MPS Input Format

MPS INPUT FORMAT
(excerpted from Advanced Linear Programming: Computation and Practice by Bruce A. Murtagh.)

This format has become the industry standard, adopted by most commercial codes, and is not restricted to the MPS series of codes developed originally for IBM computers.

Table: MPS format data line

The various sections of the data are grouped in the following order:

• NAME
• ROWS
• COLUMNS
• RHS
• RANGES (optional)
• BOUNDS (optional)
• ENDATA

We will examine each of these sections in turn.

1. NAME. This section consists of just one card, with the word NAME in columns 1-4, and the title of the problem in columns 15-22.
2. ROWS. In this section all the row labels are defined, as well as the row type. The row type is entered in field 1 (in column 2 or 3) and the row label is entered in field 2 (columns 5-12).

   The code for specifying row type is as follows:

   

   This section of data is preceded by a card with ROWS in columns 1-4, followed by a data card for each row. The first N-type row encountered is regarded as the objective, unless it is explicitly identified in the control commands.

   Linear combinations of rows may also be specified. In this case the above row types are denoted respectively by the codes DE, DL, DG, and DN, in columns 2-3. Field 2 contains the linear combination rowname. Fields 3-6 contain the rowname(s) (fields 3 and 5) and their multiplier(s) (fields 4 and 6) which form the combination. A linear combination of three or more rows requires additional cards, following the first card contiguously. In the additional cards field 1 is empty. (The right-hand sides of a linear combination row must be specified in the RHS section, described below.)

3. COLUMNS. This section defines the names of the variable, the coefficients of the objective, and all the nonzero matrix elements aij. The data are entered column by column, and all the data cards for the nonzero entries in each column must be grouped together contiguously. The section is preceded by a card with COLUMNS in columns 1-7, followed by data cards which may have one or two matrix elements per card.

   The data card has the column label in field 2 (columns 5-12), the row label in field 3 (columns 15-22), and the value of the coefficient aij(or cj) in field 4 (columns 25-36), including a decimal point). If more than one nonzero row entry for the same column is to be made on the card, then field 5 (columns 40-47) has the next row label and field 6 (columns 50-61) has its corresponding coefficient value. It should be emphasized that the use of fields 5 and 6 is optional.

   There is no need to specify columns for slack variables; this is taken care of automatically having defined the row types.

4. RHS. This section contains the elements of the right-hand side. The section is preceded by a card with RHS in columns 1-3. Since the right- hand side can be regarded as another column of the matrix, the data cards specifying the nonzero entries are in exactly the same format as the COLUMNS data cards, except field 2 (columns 5-12) has a label for the right-hand side. More than one right-hand side may thus be specified in this section; the one to be used for the current run is specified by its label in the agenda cards, to be discussed in Sec 9.3.
5. RANGES (optional). This section is for constraints of the following form:

   i.e., both an upper and lower bound exist for the row. The range of the constraint is The value of or is specified in the RHS section data, and the value of is specified in the RANGES section data. This information, plus the row type specified in the ROWS section, defines the bounds and

   If is the number entered in the RHS section and is the number specified in the RANGES section, the and are defined as follows.

   

   The section is preceded by a card with RANGES in columns 1-6. The data cards specifying the values of are in exactly the same format as the COLUMNS data cards, except field 2 (columns 5-12) has a label for the column of ranges (which can also be regarded as another column of the matrix). More than one column of ranges may be specified, but all the data cards for each column must be grouped together contiguously.

6. BOUNDS (optional). In this section, bounds on the variables are specified. The section is preceded by a card with BOUNDS in columns 1-6. The bounds are entered as a row, with a corresponding row label. The nonzero entries in this row vector correspond to columns in the matrix and must be in the same order in which the column names appear in the COLUMNS section. When bounds are not specified for a column (or the entire BOUNDS section omitted) the usual bounds, , are assumed.

   More than one bound for a particular variable may be entered, i.e., both a lower and an upper bound; when only one is specified the other is assumed to be one of the default values of or as shown in parentheses below.

   • Field 1 (columns 2-3) specifies the type of bound:

     

   • Field 2 (columns 5-12) specifies the bounds row label. (More than one bounds row may be entered, but the data must be grouped together contiguously for each bounds row.)
   • Field 3 (columns 15-22) specifies the column label corresponding to the variable
   • Field 4 (columns 25-36) specifies the bound value
   • Fields 5 and 6 are blank.
   • NOTE ADDED 5/2/2000: The handling of the MI type apparently is not standardized. In some implementations, the upper bound is assumed to be +infty (rather than 0 as in the table above) and is reset to some other value only through the use of an UP bound elsewhere in the MPS file.
7. ENDATA. This section is just one card, with ENDATA in columns 1-6, signalling the end of matrix data input.

Example:

NAME          AFIRO                                                  
ROWS
 E  R09     
 E  R10     
 L  X05     
 L  X21     
 E  R12     
 E  R13     
 L  X17     
 L  X18     
 L  X19     
 L  X20     
 E  R19     
 E  R20     
 L  X27     
 L  X44     
 E  R22     
 E  R23     
 L  X40     
 L  X41     
 L  X42     
 L  X43     
 L  X45     
 L  X46     
 L  X47     
 L  X48     
 L  X49     
 L  X50     
 L  X51     
 N  COST    
COLUMNS
    X01       X48               .301   R09                -1.   
    X01       R10              -1.06   X05                 1.   
    X02       X21                -1.   R09                 1.   
    X02       COST               -.4   
    X03       X46                -1.   R09                 1.   
    X04       X50                 1.   R10                 1.   
    X06       X49               .301   R12                -1.   
    X06       R13              -1.06   X17                 1.   
    X07       X49               .313   R12                -1.   
    X07       R13              -1.06   X18                 1.   
    X08       X49               .313   R12                -1.   
    X08       R13               -.96   X19                 1.   
    X09       X49               .326   R12                -1.   
    X09       R13               -.86   X20                 1.   
    X10       X45              2.364   X17                -1.   
    X11       X45              2.386   X18                -1.   
    X12       X45              2.408   X19                -1.   
    X13       X45              2.429   X20                -1.   
    X14       X21                1.4   R12                 1.   
    X14       COST              -.32   
    X15       X47                -1.   R12                 1.   
    X16       X51                 1.   R13                 1.   
    X22       X46               .109   R19                -1.   
    X22       R20               -.43   X27                 1.   
    X23       X44                -1.   R19                 1.   
    X23       COST               -.6   
    X24       X48                -1.   R19                 1.   
    X25       X45                -1.   R19                 1.   
    X26       X50                 1.   R20                 1.   
    X28       X47               .109   R22               -.43   
    X28       R23                 1.   X40                 1.   
    X29       X47               .108   R22               -.43   
    X29       R23                 1.   X41                 1.   
    X30       X47               .108   R22               -.39   
    X30       R23                 1.   X42                 1.   
    X31       X47               .107   R22               -.37   
    X31       R23                 1.   X43                 1.   
    X32       X45              2.191   X40                -1.   
    X33       X45              2.219   X41                -1.   
    X34       X45              2.249   X42                -1.   
    X35       X45              2.279   X43                -1.   
    X36       X44                1.4   R23                -1.   
    X36       COST              -.48   
    X37       X49                -1.   R23                 1.   
    X38       X51                 1.   R22                 1.   
    X39       R23                 1.   COST               10.   
RHS
    B         X50               310.   X51               300.   
    B         X05                80.   X17                80.   
    B         X27               500.   R23                44.   
    B         X40               500.   
ENDATA