Dr. Ron Lembke
SOLVING LINEAR PROGRAMS
USING EXCEL
Formulating in Excel
1.
2.
3.
4.
Write the LP out on paper, with all
constraints and the objective function.
Decide on cells to represent variables.
Enter coefficients of each variable in
each constraint in a block of cells.
Compute amount of each constraint
being used by current solution.
Formulating in Excel
5. Place inequalities in sheet, so you
remember <=, >=
6. Enter amount of each constraint
7. Enter objective coefficients
8. Calculate value of objective function
9. Make sure you have plenty of labels.
10. Widen columns for readability.
Standard Form
Max 7x1 + 5x2
s.t. 4x1 + 3x2
2x1 + 1x2
x1
x2
<=
<=
>=
>=
240
100
0
0
electronics
assembly
Formulating in Excel
Current
value of
variables
Constraint
coefficients
Formulating in Excel
Amount of
each
constraint
used
by current
solution
Formulating in Excel
Objective
Function
Value
Objective Function
Coefficients
RHS of constraints,
Inequality signs.
Fancy “What If” Tool
Trial and error
 Simplifies the math
 Can’t solve it for us

Solving in Excel
All we have so far is a big ‘what if” tool. We
need to tell the LP Solver that this is an
LP that it can solve.
 Choose ‘Solver’ from ‘Tools’ menu
Click “Data” then “Solver”
If No Solver, Office2010
If No Solver, Office 2007
Solving in Excel
1.
2.
3.
Choose ‘Solver’ from ‘Data’ tab
Tell Solver what is the objective function,
and which are variables.
Tell Solver to minimize or maximize
Solver Dialog Box
Set the Target Sell
Tell to minimize or maximize
Where the variables are
Solving in Excel
1.
2.
3.
4.
Choose ‘Solver’ from ‘Tools’ menu
Tell Solver what is the objective function, and
which are variables.
Tell Solver to minimize or maximize
Add constraints:


5.
Click ‘Add’, enter LHS, RHS, choose inequality
Click ‘Add’ if you need to do more, or click ‘Ok’ if
this is the last one.
Add rest of constraints
Add Constraint Dialog Box
Constraints Added
Assuming Linear
6.
You have to tell Solver that the model is
Linear. Click ‘options,’ and make sure
the ‘Assume Linear Model’ box is
checked.
Assume Linear
Assuming Linear
6.
7.
You have to tell Solver that the model is
Linear. Click ‘options,’ and make sure the
‘Assume Linear Model’ box is checked.
On this box, checking “assume non-negative”
means you don’t need to actually add the nonnegativity constraints manually.
Solve the LP: Click ‘Solve.’ Look at Results.
Office
2010
Office 2010
Options
Set maximum time
to look for a solution
 OR maximum # of
iterations

 Our
problems
should solve quickly
Solution is Found
When a solution has been found, this box comes up.
You can choose between keeping the solution and going
back to your original solution.
Highlight the reports that you want to look at.
Successful Solution
Optimality Conditions?
200
Dead Profits
4000
3000
2000
1000
0
160
T 120
1
T-shirts
80
2
3
Solution #
Each time we go to another solution,
Objective value gets better
40
0
0
50
100
S
Sweatshirts
150
200
Optimality Conditions

Simplex method
creates “dual”
 Max
has a min dual,
min has a max dual


Dual and “primal”
converge to same
value
Solution must be
optimal
Dead Profits
7000
Primal
Dual
6000
5000
4000
3000
2000
1000
0
1 2 3 4 5 6 7 8 9
Solution #
Answer Report
Gives optimal and initial values of
objective function
 Gives optimal and initial values of
variables
 Tells amount of ‘slack’ between LHS and
RHS of each constraint, tells whether
constraint is binding.

Answer Report
Sensitivity Report
Variables:
 Final value of each variable
 Reduced cost: how much objective
changes if current solution is changed
 Objective coefficient (from problem)
Sensitivity Report
Variables:

Allowable increase:
How much the objective coefficient can go up before the optimal
solution changes.

Allowable decrease:
How much the objective coefficient can go down before optimal
solution changes.


Both of these only are accurate for changes made to one
variable at a time. If you change more than one variable,
need to re-solve the LP.
Suppose t-shirts had increase of $5 decrease $10

Solution is optimal if t-shirt profits are between $15-$30
Sensitivity Report
Constraints
 Final Value (LHS)
 Shadow price: how much objective would
change if RHS increased by 1.0
 Allowable
increase, decrease: how wide a range of
values of RHS shadow price is good for.
 Also only accurate for changes made to one
constraint at a time
 To see the impact of changing more than one
constraint, we just have to re-run the problem
Sensitivity Report
Limits Report
Tells ranges of values over which the
maximum and minimum objective values
can be found.
 Rarely useful

Limits Report
Summary
Entered the LP into Excel
 Opened Solver, told it how we wanted to
solve the LP
 Interpreting results of Solver Reports

report – basic results
 Sensitivity – how much the situation would
change with different profits per unit, or
amounts of constraints
 Answer