In April 2011, Mdsuhair asked a question at the Chandoo.org Forums
This is a candidate for Solver.
This post will walk us through the solution to the problem using Solver. It uses Solver and screen shots from Excel 2007.
All versions of Excel have solver available. Users should note that the screen shots may not match your version although the functionality will, some of the functions appear in different locations in different versions of Solver.
What and Where Is Solver
What is Solver
Solver is an Excel add-in that can solve problems by enabling a Target cell to achieve some goal.
This goal may be to minimse, maximise, or achieve some target value.
It solves the problem by adjusting a number of input cells according to a set of criteria or constraints which are defined by the user.
Where is Solver
Solver is an Excel add-in supplied with Excel, but not enabled by default.
To enable solver
File, Excel Options, Add-ins, Manage Excel Add-ins, Select the Solver Add-in checkbox
Solver will now appear as a New Tab on the Data, Analysis Tab
Solver Example
This post is based around a worked example Solver Example File, the file is compatible with all versions of Excel.
Defining the Problem
Mdsuhair had a series of 8 Items each which had a value:
He wants to know which items should be combined so that the sum of the values of the items is nearly equal.
To do this we need to assign each item into a Bucket. Namely Bucket A and Bucket B.
We will put values of 1 into a Bucket for each Item to show that it is assigned to that Bucket and a value of 0 to show that the bucket is empty (In/Out) Value.
We can start by adding a Total Column, which counts items in Buckets A + Bucket B for each Item, It then totals the totals.
We also know that we need to work out the Value of each Item in each Bucket
We do this by multiplying the Items Value by the Buckets (In/Out) value
Finally we need to add up the values in each Bucket and work out the difference between them
Mdsuhair’s original problem was to minimise the difference between the sum of the values in the 2 buckets.
Now we can place values of 1 in the buckets manually and Excel will show us the value of each Bucket and the Difference between them in Cell G11.
I have applied some conditional formatting to show when a cell has a value > 0.
The problem is that there are 28 or 256 combinations of answers, and to test them all manually at 1 every 5 seconds would take 21.3 minutes, assuming we can keep up that pace and remember which was the best combination.
This is where solver comes to the fore.
Applying Solver
To apply solver we need to define a series of requirements, rules and constraints.
These requirements, rules and constraints guide solver and set limits which allow solver to quickly narrow in on the answer.
What are our rules
Our main requirement is to minimise the difference between the value of the 2 buckets.
The difference between the 2 buckets in our example is cell G11, the sum of Bucket 2 values minus the Sum of Bucket 1 values.
We want to have G11 as low as possible but greater than or equal to 0.
We also know that an item can only be in Bucket A or Bucket B, it can’t be in both and can’t be Broken apart.
That is 2 Constraints for each Item
Firstly The Total column must be equal to 1
Secondly the Buckets Values must be Integers
We also know that the Total Number of Items is 8, this is another constraint.
We will discuss how these constraints are used in the next section
The Solver Window
This section will explain the solver window and its use in defining the problem within solver.
A Blank Solver Window
A Filled Solver Window
Set Target Cell:
This is the Target cell which is the cell which you are trying to solve the problem for.
Our Target cell is G11, The difference between the 2 Buckets values
Equal To:
The Equal To: section defines what we want to do with our Target Cell.
We want to achieve the same value in each Bucket and so the difference between the Buckets will be 0.
It might sound strange but we don’t want to minimise that difference. A minimal value will be achieved when all the Items are placed in Bucket A, as our equation for G11 will then have 0 – Total which is –Total, which is more minimal than 0.
Another way to constrain this is to Change G11 to =Abs(G10-H10)
This allows us to use Min as an Equal To: Value
But for now we can just leave G11 as =G10-H10 and we will set the Equal To: section as 0.
By Changing Cells:
Changing Cells: refers to the cells which will be modified by Solver to try and solve the problem.
We want to let Solver change the number of items in each bucket, this is the range: $C$2:$D$9
Hint: You can try the Guess button next to the Range Reference and Solver will take a Guess at what cells the problem is dependent on.
Always check this if you use it, especially in complex models.
Subject to the Constraints:
Constraints are the rules which define the limits of the possible solutions to the problem
We will add several constraints for our rules:
1. The Total column must be equal to 1 for each Item
2. The Bucket Value must be an Integer
3. The total contents of the 2 buckets must be 8 items
4. You could add a further constraint that each Bucket should hold the same number of items
Hint: As a general Rule, Under Constrain rather than over constrain! You can always add more constraints later.
To do this we will use the Add Constraint Button
1. We need to add a constraint for each cell in the Range E2:E9 that it is only allowed to be = 1
This constraint must be applied for each cell in the range E2:E9
2. We need to add a constraint for each cell in the Range C2:D9 that it is only allowed to be an integer
This constraint must be applied for each cell in the range C2:D9
3. We need to add a constraint for the Total of the 2 Buckets, E10=8
You can Change or Delete Constraints if you make a mistake by selecting the appropriate constraint and using the Change or Delete Buttons
Save and Load Solves Parameters
Selecting the Options Button there is the Option to Save Model and Load Models.
Hint: The Save/Load Models has been shifted onto the main Solver dialog in Excel 2010.
Using the Save Model and Load Model options you can Save and the Load the Solver Parameters for your model. The Save Model saves the parameters in a Range of cells as shown below.
This allows an easy way to actually setup and/or change the solver parameters.
Hint: Setup one constraint using solver then Save the model. Edit the model on the worksheet and re-load the model as required.
Note: That the parameters although when saved show as True/False or Numbers are all Excel Equations, see above.
This means you can edit them to change the Constraints and Parameters as required and re-load them into solver.
I have included 3 sets of Parameters for our model.
These are:
- Base Case – Forces bucket values to be equal, Allows uneven bucket counts
- Equal Sized Buckets – Forces each bucket to contain the same number of items
- Force an error – Which forces an error in the solver model
Load each model and try them at your leisure.
Running the Solver Model
Warning: Solver is a computationally complex add-in, so once your model is setup, Save your Workbook.
Prior to running the model there are a few parameters we should look at to ensure the model solves correctly.
On the main Solver window select the Options button. (Some of these parameters are on the Main Solver window in Solver 2010)
Generally you can accept the defaults but in this case we will change the following
Assume Linear Model – Select
Assume Non-Negative – Select
Note: Solver in Excel 2010 will return a better answer without these 2 parameters enabled by default
The other 2 parameters which you may need to change from time to time is
Precision: Precision is a number from 0 to 1 and higher means more precise
Tolerance: Tolerance shows how far away from a Number, an Integer constraint is allowed to be
The use of the Estimates, Derivatives and Search parameters are beyond the scope of this post. I direct you to the Excel Help on these subjects, by selecting the Help button.
Run the Model
To Run the Model, select the Solve Button from the main Solver menu.
The main status bar in Excel will flash up a number of statistics about the internal workings of the Solver add-in. Generally these flash by and are too fast to read. If a model is too complex it may stall and you won’t see any movement for a while. Solver generally recovers from these problems itself.
Once the Solver model finishes it will display a dialog of the results and allow you to do several things
First thing to note is that “Solver Found a Solution“.
If it has found a solution, the worksheet cells will be changed to show the solution
You now have 4 options:
- Run a Report
- Save a Scenario
- Return to the model
- Check Your Results
Run a Report
Run a report by clicking the report you want.
A new sheet will be added to your workbook depending on the report but will be called:
- Answer Report 1,
- Sensitivity Report 1
- Limits Reports 1
etc.
Note, that not all reports are relevant at all times, depending on the Constraints you have applied.
Save a Scenario
Selecting the Save a Scenario button takes you to the Save Scenario dialog.
Type in a Name and the Scenario of your model is saved as a Scenario.
Scenarios as available for use in the Scenario Manager, which is accessed from the Data, What-If-Analysis Tab
Return to the model
You can return to your model and either:
- Keep Solver Solution
- Restore Original Values
Check the Results
Solver is probably the most Black Box’ish of systems within Excel. As such any results it puts out must be manually checked for suitableness before further use.
These checks for realness, should as a start confirm that the results meet all the criteria supplied.
Are the results roughly what were expected?
Are any Minimums or Maximums violated?
What If Solver Doesn’t Find a Solution?
From time to time Solver will return with an error that a “Solver could not find a feasible solution.”
When this happens it is indicating one of several possibilities:
- Your model is over or under constrained
- Your model constraints are impossible to meet
- Your model constraints have an error
Start by checking the current constraints for errors and ambiguities
Eg: in our case we have 8 items so requiring the Count of the two buckets to be 20 is impossible to meet
My Solver Answer has Strange Numbers?
In solver up to and including Excel 2007, solver would commonly return numbers like 3.5E-18.
This is 0.0000000000000000035, which is effectively 0
If your model returns these, feel free to go through the model and change them to 0, in our model we should also check as the corresponding 1, may in fact be 0.9999999999999999965.
It should be noted that this problem in Solver in Excel 2010 does not occur as often but will still occur.
What and How have you used solver in the past?
What and How have you used solver in the past?
Let us know in the comments below:
39 Responses to “Some charts try to make you an April fool all the time (or why 3d pie charts are evil)”
Another little trick they've used in that pie chart is in the positioning of the car sales in relation to each other. The way in which you present them in the column chart is from highest seller to lowest seller, left to right, which is what we're used to seeing. But in the dastardly pie chart, the two smallest selling cars (the SX4 and the Scala) are placed one either side of the Verna, which serves to make it look bigger again.
Also the perspective at which you look at the pie chart makes the Verna look bigger. From my experimintation, a perspective of around 35-37 degrees makes it look like an even bigger slice, which appears to be what the advertiser has done.
All of this manipulation would make you think of the "photoshopping" or "air-brushing" that is done on photos of models, film stars, and so on, in magazines, to give them the unattainable looks, skin, shape, etc., etc., that many aspire to, but can never reach.
This post is quite the learning experience, thanks very much.
please help!!!! im taking a computer class at SPC in clearwater. i have an excel worksheet to turn in and my pie charts are just blank no pie at all, all the other charts are working but i need #D pie chart can anyone help me to restore the 3D Pie chart??? Emergency
@Amanda
Select the Chart
Right Click it
Change Chart Type
Select a 3D Pie chart type
This is a great example of why I do not like pie charts.
I promise to never make a 3d pie chart. If I ever see one, I promise to not rotate or explode it. I also promise to create alternative charts (usually column, bar, line or scatter plots) so that my audience can see the truth better.
And oh yeah, I promise to bake & eat pies whenever possible. Apart from cakes, pastries, ice creams, biscuits and other assorted fun foods that is.
signed David Onder
Reminds me of the quote ... statistics are like bikinis ... what they reveal is suggestive, what they conceal is vital.
I love that Quote and you are so right, now to get the upper management to understand that!!!
Oh .. and wont it be awesome if u can create a quick decision tree tool for jo so that she can buy shoes :p ... perhaps link it to jabong.com or flipkart.com account and boom ... a spreadsheet shopping tool!
There are a only two acceptable pie charts: actual pie and cheesecake.
My own commitment to the truth is to incorporate pereto graphs (Few, 2006) into most of my bar/column graphs. The pereto is activated by a non-printing check box form control. This method has proven its worth on a number of occasions when presenting data and demonstrating its integrity when challenged - Also gets a kudos point from the boss for foresight, preparedness and professionalism :-).
Leonk
Hi Leon,
Can you elaborate? I'm aware of pareto as the 80/20 rule what do you mean by you "include" it?
@JungleJme
A Pareto Chart is a Ranked Column chart
With the column of the highest Rank occurring at the left and the Smallest column at the right
It highlights the issues with most impact easily
Have a read of: http://chandoo.org/wp/2009/09/02/pareto-charts/
A little part of me dies inside whenever I see presentations from upper level technical management that includes exploded 3D pie charts.
I promise to never make a 3d pie chart. If I ever see one, I promise to not rotate or explode it. I also promise to create alternative charts (usually column, bar, line or scatter plots) so that my audience can see the truth better.And oh yeah, I promise to bake & eat pies whenever possible. Apart from cakes, pastries, ice creams, biscuits and other assorted fun foods that is.signed Luke M
So if the goal is to mislead, 3-D pie charts are great. There is a use for everything.
Definitely agree with you. They did the appropriate thing as a marketing scheme. The chart is not "wrong" in any way, just misleading to the eye.
I think it's an excellent ploy.
I think these are an excellent display of the versatility of storytelling that is allowed by the champion of charts, the pie. Great work Chandoo. See my site for some further examples of effectively working with pie charts. eagerpies.com
Well done Chandoo, all points clearly made; I'd add that there are lies, damned lies, statistics, pie charts and tweaked pie charts.
I never recommend a pie chart but some of my custoners are so stupi are sure their requirements are correct. And the customer is always right (when he is the boss). So no pledge but lots of support.
When I teach charts I ask what is the purpose of charts? Fairly sharp students talk about information over data. The purpose is to make better decisions happen. The accuracy is essential, the usability is essential, but the real gain is when the manager sees what to do to make the figures better.
Why do you have strikethru option in replies that is visble when editing but lost when posted? Of course is this does show a strikethru I must have got it wrong; let's see..
... no thought not. Register aplea for strikethru to work. Thanks
Hand on experience, thank you for sharing this.
My favourite (if that's the right word) is Stve Jobs at
http://www.myspace.com/crazyalaskandude/photos/30206354
Some people must be assumed to know better, in which case it must be intentional.
There's a classic book called How to Lie with Statistics, and another called How to Lie with Maps. Time for How to Lie with Charts?
A time and a place for everything, in my opinion. E.g. pie charts are good for communicating specific things to a wide and general audience, because everyone feels comfortable with the form at least.
3D pie charts are good for giving the appearance of analysis to people who wouldn't read them anyway.
In Excel, I use flattened 3D pie charts because they let me control the rotation of the chart to put the most important slices where I want them. That said, I don't use pie charts very often because my audience doesn't demand them
Sorry, but all kind of 3d stuff is horrible! Better, let's back a pie!
Sorry, but all kind of 3d chart stuff is horrible! Better, let's back a pie!
Ha Ha you are right, but why 3D on a flat screen that doesn't work I think and in the end it's all about the data right..
Call this the chandoo effect!!! Did u check out the same advertisement with a different type of chart in yesterdays newspapers??? Even the marketing managers listen to chandoo.
I've always disliked pie charts for this reason and exploded 3d pie charts makes a liar out of their creators. its like the old man and his fish story.... I promise to never make a 3d pie chart (unless its as a joke). If I ever see one, I promise to not rotate or explode it. I also promise to create alternative charts (usually column, bar, line or scatter plots) so that my audience can see the truth better.
And oh yeah, I promise to bake & eat pies whenever possible. Apart from cakes, pastries, ice creams, biscuits and other assorted fun foods that is.
I teach mathematics at high school, and this article will now feature as a regular teaching tool in the topic Misleading Graphs. Thank you.
...and along those lines, I realise I need to create more exploded 3D pie charts, more over-formatted graphs and more line graphs for categorical data to demonstrate poor graph choice.
...and the staircase graph is even worse than the 3D pie chart. When you analyse it in terms of the amount of yellow on the graph compared to any other colour - particularly green which was second - it appears that Verna holds at least 50% market share.
I ran through this graph as a lesson on Misuse of Graphs. We placed a 5mm grid over the image of the graph and counted the squares. The image is 58% yellow. This surprised the students because they were analysing the chart and interpreting it as about 40%. I remarked that the 58% yellow was influencing their judgement. It was a very good lesson.
Thanks for this great teaching resource.
For most practical reasons, I believe there is no need to use a 3D chart unless a Z-axis is needed for your data -- and pie charts need not be 3D since they don't need to show any axis!
Your method of telling the whole thing in this paragraph is genuinely good, every one be capable of simply
understand it, Thanks a lot.
I agree about pie charts. I didn't recognize the name "Verna" so I had to Google it: Hyundai sells the same car in the US as the "Accent."
I cant stand 3d pie charts. 2d ones are bad enough. And im my opinion the staircase chart is even worse. Note that with the verna we see two sides which gives it a visible width on the page/screen about three times as wide as the second highest scoring one, where we can only see one side of it.
However, I won't make the promise. Whilst I think acurate representation of stats is a morale obligation of those who need to present impartial data, you have to admire the marketing team for not missing a single trick.
Unfortunately with slick charts with the lighting and 3d effects, it makes acurate flat charts look boring and unprofessional to the uniformed 90% who view style over substance.
As an example of this, I was reading information packs from vendors, and out of the dozen or so, not a single one had flat charts....
Hi, Chandoo!
Can we download some chart template like in your post? ))
It is really pretty.
[…] Ah good day to my Tableau disciples. Peace be with you. May your day be free of exploding 3D pie charts… […]
[…] ovšem uvádí Chandoo, kolá?ové grafy lze naproti tomu dob?e využít k manipulaci. Linkovaný p?íklad s videem […]
[…] Even people who have the best of intentions create graphics that mislead just because they don’t know about statistics, they don’t know about logic, they about the principles of visualization. It’s not their fault, just like it was not my fault 10 or 15 years ago. Nobody had educated me. It was only through the process of reading books, studying, and learning from other people that I discovered the many mistakes that I’d made in the past, for example, creating 3D pie charts. […]
I think if the point is to create BS, everything should be not only in 3d but in 4d!
4d FTW
[…] makes it very difficult to visually compare data. A good example of how misleading a 3-D charts can be found here. Less is more. Make your visualizations as simple and clean as possible, it makes them much easier […]