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 “Make a Quick Thermometer Chart to Compare Targets and Actuals”
You'll probably have some readers insist on bullet charts, which in my experience are no easier to read.
Note on the case where actuals may exceed targets, the target has to be the second series in the chart, not the first, so it appears in front of the actual.
@Jon.. good point. And yes, readers are already saying bullets are the way to go. Atleast @dmgerbino said it on twitter: http://twitter.com/dmgerbino/status/6761754333
But I feel the same as you did. Bullets need orientation to get started and not that easy to construct (here is a tutorial btw... http://chandoo.org/wp/2008/07/21/dashboard-bullet-graphs-excel/ )
When you just have to compare 2 sets of values, a chart like above is good and easy enough.
And yes, thank you for saying that data series order should be correct to show the target on top.
I think bullet charts are a good alternative. I'm not a huge fan of the formatting that you used above where the outline is so thick.
Another option would be to combine a line graph (plan/goal amounts) with the columns (actual) and select the option to remove the line. This leaves just the value (marker), which can be increased in size to leave only a line about the size of the bar. It's an easy and cleaner way to show actual to plan/goal. Does that make sense?
Tony -
I would use columns (or area) for goal, and lines and markers for actual.
What about if you go over the target? The chart doesn't work so well then.
The technique described today is a near bullet chart. As I stated early this morning on Twitter (link: http://bit.ly/4K3yPM ) , I am a fan of Stephen Few's Bullet Graph.
Hubert Urruttia and I started with Charlie Kyd's method, but as Jon Peltier and Chandoo said, they are not easy to contruct. We moved onto prototyping with Fabrice Rimlinger's SPARKLINES FOR EXCEL and now use XLCube's (BonaVista) Micro Chart tool. Both of these tools allow you to create bullet charts just as easy as any Excel chart type.
As far as reading and interpreting them, this chart type has been the easiest for us to present.
There are many chart types. Today's "Make a Quick Thermometer Chart to Compare Targets and Actuals" is fine for a start, but your ultimate goal should be to create Bullet Graphs. AS Stephen Few states in his overview, "The bullet graph was developed to replace the meters and gauges that are often used on dashboards. Its linear and no-frills design provides a rich display of data in a small space, which is essential on a dashboard. Like most meters and gauges, bullet graphs feature a single quantitative measure (for example, year-to-date revenue) along with complementary measures to enrich the meaning of the featured measure. Specifically, bullet graphs support the comparison of the featured measure to one or more related measures (for example, a target or the same measure at some point in the past, such as a year ago) and relate the featured measure to defined quantitative ranges that declare its qualitative state (for example, good, satisfactory, and poor). Its linear design not only gives it a small footprint, but also supports more efficient reading than radial meters."
@dmgerbino
Since @dmgerbino had to bring my name up I guess I should throw in my two cents.
@dmgerbino and I have both implemented Bullet Charts with great success. What is most interesting about this fact is that we have had a harder time implementing Sparklines than Bullet Charts. The reason for this revolves around the simple fact of familiarity. I will explain. People look at a Sparkline and they think it is a really small Line Chart and it is not. People are familiar with Line Charts since they have been around since 1786 when they were created by William Playfair. Bullet Charts on the other hand are different so they almost demand an explanation. Because of this there was a lot of face time that was needed to explain these charts but once people got them they understood the concept. This is similar to when I introduced Cycle Plots http://bit.ly/87ydVG (Thank you @nbrgraphs!) or Horizon Charts http://bit.ly/6PVavj.
Now about the Thermometer Charts… The first thing I want to address is Tony Rose’s statement. I totally agree that the outline on the chart is too think. It might come of as being a whole new series or a new variable. What I have done in instances like this is I have created a Bar Graph and Scatter Plot mixture. Then I have turned off the Data Series on the Scatter Plot and turned on the Horrizontal Error Bars on the Scatter Plot. The new horizontal line stands for the Plan and the Bar is the actual. The reason why I find this more useful is because this technique works if you have exceeded plan. Actually, I do not understand how Chandoo’s method would display the data if Plan is surpassed.
This reminds me of another blog post that @dmgerbino, @Jon_Peltier, and myself commented on over a year ago. http://bit.ly/PNdO Actually, I talk about similar things in regards to familiarity to charting techniques.
- @hubert_urruttia
[...] we have a post on using thermometer charts to quickly compare actual values with targets. Today we follow up the post with 10 charting ideas you can use to compare actual values with [...]
Hi Chandoo
How do I increase the width of the bar chart and also make the long axis labels come in the same line?
Thank you,
Rajiv
@Rajiv
Select the outer part of the chart "Chart Area" and note the cursor will change to arrows
drag the edges to what ever size you want
You can hold the Alt key as you drag and the chart will snap to the cell boundaries
Now click on the chart area inside the chart "Plot Area" and note that a box with small circles appears around it
drag the circles on the edge of that box to suit
You can hold the Alt key as you drag and the chart will snap to the cell boundaries
@ Hui
Thank you for your comments. But my question was not for the "Plot Area" instead I wanted to know about how should I increase the width of the individual bar charts because with my data all the individual bars are coming to be thin and I want to make them appear broader.
Thank You
@Rajiv
Right click on the Series you want to change and select Format Data Series
Under Series Options goto Gap Width and decrease it to suit
[...] Make a Quick Thermo-meter Chart using Excel [...]
Thank you for the great chart and explanation!
How do I show two amounts (Signed Revenue and Pipeline) as stacked within the Target amount?
@CL... you can use stacked column charts and follow the same technique to get this. See attached file for an example - http://img.chandoo.org/playground/thermo-meter-with-additional-details.xlsx
Chandoo - thanks for the quick response! What if I want the data label for the pipeline to be the actual pipeline value, not the signed rev + pipeline value? i.e. 15 instead of 55
Thanks!
How would i do this in excel 2003?
[...] Thermo-meter charts are very good to show how actual value compares with target (or budget). But how can we add another point for say Last Year value to the chart with out cluttering it. [...]
Hi Guys,
As Matt said,
"What if you if you go over the target?"
Is there a way to make it change color? or at least to show what the target was?
I am planning to use this with a "Forecasted vs Real" production chart but I do not know how to show overproduction.
Any clue?
Thanks
How do I do this if I have 2 bars I want side-by-side? ie 2012 Mean with 2012 benchmark overlapping and then 2013 mean with 2013 benchmark overlapping? I want the 2012 and 2012 mean bars sie by side to compare multiple categories.
Sorry, I meant to say the 2012 and 2013 mean bars side by side
I have a problem in that my PM wants a chart that shows a stacked column (Labor and Expense) and then have the overall buget shown as a thermo.
Everytime I try to do this, I either end up with all three being stacked or all of them being seperated.
Help?
Or if someone knows how to only outline the top and sides of a chart series....then I would have this solved. (Make a stacked column with labor, expenses, and remaining budget, then clear the fill and outline only the top and sides.) I just can't figure out how to do that/ not sure if excel will let me only outline part of a chart series.
[...] Thermometer chart to show budget vs. actual performance [...]
Your home is valueble for me. Thanks!...
I've created the thermometer chart as the Chandoo tutorial described. How do I move my columns closer together? I don't want wider columns; I want to move my narrow columns closer together. Thank you!
Dear Elite members,
could you please let me informed whether we could incorporate color formating in this thermometer approach i.e. if my actual performance is <Min then meter color sud go Red, in between min & target it sud change to Amber & target and above sud change to Green. pls advise. thanks,
I think the only way to do that would be with VBA programming.
@Abhinav
Yes, Simply use a stacked column chart, colored appropriately
Or
You may also want to read about Bullet Charts
@ Hui,
Could you pls demonstrate this with the help of an example.
let's have the below sample data
Actual=12
Min=10
Target=15
Max=20
if Actual>=Min then bar color sud be Red
in between Min & Target= Amber
between target(inclusive) & Max = Green
greater than or equal to Max= Blue
Thanks in advance
Abhi
Great blog post with awesome sample data. I've implemented two of the top "power tips" by changing the colour of the actual values, AND setting Actual to be 40% transparent. Looking good.
[…] easy with these charts. Use them sparingly. As a rule a thermo-meter chart would be better (easy to make, takes less space, scalable) for situations like […]
[…] easy with these charts. Use them sparingly. As a rule a thermo-meter chart would be better (easy to make, takes less space, scalable) for situations like […]
I recently purchased the template bundle and love the ease of use - thank you!
I would like to ask if it is possible to add an important 'block' to the dashboard to illustrate an important status for my executive team; 'billing status'? (ie budget / amount billed) something like that?
Thank you!
@Cheif449.. Thanks for your purchase and kind words.
You can add this easily to the dashboard. Follow below steps.
1. Unprotect the dashboard worksheet.
2. Add a text box (Insert > Drawing Shapes) to the dashboard
3. Put any text inside it as per your need.
4. Format it as needed.
5. Protect the dashboard again.
How do you do this in Excel 2010 - I am not seeing that option in Format data series.
how would we check target and actual sale for multiple years
Select any of the bar, right click and format data series