19 –Solver - Baldwin Wallace...

19 – Solver

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Professor Shoemaker

There is class of problems known as Product Mix problems.

Suppose you need to make two kinds of widgets and you have only so much material/time/money to make them.

How many of each widget should I make?◦ i.e. what should be the “mix” of widgets?

Excel - Professor Shoemaker

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Mix problems are an example of optimizationproblems.

That is: to find the optimal solution given the limitations you have to live with.


In our example the objective is to make as many widgets as possible

◦ To Maximize the number of Widgets produced


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Mix problems always have constraints that limit the choices you can make to solve the problem.


Constraints are just the facts of life…

Some Examples◦ You have only 5,000 pounds of Nickel available◦ You have only 8,000 pounds of Copper available◦ You must make at least 50 small widgets◦ You must make at least 75 large widgets

Constraints limit the objective


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Optimization problems always have variablesthat are adjusted in an attempt to achieve the objective.

In our example, the quantity of each type of widget will be varied in an effort to make the maximum number of widgets.


The three important aspects of an optimization problem:

An Objective to minimize or maximize

Constraints – that limit your choices

Variables – values that are changed in an attempt to achieve the objective


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17-Solver.xlsx


Two types of Widgets to make

Amount of metals each

Widget needs

Amount of each metal needed to make that quantity of Widgets

If we make 2 Small and 3 Large this is the total pounds of Nickel and

Copper we’ll need


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How many of each type we’ll

make - Variables

Total Widgets produced. The

Objective. We want to maximize this number.

Constraints


The Constraints limit the values in the plan at the top


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You must produce at least 50 small and 75 large widgets. These will have to be

at least 50 and 75 when the solution is

complete.


You have at most 5,000 pounds of Nickel and 8,000 pounds of Copper available

These cannot exceed 5,000 and 8,000

when the solution is complete.


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You can’t produce 1/3 of a widget. You have to produce them in whole number – integer amounts. These will have to be

integers when the solution is complete.


It’s not available by default. You may have to add it


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First link the Objective and Variable Cells

Try running the Solve now. What happens?


Adding a Constraint. Click on Add


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Constraint: Limit the Nickel to 5,000 pounds

Also add the constraint for Copper


With just the metal constraints in, try running the solver.

What happens?


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The Solver found a solution, but didn’t make any of the Large model widgets.

Why?


Add the two constraints to require some of each model of widget

Also add the Integer constraint


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The complete setup

Go ahead and Solve it

Then select Answer before you click on Ok


283 is the maximum number of widgets we can make given the constraints

The solution has us making 208 small and 75 large widgets.


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Whenever a solver achieves an optimal solution one or more of the constraints prevented it from going further.

In this case, one or more constraints prevented the solution from making more widgets

Two of the constraints prevented us from making any more widgets. Which ones?


The requirement to make at least 75 large widgets limited the total

Try changing the Minimum quantity of Large constraint from 75 to 25 and solve again. How many more widgets can you then make?


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The 5,000 pound limit on Nickel also prevented us from making more widgets

We used up 4,995 of the available 5,000 pounds of Nickel. With only 5 pounds left over, we couldn’t make one more of either widget.


When a constraint limits further optimization the constraint is called binding.

If a constraints binds but there’s still a little left over the amount left is called the slack.

The Answer Report shows the constraints


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The Nickel isn’t shown as binding since there was some slack,

But in fact it did bind the solution since there wasn’t enough Nickel to make one more widget


Your boss: How can we make more widgets? Answer: Get me more Nickel or let me make

fewer Large widgets.

How many widgets can you make if I get you a additional 1,000 pounds of Nickel? ◦ Then what binds the solution?


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The three important aspects of an optimization problem:

An Objective to minimize or maximize

Constraints – that limit your choices

Variables – values that are changed in an attempt to achieve the objective


The Solver feature lets you determine the optimal solution

It shows you which constraints limited further optimization

It lets you answer What If questions


19 –Solver - Baldwin Wallace...

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