denise sakai troxell (2000) solving nonlinear optimization problems with excel solver for microsoft...
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Denise Sakai Troxell (2000)
Solving Nonlinear
Optimization Problems
with Excel Solver
for Microsoft Excel 2000
Denise Sakai Troxell (2000)
A Nonlinear Optimization Problema simple Inventory Model*
A manufacturer would like to produce 98,000 units of a certain product in a year, in lots of a fixed size.
The fixed setup cost per lot is $500 and the production cost per unit is $5.
The average inventory during a year is half of the lot size and the average annual inventory carrying cost per unit is $0.50. What is the fixed lot size that minimizes the balance between production and inventory carrying costs?
* from Mathematics with Applications in Management and Economics
by Gordon Prichett and John Saber, Richard D. Irwin, Inc., 7th ed., 1994.
Denise Sakai Troxell (2000)
Formulate the Problemobtain the function to be optimized
number of lots
number of lots
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
The objective is to find the lot size x, where 0 x
98,000, that minimizes the balance between production
and inventory carrying costs given by the function
fixed cost per
lot
fixed cost per
lot
Fixed CostFixed Cost
Denise Sakai Troxell (2000)
Formulate the Problemobtain the function to be optimized
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Fixed CostFixed Cost
production cost per
unit
production cost per
unit
Variable Cost
Variable Cost
The objective is to find the lot size x, where 0 x
98,000, that minimizes the balance between production
and inventory carrying costs given by the function
Denise Sakai Troxell (2000)
Formulate the Problemobtain the function to be optimized
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Fixed CostFixed Cost Variable Cost
Variable Cost
Production CostProduction Cost
The objective is to find the lot size x, where 0 x
98,000, that minimizes the balance between production
and inventory carrying costs given by the function
Denise Sakai Troxell (2000)
Formulate the Problemobtain the function to be optimized
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Production CostProduction Cost
average carrying cost
per unit
average carrying cost
per unit
average number of units in inventory
average number of units in inventory
Carrying CostCarrying Cost
The objective is to find the lot size x, where 0 x
98,000, that minimizes the balance between production
and inventory carrying costs given by the function
Denise Sakai Troxell (2000)
Formulate the Problemobtain the function to be optimized
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Production CostProduction Cost
Carrying CostCarrying Cost
The objective is to find the lot size x, where 0 x
98,000, that minimizes the balance between production
and inventory carrying costs given by the function
NOTE: We assume that x can be noninteger
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverstart with a blank sheet
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverenter labels
Enter labels in cells A1:B1
Enter labels in cells A1:B1
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverenter labels
NOTE: These labels are not essential for the use of
Solver
NOTE: These labels are not essential for the use of
Solver
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverenter the formula of the function to be optimized
Variable values in cell
A2
Variable values in cell
A2
Function formula in cell
B2
Function formula in cell
B2
NOTE: These cells will be colored to indicate that they are essential for
Solver
NOTE: These cells will be colored to indicate that they are essential for
Solver
x f(x)
Remember…
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverenter the formula of the function to be optimized
Click on cell B2Click on cell B2
Remember…
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverenter the formula of the function to be optimized
Type in the formula =(98000/A2)*500+98000*5+(A2/2)*0.50
Type in the formula =(98000/A2)*500+98000*5+(A2/2)*0.50
Remember…
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverenter the formula of the function to be optimized
Hit EnterHit Enter
Remember…
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
NOTE: The formula in cell B2 is not defined if cell A2
contains the value 0 or it is blank.
NOTE: The formula in cell B2 is not defined if cell A2
contains the value 0 or it is blank.
Denise Sakai Troxell (2000)
Preparing the Worksheet for Solverenter the formula of the function to be optimized
NOTE: Avoid the error message #DIV/0! in cell B2 by typing in an initial value different from 0
in cell A2
NOTE: Avoid the error message #DIV/0! in cell B2 by typing in an initial value different from 0
in cell A2
Denise Sakai Troxell (2000)
Using Solverinvoke Solver
Click on ToolsClick on Tools
Denise Sakai Troxell (2000)
Using Solverinvoke Solver
Click on SolverClick on Solver
Denise Sakai Troxell (2000)
Using Solverinvoke Solver
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
Click on cell B2Click on cell B2
NOTE: The cell displayed in the Set Target Cell: box must contain the formula of the function being optimized
(minimize cell B2)
NOTE: The cell displayed in the Set Target Cell: box must contain the formula of the function being optimized
(minimize cell B2)
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
Check the
Min: circle
Check the
Min: circle
NOTE: The cell displayed in the Set Target Cell: box must contain the formula of the function being optimized
(minimize cell B2)
NOTE: The cell displayed in the Set Target Cell: box must contain the formula of the function being optimized
(minimize cell B2)
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
Click on the By Changing Cells:
box
Click on the By Changing Cells:
box
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
Click on cell A2Click on cell A2
NOTE: The cell displayed in the By Changing Cells: box must be the cell containing variable values
(cell A2)
NOTE: The cell displayed in the By Changing Cells: box must be the cell containing variable values
(cell A2)
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
Click on AddClick on Add
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
Click on cell A2Click on cell A2
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
Click on the Cell Reference: box
Click on the Cell Reference: box
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
Make sure <= is displayed
Make sure <= is displayed
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
Click on the Constraint: box
and type in 98000
Click on the Constraint: box
and type in 98000
Denise Sakai Troxell (2000)
Using Solvercomplete the Solver Parameters dialog box
Click on OKClick on OK
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x
98,000)
Denise Sakai Troxell (2000)
Using Solverset the Options
Click on OptionsClick on Options
Denise Sakai Troxell (2000)
Using Solverset the Options
Check the box Assume Non-
Negative
Check the box Assume Non-
Negative
NOTE: The formula (in the Target Cell B2) is non-linear on the non-negative variable (x
in A2)
NOTE: The formula (in the Target Cell B2) is non-linear on the non-negative variable (x
in A2)
Denise Sakai Troxell (2000)
Using Solverset the Options
Accept the remaining default options by clicking
on OK
Accept the remaining default options by clicking
on OK
NOTE: The formula (in the Target Cell B2) is non-linear on the non-negative variable (x
in A2)
NOTE: The formula (in the Target Cell B2) is non-linear on the non-negative variable (x
in A2)
Denise Sakai Troxell (2000)
Using Solverexecute Solver
Click on SolveClick on Solve
Denise Sakai Troxell (2000)
Using Solverread solution
A lot size of 14,000 units
minimizes the balance between production
and inventory carrying costs at $497,000.00.
A lot size of 14,000 units
minimizes the balance between production
and inventory carrying costs at $497,000.00.
NOTE: Solver uses a method known as GENERALIZED REDUCED
GRADIENT
NOTE: Solver uses a method known as GENERALIZED REDUCED
GRADIENT
Denise Sakai Troxell (2000)
Using Solverend execution
Click on OKClick on OK
Denise Sakai Troxell (2000)
Using Solverend execution
Denise Sakai Troxell (2000)
Final CommentsSolver might not find the solution…
Try to enter different initial lot sizes (in cell A2), for example, 1, 49000, or 98000 and execute Solver.
How to
handle
problems
with
Solver?
Click on the button if you want some tips now
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