For larger models, the problem snapshot—a symbolic depiction of the problem’s constraints, variables, and values—can be helpful in understanding the model’s structure and in identifying errors. This compact problem picture shows, for each nonzero coefficient in the objective function and constraints, a symbol indicating the value or magnitude of the coefficient. The following symbols are used, preceded by ‘–’ if the value is negative:

Symbol |Coefficient value| (blank) 0 1 – 9 Integer, from 1 to 9 m < 1/1,000,000 f < 1/100,000 e  < 1/10,000 d  < 1/1000 c  < 1/100 b  < 1/10 a  < 1 A  < 10 B  < 100 C  < 1,000 D  < 10,000 E  < 100,000 F  < 1,000,000 M  > 1M

Example model and picture

              *** LP MODEL ***

Maximize CONTRIB) SELL1 + 1.5 SELL2 + 2.25 SELL3 + 3.5 SELL4 + 7.5 SELL5 - 0.65 INPUT - 0.1 KEEP1 - 0.15 KEEP2 - 0.25 KEEP3 - 0.4 KEEP4
subject to:
STAGE1)  - SELL1 + 0.8 INPUT - KEEP1 = 0
STAGE2)  - SELL2 + 0.85 KEEP1 - KEEP2 = 0
STAGE3)  - SELL3 + 0.7 KEEP2 - KEEP3 = 0
STAGE4)  - SELL4 + 0.75 KEEP3 - KEEP4 = 0
STAGE5)  - SELL5 + 0.6 KEEP4 = 0
CAP1)   INPUT <= 10000
CAP2)   KEEP1 <= 6000
CAP3)   KEEP2 <= 6000
CAP4)   KEEP3 <= 5000
CAP5)   KEEP4 <= 1500
DEMAND1) SELL1 <= 10000
DEMAND2) SELL2 <= 5000
DEMAND3) SELL3 <= 7000
DEMAND4) SELL4 <= 8000
DEMAND5) SELL5 <= 1000

     *** PROBLEM SNAPSHOT ***

           S S S S S I K K K K
           E E E E E N E E E E
           L L L L L P E E E E
           L L L L L U P P P P
           1 2 3 4 5 T 1 2 3 4

CONTRIB : -1-A-A-A-A a b a a a MAX
STAGE1  : -1         a-1       = 0
STAGE2  :   -1         a-1     = 0
STAGE3  :     -1         a-1   = 0
STAGE4  :       -1         a-1 = 0
STAGE5  :         -1         a = 0
CAP1    :            1         < D
CAP2    :              1       < D
CAP3    :                1     < D
CAP4    :                  1   < D
CAP5    :                    1 < D
DEMAND1 :  1                   < D
DEMAND2 :    1                 < D
DEMAND3 :       1              < D
DEMAND4 :         1            < D
DEMAND5 :           1          < C

In the snapshot report, the problem variable names are listed vertically across the top of the diagram, and over their respective coefficient symbols. Each constraint is shown with its label and symbols for every nonzero coefficient, the relation (<, >, =), and right-hand side (where zeros may appear).

The snapshot above clearly reveals the model’s partial network structure, since some variables appear in exactly two constraints and have coefficients of +1 and -1. And while most of the coefficients do not exceed 10, upper bounds on the variables (from the CAPi and DEMANDi constraints’ RHS values) are between 1,000 and 10,000