Solving Linear programs using excel
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Transcript of Solving Linear programs using excel
SOLVING LINEAR PROGRAMS USING EXCEL
Dr. Ron Lembke
Formulating in Excel
1. Write the LP out on paper, with all constraints and the objective function.
2. Decide on cells to represent variables.3. Enter coefficients of each variable in
each constraint in a block of cells.4. 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 constraint7. Enter objective coefficients8. Calculate value of objective function9. Make sure you have plenty of labels.10. Widen columns for readability.
Standard Form
Max 7x1 + 5x2
s.t. 4x1 + 3x2 <=240 2x1 + 1x2 <=100x1 >=0
x2 >=0
electronicsassembly
Constraintcoefficients
Current value of variables
Formulating in Excel
Amount of eachconstraint used by current solution
Formulating in Excel
RHS of constraints,Inequality signs.
Objective Function Coefficients
Formulating in ExcelObjective Function Value
Fancy “What If” Tool
Trial and error Simplifies the math Can’t solve it for us
Solving in ExcelAll 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. Choose ‘Solver’ from ‘Data’ tab2. Tell Solver what is the objective function,
and which are variables.3. Tell Solver to minimize or maximize
Solver Dialog BoxSet the Target SellTell to minimize or maximizeWhere the variables are
Solving in Excel
1. Choose ‘Solver’ from ‘Tools’ menu2. Tell Solver what is the objective function, and
which are variables.3. Tell Solver to minimize or maximize4. Add constraints:
Click ‘Add’, enter LHS, RHS, choose inequality Click ‘Add’ if you need to do more, or click ‘Ok’ if this
is the last one.5. 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. 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 non-negativity constraints manually.
7. Solve the LP: Click ‘Solve.’ Look at Results.
Office 2010
Office 2010 Options
Set maximum time to look for a solution
OR maximum # of iterationsOur 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 goingback to your original solution.Highlight the reports that you want to look at.
Successful Solution
Optimality Conditions?
0 50 100 150 200
160
40
80
120
0
200
Sweatshirts
T-shirtsT
S
1 2 30
1000200030004000
Dead Profits
Solution #
Each time we go to another solution,Objective value gets better
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
1 2 3 4 5 6 7 8 90
1000
2000
3000
4000
5000
6000
7000Dead Profits Pri
mal
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
Answer report – basic resultsSensitivity – how much the situation would
change with different profits per unit, or amounts of constraints