Using Solver to Assign Items to Buckets

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In April 2011, Mdsuhair asked a question at the Chandoo.org Forums

What formula can I use to divide a group of numbers into 2 groups so that the Sum of each of the 2 groups is as equal as possible?

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:

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38 Responses to “Time to showoff your VBA skills – Help me fix ActiveSheet.Pictures.Insert snafu”

  1. shokks says:

    I tried your code with 2003, it works.

    But, I know Addpicture does not take URLs anymore with 2007 onwards, perhaps its the same with picture.insert as well.

    http://support.microsoft.com/kb/928983/en-us

    The above link gives the solution as "picture fill in a shape such as a rectangle".

  2. Vince E. says:

    Tried to recreate this, but it worked fine for me. I just took the image of the error you showed in the post. Is there more info that can narrow this down a bit?

  3. Ian Hinckley says:

    Hi

    Not sure if this is what you're after, but I just tried this

    Sub Macro1()
    ActiveSheet.Pictures.Insert("http://www.google.co.uk/intl/en_uk/images/logo.gif").Select
    End Sub

    Tied a button to it on the sheet and it seems to work; hope this helps a little

    Ian

  4. Chandoo says:

    @All.. the issue is in Excel 2007. In 2003 ActiveSheet.Pictures.Insert seems to work fine. Unfortunately, I have design this in Excel 2007.. that is why I posted it here..

  5. Ian Hinckley says:

    v2

    Sub Macro1()
    Set n = ActiveSheet.Pictures.Insert("http://www.google.co.uk/intl/en_uk/images/logo.gif")
    With Range("c12")
    t = .Top
    l = .Left
    End With
    With n
    .Top = t
    .Left = l
    End With
    End Sub

    Ian

  6. Ian Hinckley says:

    That didn't come out very well. This positions at c12, so can change easily:
    Sub Macro1()
    Set n = ActiveSheet.Pictures.Insert("http://www.google.co.uk/intl/en_uk/images/logo.gif")
    With Range("c12")
    t = .Top
    l = .Left
    End With
    With n
    .Top = t
    .Left = l
    End With
    End Sub

    Works OK in 2007

    Ian

  7. Chandoo:
    Try 'ActiveSheet.Pictures.Insert'

    With ActiveSheet.Pictures.Insert("C:\Example.png")
    .Left = ActiveSheet.Range("A1").Left
    .Top = ActiveSheet.Range("A1").Top
    End With

  8. Jon Peltier says:

    activesheet.pictures.insert "C:\Documents and Settings\Jon Peltier\Desktop\2007 stuff\insert_charts_2007.png"

    Works for me in 2003 SP3 and in 2007 SP2.

    Check the URL, and make sure you have internet connectivity.

    What also works, and is newer (pictures.insert was supposedly deprecated in '97):

    activesheet.shapes.addpicture "C:\Documents and Settings\Jon Peltier\Desktop\2007 stuff\insert_charts_2007.png", false, true, 200,200,100,100

    Unfortunately you must specify dimensions (the last four arguments) and you don't necessarily know them. But the picture size is still related back to the original picture size, so you could use scaleheight and scalewidth to fix this.

  9. Chandoo: I just re-read your post.

    The code I posted works for me. However, I'm using a local picture. If you try to add a picture from the web, this won't work.

    I remember solving this problem before by adding a rectangle shape first, then using the Shapes.AddPicture method to get a picture from the web.

    I'll find that code and post it here.

  10. Chandoo says:

    Some more updates... The code "ActiveSheet.Pictures.Insert (path)" works fine in Excel 2007 at home. Strange it failed miserably on my work laptop. Do you think this has got something to do with SP2 of MS Office 2007 or something like that?

    @Ian, Jon: Thanks for the code snippets. I guess I will use my home installation of excel to do this.

  11. Chandoo:

    Try this on your work laptop:

    Sub test()
    ActiveSheet.Shapes.AddShape msoShapeRectangle, 50, 50, 100, 200
    ActiveSheet.Shapes(1).Fill.UserPicture _
    "http://www.datapigtechnologies.com/images/dpwithPig6.png"
    End Sub

  12. Jon Peltier says:

    I didn't mean to post code with a local file, because both approaches worked with an internet image as well. This is in Excel 2007 SP2.

    activesheet.pictures.insert "http://peltiertech.com/images/2009-07/col_area_noblanks.png"

  13. Jon: Looks like I have SP1 on my client machine! I wasn't paying attention.

    Just checked my home computer where I have SP2, and you're right...looks like they fixed it.

  14. Jon Peltier says:

    I didn't even bother testing in SP1, though I could if anyone cares enough.

  15. teylyn says:

    I'm afraid I don't have a solution, but I find it remarkable that after attaining a certain status in the Excel world, Chandoo does not need to post on an Excel discussion forum to get help for an Excel problem. Instead, he posts on his blog and all the gurus come rushing to his help.

    Isn't Web 2.0 great?

  16. Jon Peltier says:

    Teylyn - I saw Chandoo's tweet first, and followed the link back to his blog.

  17. Chandoo says:

    @Mike.. thank you. I have seen the fill rectangle solution before posting the query here. For that matter, I have also tried the solution of embedding a browser control on a spreadsheet. both of these seemed a bit extreme. That is why I have asked it here.

    But I guess I will end up using it if I had to build this in work laptop.

    @Teylyn: I have thought of posting this in a forum. (Unfortunately I have not been to any excel group in the last 5 years. Last time I was active was when I built a jave based excel sheet construction solution using POI.HSSF classes of Apache... ) After searching for a few hours, I found several forum posts where others had same problem and the solution recommended (using .left and .top parameters) is not working for me. Incidentally most of these solutions are from a certain Jon Peltier 😛

    I thought may be the problem is interesting for fellow blog readers. So I posted it here.

  18. Justin B says:

    Hi,
    Adapting the code in the question,

    [code]
    Sub InsPicture()
    pPath = "http://chandoo.org/images/pointy-haired-dilbert-excel-charts-tips.png"
    With ActiveSheet.Pictures.Insert(pPath)
    .Left = Range("a1").Left
    .Top = Range("a1").Top
    End With
    End Sub
    [/code]

    Seems to work fine

  19. Jon Peltier says:

    Looks like it was a problem in 2007 up to SP1, which was corrected in SP2.

  20. Chandoo says:

    @Jon.. seems like the case. I just checked the version at work laptop. it is 12.0.6331.5000 (SP1).

    Thank you so much every one. I really appreciate your time and suggestions in solving this.

  21. Jon Peltier says:

    Glad to help. I couldn't understand why something so straightforward wasn't working.

  22. Kieranz says:

    Hi All
    Is there a way of inserting a motion clip eg animated gif or swf or flv?
    Thks

    • Chandoo says:

      You can insert animated GIFs by inserting them in a browser control through VBA. For other types of movies, I can guess you can insert them as clip art.

  23. ashvini says:

    I WANT THE INSERT PICTURE BY USING COADING

  24. Lutz says:

    so currently i was struggling same as you, chandoo, with the insert picture method in excel 2007/10 from an url and came along your thread here.

    so i re-designed the code on the addshape method as mike was suggesting it and all of the sudden it works just fine.

    thanks alot to you guys, you were a great help
    a big salut from switzerland

  25. Santiago says:

    Hi guys,

    I need help copying and pasting an image with the path in a cell.
    I leave the code.

    And thank you very much!

    Sub Copiarimg()

    Dim pic As Picture

    With ActiveSheet

    Set pic = .Pictures.Insert(Range("f2").Value)

    With .Range("e9:g22")
    pic.Top = .Top
    pic.Left = .Left
    pic.Width = .Width
    pic.Height = .Height
    End With
    End Sub

  26. I've played around with the approaches in these comments, and the code below is what I've come up with. The ImagePath can be a local file or a URL. As Jon mentioned above, the trick is to set an arbitrary value for the width and height, then call the ScaleWidth and ScaleHeight methods afterward to reset the picture to its original size. Once the LockAspectRatio property is set, you can change the picture width and the height will automatically scale (or vice-versa).

    Sub AddPictureToRange(TopLeftCellAddress As String, ImagePath As String)

    Dim pic As Shape
    Dim l As Single, t As Single
    Dim temp As Single

    l = Me.Range(TopLeftCellAddress).Left
    t = Me.Range(TopLeftCellAddress).Top
    temp = 10# ' arbitrary value

    Set pic = Me.Shapes.AddPicture(ImagePath, msoFalse, msoTrue, l, t, temp, temp)
    pic.ScaleHeight 1#, msoTrue
    pic.ScaleWidth 1#, msoTrue
    pic.LockAspectRatio = msoTrue

    End Sub

  27. dip says:

    I need some help with inserting pictures. I have an excel file with a column of item numbers next to this row I want to insert a picture of this item. The pictures are coded with the item number so I tried to insert it with one of the codes above:

    Sub InsPicture()
    pPath = "http://img.bricklink.com/P/80/55236.gif"
    With ActiveSheet.Pictures.Insert(pPath)
    End With
    End Sub

    That worked but I need to do that for every row separtly.
    So I tried in the code
    pPath = "http://img.bricklink.com/P/80/"&Text(a1;"#")&".gif"

    But that gives errors.

    Anybody ideas?

  28. alex says:

    Hi Nicholas, I used your solution in a related problem in Excel 2003 and it worked flawlessly..thank you!

  29. Richard says:

    Hi Mike Alexander,

    Your solution with some changes was helpful in my problem in XL 2007, thanks.

  30. seejay says:

    Hi,

    thanks all. In addition, I had a problem with multiple pictures inserting (every new picture replaced the prior one). I've changed it a bit, may be helpful..

    Sub test()
    ActiveSheet.Shapes.AddShape msoShapeRectangle, 50 , 50, 100, 200
    ActiveSheet.Shapes(1).Fill.UserPicture _
    "http://www.datapigtechnologies.com/images/dpwithPig6.png"
    ActiveSheet.Shapes(1).Copy
    ActiveSheet.Paste
    End Sub

  31. Jon Peltier says:

    Try this instead:
     
    Sub test()
    ActiveSheet.Shapes.AddShape msoShapeRectangle, 50 , 50, 100, 200
    ActiveSheet.Shapes(ActiveSheet.Shapes.Count).Fill.UserPicture _
    "http://www.datapigtechnologies.com/images/dpwithPig6.png"
    End Sub

    • Kez says:

      Thanks to everyone, this thread has been very helpful. However, image inserting still doesn't work quite as expect for me.

      While I can get a picture inserted into an Excel 2010 worksheet using either:

      1) ActiveSheet.Shapes(ActiveSheet.Shapes.Count).Fill.UserPicture...
      2) ActiveSheet.Pictures.Insert(pPath), and
      3) Shapes.AddPicture...

      unfortunately the images all insert with a display size determined not by the actual pixel dimensions of the image but by the dpi resolution.

      So for example, if I insert two copies of the exact same 600x600 pixel image, one with a 300dpi resolution and the other with 72dpi, they display at vastly different sizes on screen.

      While this might be intended behaviour for Excel in order to maintain a WSYWIG printing layout, I actually need a way to insert the image based on the the actual pixel dimesnsions and ignoring the dpi resolution.

      Any help appreciated.

      Thanks
      Kez

  32. Kez says:

    Not doing an intentional bump, but realised I posted in rely to one of the repsonses here instead of to the main thread, so reposting.
    =====

    Thanks to everyone, this thread has been very helpful. However, image inserting still doesn’t work quite as expected for me.

    While I can get a picture inserted into an Excel 2010 worksheet using any of the below methods:

    1) ActiveSheet.Shapes(ActiveSheet.Shapes.Count).Fill.UserPicture....
    2) ActiveSheet.Pictures.Insert(pPath), and
    3) Shapes.AddPicture....

    unfortunately the images all insert with a display size determined not by the actual pixel dimensions of the image but by the dpi resolution.

    So for example, if I insert two copies of the exact same 600×600 pixel image, one with a 300dpi resolution and the other with 72dpi, they display at vastly different sizes in Excel on screen.

    While this might be intended behaviour for Excel in order to maintain a WYSIWYG printing layout, I actually need a way to insert the images based on the the actual pixel dimesnsions and ignoring the dpi resolution.

    Any help appreciated.

    Thanks
    Kez

  33. Kez says:

    Well, answered my own question 🙂

    For those who might be interested, you can use this function:

    Public Function GetPicDims(strFilePath As String, strFileName As String) As String
    GetPicDims = CreateObject("Shell.Application").Namespace((strFilePath)). _
    ParseName(strFileName).ExtendedProperty("Dimensions")
    End Function

    to get the dimensions of the image you want to insert. Then you can parse the return string and use the width and height values to add a rectangle shape of the appropraite size, like:

    ActiveSheet.Shapes.AddShape msoShapeRectangle 50, 50, iWidth, iHeight

    which you then fill with the picture:

    ActiveSheet.Shapes(ActiveSheet.Shapes.Count).Fill.UserPicture "c:\temp\test.jpg"

    This way the picture gets inserted using the pixel dimensions and the (print) resolution gets ignored.

    If desired, the GetPicDims function can be made more generic to get other ExtendedProperties.

    Regards
    Kez

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