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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49 Responses to “Project Management Dashboard / Project Status Report using Excel [Part 6 of 6]”

  1. [...] display milestones Part 4: Time sheets and Resource management Issue Trackers & Risk Management Project Status Reporting – Dashboard Bonus Post: Using Burn Down Charts to Understand Project [...]

  2. Alex says:

    Excellent!

    I was looking forward to this and you've done it again...Shame I can't claim it was all my own work 😉

    ps hope you're getting enough sleep

  3. Izabel says:

    Excelent !!! Tks to share your knowledge with us.
    Izabel
    Sao Paulo - Brazil

  4. Miguel says:

    Nice job!.

    I'm also keen on PM Excel Dashboards. Please, take a look at

    http://screencast.com/t/TyaxH5r4mDf

    That's one example of my Project control Spreadsheets.

    Cheers

  5. [...] haired Dilbert hat zum Abschluss einer Artikeserie zum Thema Projektmanagement mit Excel eine Anleitung zum Bau eines Projekt-Dashboards veröffentlicht. Ein Dashboard ist eine Visualisierungsform für große Mengen von meist [...]

  6. Rishil says:

    Quite a nice and helpful article. I am sure excel is one of the most used application across many many big companies. And your info on project status update using excel would surely be usefull. Keep up the good work on this blog site. Also to share there are some open source flash-based graphing and charting solution which caould also be used on any project..
    http://askwiki.blogspot.com/2009/07/how-to-create-quality-charts-using.html

  7. Chandoo says:

    @Alex, Izabel .. thank you 🙂

    @Miguel: Thank you. Your dashboard looks very good. It is inclined towards the budget and finances of the project. I have kept those aspects out of this series. May be I will revisit the financial aspect of projects at a later point.

    @Rishil: Thank you. Yes, you can create flash based charts (or even simple image based charts) and embed them in a project dashboard that can be published to the team using intranet (like sharepoint). This is how large companies usually do it. Thanks for sharing the Askwiki article.

  8. Tim says:

    Great looking dashboard!! Do you have a version for the Mac versions of Office available?

    Thanks

  9. ravi says:

    Chandoo,
    this is great piece of collating info.I liked it and shall try using it in office.
    Thanks for the all hard work behind this.

  10. Mrigank says:

    Chandoo,

    Kudos. This is really as simple as it gets for laymen. We did this sort of stuff in Consulting - but this can now become really simple for people. Will have my team look at this! Great work.

    thanks,

    Mrigank

  11. [...] I suggest reading my 7 part series on project management using excel. Starting with Excel Gantt Charts to Project Dashboards. [...]

  12. bw says:

    Just downloaded the project management template bundle...great!

    Have you done anywork on a Project Portfolio Dashboard template?

  13. Chandoo says:

    @Bw... Thanks for getting a copy of the templates. 🙂 I have worked on few assignments where we built such templates. But these are similar to other regular dashboard templates. I will share some of these ideas in a later post someday. Meanwhile if you have any ideas on how to structure project portfolio dashboard, let me know using comments or email.

  14. [...] to display milestones Time sheets and Resource management Issue Trackers & Risk Management Project Status Reporting – Dashboard Bonus Post: Using Burn Down Charts to Understand Project [...]

  15. [...] display milestones Time sheets and Resource management Part 5: Issue Trackers & Risk Management Project Status Reporting – Dashboard Bonus Post: Using Burn Down Charts to Understand Project [...]

  16. [...] to display milestones Time sheets and Resource management Issue Trackers & Risk Management Project Status Reporting – Dashboard Bonus Post: Using Burn Down Charts to Understand Project [...]

  17. Josh L says:

    Thanks fro the great ideas! To get a sense of the layout and design of a Dashboard more geared toward Cost and Schedule anaysis, check out the example Dashboard at http://www.ProjectDashboards.com which was built entirely in excel.

  18. DS says:

    hey,

    i just need a simple Chart where by i can show some of the projects by % wise. no dates required.

    1st column Project name and 2nd column will be status (filled with %). can you pls help me out.

    Thanks.

  19. Chandoo says:

    @DS... if you have excel 2007, you can use data bars in conditional formatting for this purpose.

  20. Larph says:

    Hi Chandoo - this series is an excellent resource and tutorial, thank you for sharing.

    When I sat down to consider what my dashboard should look like, one of the most important features for me is to be able to maintain version control and to show simply on what version is on display.

    Apart from the naming convention of the file name, is there a good way to do this within a dashboard? I'd be interested to hear your thoughts!

  21. Chandoo says:

    @Larph: Welcome 🙂

    > You can do version control thru Macros (but always remember that your audience can disable macros)

    > Another option is to use a static time stamp / version number in the title page of dashboard that you update manually whenever you make changes to the file

    > In excel 2010, you can keep track of file versions from File menu. This can be used to select a previous version of dashboard.

    > Best option is to use a version control system like SVN or upload files to Sharepoint or something like that. This will take care of versioning for you (although it is a bit technical and dashboard audience may have difficulty figuring the versions out).

    > The easiest option is to use filenames and the CELL() formula to get the version number (or date) from the filename so you can show it on the dashboard.

  22. Di says:

    Hi Chandoo... I'm following you from Brazil...
    I would like to thank you for the tips about excel, mainly with dashboards ... It helped me a lot …
    Take care...

    Di

  23. Kelly Fidei says:

    On the dashboard when I print, the text is blanked out in the middle of the Issues list - suggestions on how to fix?

  24. Neil Joseph says:

    Hi Chandoo, do you have an equivalent Project Management Dashboard / Project Status Report for MS Office 2010?

  25. Paul Brown says:

    As a Microsoft trainer I'm interested in your choice of Excel for project management. I'm assuming that you've tried Microsoft Project and have decided not to use it? We get folks on our MS Project courses who've tried to use Excel for PM purposes and none of them have made such an impressive project plan, but I wonder is it worth all the effort?

  26. Arc Nteimam Finomo says:

    This looks very interesting. How may I be a part of this

  27. Stephanie says:

    Does this template work in Google Spreadsheets?

  28. Thierry Lutonto says:

    Many thanks for sharing your expertise with us. Keep up the good work 🙂

  29. ppm software says:

    Heya i'm for the first time here. I came across this board and I to find It really helpful & it helped me out a lot. I am hoping to offer one thing again and aid others like you helped me.

  30. Adam G says:

    Hi Chandoo,
    Your PM dashboards impressed me so much that I've downloaded the Portfolio and Project Management package.  All of the documents look very professional.
    I was going through the Portfolio dashboard and I had a question.  
    When I enter in additional holidays they are highlighted in the gantt chart.  Is it possible so that the name of the holiday shows up in the highlighted area of the gantt chart.
    Thanks
    Adam

  31. alan foster says:

    can you confirm that the downloads will work on a mac - excel for mac v14.3.6

    thanks

  32. Paul says:

    Made a slight variation on the schedule sheet,

    1. Add a date column for start
    2. In week column cell use =weeknum() and link to date cell
    3. Hide week column

    When you enter in a date for each task the week number is populated accordingly
    simple but more effective, you can also dynamically link the date cell to your MSP project file for even more automation!!

  33. Irick Burris says:

    I purchased a copy of the project management dashboard excel file. I misplaced the password to unlock the file and make modification. Can you please resend the password.

    Thank much in advance...

  34. ninemsn.com.au says:

    Hi there! I just would like to give you a big thumbs up for your great info
    you've got right here on this post. I'll be returning to your website
    for more soon.

  35. Vijay says:

    I bought ur project management template just want to know how to hide the budget section from portfolio?

  36. Squirrel says:

    Hi, Thanks - very good job you've prepared!
    You've inspired me as well 🙂
    Best regards

  37. mj says:

    Hello!
    I am using a gantt chart template which i got from your website. All is good just when I add all my acitivities in data spreadsheet and then go back to gantt chart to view them, I only see first 9 and then I need to keep scrolling for the next ones. is it possible to see most of the activities if not all in the single frame.
    thanks for answering!

  38. Sanford says:

    This is my first time pay a visit at here and i am actually happy to read all at alone place.

  39. gerald says:

    I am interested in your dashboard; downloaded the locked version, unable to use it...do you have a user guide that is available that I can see and use on the locked version?

  40. Arun says:

    Please send me daily newsletter

  41. Ramya says:

    Hi,
    I downloaded the PM dashboard and the gantt chart only has dates till the year 2016. How do I change this to include 2017 FY as well.
    When I enter a activity for this year , it fails to show up on the chart.

  42. Hari says:

    Hi

    Would.like to purchase the project management .kits

    Pls share the payment link in INR

    Also share your contact number to speak with you

    Regards
    Hari
    9384825926

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