Solver Nonlinear Optimization

Solving Nonlinear Optimization Problems with Excel Solverfor Microsoft Excel 2000
Denise Sakai Troxell (2000)
A Nonlinear Optimization Problem
a 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.
number of lots
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
x 2
Fixed Cost
Variable Cost
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Fixed Cost
Variable Cost
Production Cost
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Production Cost
average number of units in inventory
Carrying Cost
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
Production Cost
Carrying Cost
NOTE: We assume that x can be noninteger
f(x) = 98,000 (500) + 98,000 (5) + x (0.50)
x 2
enter labels
enter labels
NOTE: These labels are not essential for the use of Solver
enter the formula of the function to be optimized
Variable values in cell A2
Function formula in cell B2
NOTE: These cells will be colored to indicate that they are essential for Solver
x
f(x)
Remember…
x 2
Click on cell B2
x 2
Type in the formula =(98000/A2)*500+98000*5+(A2/2)*0.50
Remember…
x 2
Hit Enter
NOTE: The formula in cell B2 is not defined if cell A2 contains the value 0 or it is blank.
Remember…
x 2
NOTE: Avoid the error message #DIV/0! in cell B2 by typing in an initial value different from 0 in cell A2
Click 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)
complete the Solver Parameters dialog box
NOTE: The cell displayed in the Set Target Cell: box must contain the formula of the function being optimized (minimize cell B2)
Check the Min: circle
Click on the By Changing Cells: box
Click on cell A2
NOTE: The cell displayed in the By Changing Cells: box must be the cell containing variable values (cell A2)
Click on Add
NOTE: The Subject to the Constraints: box must contain the constraints on the variable values (x 98,000)
Click on cell A2
Click on the Cell Reference: box
Make sure <= is displayed
Click on the Constraint: box and type in 98000
Click on OK
set the Options
NOTE: The formula (in the Target Cell B2) is non-linear on the non-negative variable (x in A2)
Check the box Assume Non-Negative
set the Options
NOTE: The formula (in the Target Cell B2) is non-linear on the non-negative variable (x in A2)
Accept the remaining default options by clicking on OK
Using Solver
read solution
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
Solver 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

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Solver Nonlinear Optimization