.  Theorem 2. Merger of the full two-stage chain is efficient if and only if the mergers of the sub-chain members are both efficient.  Similar theorems hold for the case with many sub-chain members 17

19.  Leader-follower relations Direct input Shared input Intermediate output/input Direct output Leader Follower The framework with limited resource E 18

20. o Constrained resource, leader-follower relation 19

21.  Bilevel programming problem (BLP) : A hierarchical optimization problem consisting of two levels.  The upper level/ the Leader’s level/ the dominant level  The lower level/ the Follower’s level/ the submissive level  A Bilevel Linear Programming given by Bard (88) is formulated as follows: 20

22.  Proposition  The system efficiency is a convex combination of both the leader and follower efficiency.  The system is efficient iff the sub-systems are efficient.  Merging of the system is efficient iff merging of the sub-systems is efficient. 21

23.  Dominant level (the Leader) gains much more potential improvement profit than what the lower level (the Follower) gains.  α -Strategy: To encourage the Follower to participate, the Leader promises to share α percentage of his profit to the Follower. 22

24.  α -Strategy: The efficiency ratio of the Leader under α strategy The efficiency ratio of the Follower under α strategy 23

25. o Introduction o Background model o Our model o Case Study o Conclusion 24

26. ▪ Data from 36 branches (DMUs) for 6 variables ▪ Mortgage banking chain input-output framework 25

27.  36 branches  efficiency analysis of the mortgage banking operations  consider mergers of the branches as a form of intra-firm re-organization.  potential savings by merging two branches at a time  630 combinations using both the CRS and VRS DEA chain merger models 26

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29. 28 the 1 st sub-chain (>100%) under CRS and VRS. full-chain (>100%) under CRS and VRS.

30. 29 merger efficiency distribution. Harmony efficiency Scale efficiency

31. 30 VRS merger efficiencyHarmony efficiency Scale efficiency

32. 31 CodeMergerMEScale D15291.49430.95031 D25281.46770.93631 D35231.44530.93501 D45301.34270.91358 D55351.33090.87452 D65311.33080.91817 D723281.31550.95172 D8451.31370.93138 D923291.30950.94289 D105171.30570.92251

33. Mergerleaderfollower system 4,51.1250.99 1.092 3,41.0980.99 1.072 5,81.091.001 1.067 4,71.0811.001 1.059 3,81.061.001 1.045 1,41.0590.9 1.042 1,81.0570.99 1.041 7,81.0470.99 1.035 5,61.0420.99 1.031 4,61.0351.001 1.027 The top 10 promising mergers under CRS 32

34.  Coordinated effective merger Merger efficiency scores of the Leader, the Follower and the whole system are all greater than 1. Merger leaderfollower system 5,81.091.0011.067 4,71.0811.0011.059 3,81.061.0011.045 4,61.0351.0011.027 6,81.0231.0011.018 2,81.0141.0011.011 The promising coordinated mergers under CRS 33

35. o Introduction o Background model o Our model o Case Study o Conclusion 34

36. 3 things  Creation of chain merger DEA model  Effects captured and decomposed at both chain and sub-chain levels  a case study in banking intra-firm division merger operations Future work  Assumptions to be validated  Breakup of firms  Comparison with other methods, e.g., game models. 35

37.  Thanks!  Questions? 36

38.  Model 37

39.  Model 38