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)

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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

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

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

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

 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

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

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

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 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

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

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

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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

 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

 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

 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

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

o Constrained resource, leader-follower relation 19

 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

 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

 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

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

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

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

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

29 merger efficiency distribution. Harmony efficiency Scale efficiency

30 VRS merger efficiencyHarmony efficiency Scale efficiency

31 CodeMergerMEScale D D D D D D D D D D

Mergerleaderfollower system 4, , , , , , , , , , The top 10 promising mergers under CRS 32

 Coordinated effective merger Merger efficiency scores of the Leader, the Follower and the whole system are all greater than 1. Merger leaderfollower system 5, , , , , , The promising coordinated mergers under CRS 33

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

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

 Thanks!  Questions? 36

 Model 37

 Model 38