Using WinQSB to solve Linear Programming Models
Assume we wish to solve the transship problem
depicted in the following network diagram
First, formulate the model in standard
LP form. All constraints must have
variables on the left side and a constant
on the right.
50
60
1
2
2
4
5
40
Minimize Z= 2x14 + 4x24 + 5x34 + 8x45 + 9x46
8
4
5 35
9
6 25
3
From the transshipment node: 1 unit of
output requires 2 units of input
Subject To: x14 <= 50
x24 <= 60
x34 <= 40
x45 = 35
x46 = 25
x14 + x24 + x34 – 2x45 – 2x46 = 0
Now you are ready to
move to the software.
From the WinQSB
software set select “Linear
and Integer Programming”
2. Complete all
parameters. For the
example problem,
the completed
parameters will
appear as follows
1. Under the
File drop-down
menu, select
“new problem”
and this dialog
box will appear
3. After selecting OK the
Spreadsheet form will
appear on the screen
2. The column
headings reflect our
new variable names
1. Rename the variables.
Select “Variable Names”
under the “Edit” pulldown menu and type the
new names in the white
column.
4. The lowerBound
of each variable
should be 0 and the
UpperBound should
by M (short hand for
very large)
3. Enter the objective function (row 1) and
the six constraints (rows C1-C6). The
spreadsheet cells contain the coefficients
of each decision variable in the objective
function and each constraint.
5. For larger models, the spreadsheet format may be difficult to use. In
these cases, switch to the normal model format in order to type the
constraint set and objective function. Select “Switch to Normal Model
Form” under the “Format” pull-down menu. The input screen changes
to the following:
Normal Model Format
To solve the formulation select “solve the
problem” under the “Solve and Analyze” pulldown. Alternatively, select the running man icon
Solution and post
optimality report
Don’t forget to save
the formulation by
selecting “Save
Problem” from the
“File” pull-down.
You will be best served to use the software on your own computer system.
However, if you use the lab, note that the lab’s network may have trouble
printing the solution. You may need to copy and paste a “print screen” into
a package (such as Word) to print your complete solution