Outline
1. Description of Structure/Bid Procedures

2. Optimization

Exhibits
5-A. CRA Eligible Letters

5-B. Placed-Based Survey

5-C. Financing Package


 PROJECT TIMELINE

1995 1996 Oct. Nov. Dec. Jan. Feb. Mar. April. | | | | | | | | ----------------------------------------- | Structuring | (11/1-1/15)


1. DESCRIPTION OF STRUCTURE/BID PROCEDURES

The goals of the structure/bid procedures are to:

To achieve the preceding goals, the CT recommends the following:

2. OPTIMIZATION

The optimization model used for the purposes of bid award was created by Bell Laboratories. In brief, the model analyzes all bids and finds the exact bid or combination of bids that maximizes total revenue to the seller.

In this instance, there are 750 mortgage loan blocks, and each bidder can submit up to 10 bids consisting of one or more mortgage loan blocks. All bids will be entered into the model, and the model will find the combination that maximizes total revenue.

The following example illustrates how the model works:

HUD's Southeast Sale:

Approach and Optimization Model:

  • Bid Optimization

    Example:

    Bid               1       2       3      4       5 
    
    ------------ ------ ------- ------- ------ ------- 
    
    Price           $60     $20     $71    $40     $50 
    
    ------------ ------ ------- ------- ------ ------- 
    
    Mortgage 1        0       0       0      1       0 
    
    Mortgage 2        1       0       1      0       0 
    
    Mortgage 3        1       0       1      0       1 
    
    Mortgage 4        0       1       1      0       1 
    
    Mortgage 5        0       0       0      1       0 
    
    
    

    Maximize: Z = 60x1 + 20x2 + 71x3 + 40x4 +50x5

    Subject to: 0x1 + 0x2 + 0x3 + 1x4 + 0x5 1

    1x1 + 0x2 + 1x3 + 0x4 + 0x5 1

    1x1 + 0x2 + 1x3 + 0x4 + 1x5 1

    0x1 + 1x2 + 1x3 + 0x4 + 1x5 1

    0x1 + 0x2 + 0x3 + 1x4 + 0x5 1

    xj = 0 or 1 for all xj in x

    Knapsack Problem Formulation:

    Maximize: ptx
    Such that: Ax <= e
    xj = 0 or 1 for all xj in x
    p = (p1, p2, ..., pn): Represents a Price Vector
    x = (x1, x2, ..., xn): Represents a Bid Vector
    e = (1, 1, ..., 1n): Represents a Unit Vector
    1 if Mortgage I is selected by bid j
    Each entry aj =
    0 otherwise
    (where each row A represents a mortgage and each column in A represents a bid).

    Southeast Auction Statistics:

    Southeast Auction Bidding Data:


       Number of     Percentage (%)    # of Bids    
       Mortgages                                    
        Covered                                     
    
                                                    
    
           1            69.50355          490       
    
           2             5.67375           40       
    
           3             2.69503           19       
    
           4             1.13475           8        
    
           5             0.85106           6        
    
          6-10           3.82979           27       
    
         11-20           4.82270           34       
    
         21-30           4.11348           29       
    
         31-40           0.99291           7        
    
         41-50           0.70922           5        
    
         51-60           1.13475           8        
    
         61-70           0.42553           3        
    
         71-80           0.56738           4        
    
         81-90           0.85106           6        
    
         91-100          0.56738           4        
    
        101-110          0.14184           1        
    
        111-120          0.14184           1        
    
        121-140          0.00000           0        
    
        141-150          0.14184           1        
    
        151-160          0.28369           2        
    
        161-170          0.85106           6        
    
        171-174          0.56738           4        
    
    
    

    Exhibit 5-A. "MAP" - CRA Eligible Letters


    Exhibit 5-B. Placed-Based Survey

    Exhibit 5-C. Financing Package