Van Gysel asked in a recent post at Chandoo.org for a way to calculate the costs of running a plantation. The twist is that the costs vary by year, and based on the age of the trees.
The following is a slightly simplified version of the solution I offered:
=SUM(IFERROR(LOOKUP(“Year”&MMULT(N($B$3:B$7>0),TRANSPOSE(COLUMN($B$3:B$7)^0)), $B$11:$I$11, $B12:$I12),0)*B$3:B$7) Ctrl+Shift+Enter
Today I am going to try and explain how the formula works.
As always at Formula Forensics, you can follow along with a sample file: Download Here
The Problem
In a plantation, the costs for planting and maintaining trees vary based on the age of the trees and by year. The table below shows the acres of trees planted per year and the yield and costs per year that vary based on the age of the trees.
Let us look at the calculations needed for each year.
Year 2013
- 300 acres of trees were planted in 2013. Calculations for 2013 are as follows. (Only Yield calculation is shown, but the process is similar for Nursery costs, Fertilizers, etc.)
- The trees do not yield any fruits in the first year. As such, Yield for year1=300*0=0
That was easy!
Year 2014
- 700 additional acres of trees will be planted in 2014. Calculations for 2014 are as follows. (Again, only Yield calculation is shown, but others are calculated similarly.)
- 300 acres of trees are 2 years old. 700 acres are 1 year old.
- The 300 acres from 2013 now yield fruit since it is year2. However, the new trees (700 acres) do not yield any fruits yet. So total yield for 2014=300*Year2Yield+700*Year1Yield=300*5+700*0
Year 2015
- 1000 additional acres are to be planted in 2015. Calculations for 2015 are as follows:
- 300 acres are from 2013 (3 years old); 700 acres are from 2014 (2 years old); 1000 acres are from 2015 (1 year old).
- Yield for 2015=300*Year3Yield + 700*Year2Yield + 1000*Year1Yield = 300*10 + 700*5 + 1000*0
Year 2016
- 1000 additional acres are to be planted in 2016. Calculations for 2016 are as follows:
- Yield for 2016=300*15+700*10+1000*5+1000*0
How do we simulate the above calculation in an Excel formula?
A Solution
Let us first look at how we performed the calculations above manually, using the 2016 Yield as an example.
- We took each acreage value in 2016, and determined its age by counting how many years it has been since that acreage was planted. You might have observed that the age can be counted by the number of times a value has been repeated up to that point. (In other words, if I planted 300 acres in 2013, I should see that same amount in 2014, 2015 and 2016.) As such, 300 acres is repeated 4 times. 700 acres is repeated 3 times. 1000 acres is repeated 2 times. And the latest planting of 1000 acres exists only once.
- Once we determine the age for a given acreage, we looked up the yield for that age in the second table
- We then multiplied the acreage with the corresponding yield value.
Calculation #1 can be expressed as follows:
- Age for acreage 1 (first planted in 2013)=count of B3:E3 where value is greater than zero. i.e. COUNTIF(B3:E3,”>0”)
- Age for acreage 2 (planted in 2014)=count of B4:E4 where value is greater than zero. i.e. COUNTIF(B4:E4,”>0”)
- Age for acreage 3 (planted in 2015)=count of B5:E5 where value is greater than zero. i.e. COUNTIF(B5:E5,”>0”)
- Age for acreage 4 (planted in 2016)=count of B6:E6 where value is greater than zero. i.e. COUNTIF(B6:E6,”>0”)
- Age for acreage 5 is zero since nothing has been planted for 2017 yet in 2016
The above approach would work if we were calculating the age one row at a time. However, that can become tedious really fast. We need to perform the calculation for the full range (B3:E7) together, but return the counts for each row individually.
Excel’s MMULT function comes to the rescue!
MMULT (which stands for Matrix Multiply) multiplies two matrices and returns a third matrix based on rules for matrix multiplication. I am planning to devote a whole article to explain the MMULT function. As such, for this article, we will summarize the utility of the function as “take a 2-dimensional array, add each column’s value for each row, and return a 1-column array”.
MMULT requires that its arguments be numeric.
So to obtain the counts for the year 2016, we can use the following:
MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0))
As you can see from the picture below, MMULT’s results are the addition of each column for each row.
In the above formula, you may have noticed that the range uses absolute and relative referencing (signified by the $ sign or lack thereof). This is to ensure that the range grows or shrinks as needed. The upper left address is held constant ($B$3). However, the lower right address for the range has columns that vary but row that is fixed on row #7. This ensures that the formula would work if we copy to the left, right, etc. in the final results.
Now that we have the age for each acreage value, we can look up the corresponding yield value using (what else?) LOOKUP function.
But before we can use LOOKUP, we will need to convert the numeric values returned from MMULT into the strings Year1, Year2, etc. found in the Costs table. Of course, you know how to do that… concatenate the string “Year” to the result from MMULT
“Year”&MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0))
For the 2016 example, we get {“Year4″;”Year3″;”Year2″;”Year1″;”Year0”}
We can now use LOOKUP as follows:
LOOKUP(“Year”&MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0)), $B$11:$I$11, $B12:$I12)
You may recall that LOOKUP looks up a value in the array indicated by the second argument, and returns the corresponding value from the third array argument. In this case, instead of looking up a single value, we look up an array of values (supplied in the first argument) to the function.
The above formula translates to the following:
LOOKUP({“Year4″;”Year3″;”Year2″;”Year1″;”Year0”}, {“Year1″,”Year2″,”Year3″,”Year4″,”Year5″,”Year6″,”Year7″,”Year8”}, {0,5,10,15,20,25,30,35})
The result from LOOKUP is {15;10;5;0;#N/A}
(The last value is #N/A because there is no acreage value for 2017 yet (as of 2016 column). The concatenation resulted in Year0 which does not exist in the “Age of The Trees” range (B11:I11) above.)
By using IFERROR(LOOKUP(…),0) we get {15;10;5;0;0}
We can now multiply the above result with the acreage values for 2016 to get {4500;7000;5000;0;0}
Finally, we SUM the values to get 16500
Putting it all together, we get the following formula (shown for Production for year 2016)
=SUM(IFERROR(LOOKUP(“Year”&MMULT(N($B$3:E$7>0),TRANSPOSE(COLUMN($B$3:E$7)^0)), $B$11:$I$11, $B12:$I12),0)*E$3:E$7)
One of the benefits of the above formula is that you can copy the same formula to calculate values for additional years, as well as other plantation costs.
Download
You can download a copy of the above file and follow along: Download sample file.
Let me know (using the comments below) what you think of the above approach and solution, as well as any other approaches you have utilized to solve a similar problem. In the meantime, I wish you continued Excellence!
-Sajan.
Other Posts in this Series
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30 Responses to “Rescue oddly shaped data – Battle between Formulas, VBA and Power Query”
Nice use of Power Query! Power Query is simply awesome! But somehow a lot of people are punishing themselves by not using it (not learning it).
An imperfect 4th approach for consideration... no codes at all...
Select myrange.
Go to Special --> Blank
Delete Cell --> Shift cell left
90% done... now we just need to move the data of 2nd column to the bottom of 1st column
Of course... Power Query is the best.
Cheers,
There is another way but it involves multiple steps:
Copy the values in column E, move the cursor to F5, Paste Special with Skip Blanks, OK
Copy the values in column D, move the cursor to F8, Paste Special with Skip Blanks, OK
And so on.
This works perfectly, albeit a little clumsily apart from the values in B17 and C16, which can be moved with simple copy and paste
Power Query Forever! I do not know how I survived for so long without knowing and using this tool, I can not recommend it to my colleagues, but by the way they prefer to suffer to learn.
My congratulations here from Brazil.
I rolled my eyes when I saw that data
Using decimal places is a nice trick to order data, thanks for that
And tweaking the first formula a bit, you can use OFFSET instead of INDIRECT
=OFFSET($A$1, MIN(IF(myrange, ROW(myrange)), ROWS(A$1:A1))-1, RIGHT(TEXT(MIN(IF(myrange, ROW(myrange) + COLUMN(myrange)*0.00001), ROWS(A$1:A1)), ".00000"), 5)-1)
Tried the above formula with the downloaded oddly shaped data file and I could not get it to work. I get #value without ctrl+shift+enter, and #ref with ctrl+shift+enter.
Sorry, it was SMALL, not MIN.
Add with CTRL+SHIFT+ENTER.
Thank you for your formula. Like the indirect formula I tested this one in older versions of EXCEL and it worked without ALTERATION in EXCEL 95. Very impressive.
Too complicated
Use =Sum to summarize all the sells to the left and Bobs Your Uncle
@Bertie... I am afraid that won't work when you have more than one value in a row.
I tested this formula in versions of Excel all the way back to Excel 95
=IF(ISERROR(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(MyRange"",ROW(MyRange)+COLUMN(MyRange)*0.00001),ROWS(A$1:A9)),"00000.00000"),".","C"),FALSE)),"",(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(MyRange"",ROW(MyRange)+COLUMN(MyRange)*0.00001),ROWS(A$1:A9)),"00000.00000"),".","C"),FALSE)))
So there are multiple ways of cleaning up messy data by formulas.
Wow.. Excel 95. Who knew people still use that. But as you have shown, Excel has all these beautiful and powerful functions for 23 years. It has data sciency stuff before DS was even a thing.
I had a problem with pasting the formula in the original post.
Formula should be: =IF(ISERROR(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(myrange"",ROW(myrange)+COLUMN(myrange)*0.00001),ROWS(A$1:A1)),"00000.00000"),".","C"),FALSE)),"",(INDIRECT("R"&SUBSTITUTE(TEXT(SMALL(IF(myrange"",ROW(myrange)+COLUMN(myrange)*0.00001),ROWS(A$1:A1)),"00000.00000"),".","C"),FALSE)))
EXCEL even in a 16 bit version, is a very robust and capable program.
I don't like the VBA code. If you have a blank row in MyRange, the last entry in the range is doubled up in the paste.here range.
Not really. The macro is writing one cell at a time from paste.here. You have to clean the range before, which I was too lazy to write. But a line like Range(range("paste.here"), range("paste.here").end(xldown)).clearcontents should do the trick.
Adding Range(range("paste.here"), range("paste.here").end(xldown)).clearcontents fixed the problem.
for step split column by delimiter i am not getting option of split into rows or columns. Can you help me in this
Thanks Chandoo for promoting Power Query.
To simplify further, you can "Unpivot Columns" instead of right click on the newly created column and split it by comma in to rows in step 3 of Power Query.
i used
=LOOKUP(10000,B5:F5)
and got the answers. I just plagiarized this formula somewhere and use it, maybe you can explain why it works.
Regards
@Johan... I am not sure if the formula works correctly. When I tested it with the sample data in this post, it showed #N/As in two cells. Essentially, it will only give first value in each row. So if a row has multiple values, then subsequent values are missed. LOOKUP() function goes thru a list and finds the first value that is less than or equal to the input - in this case 10000 in B5:F5.
I have the need to convert pdf's to excel on occasion and they often come out a mess like this. I have used:
Cell G2 =COUNT(myrange)
Cell G3 =IFERROR(IF(G2-1<1,"",G2-1),"") copied down to G100
Cell H2 =IFERROR(LARGE(myrange,G2),"") copied down to H100
Waouw...
=IFERROR(INDIRECT("R" & SUBSTITUTE(TEXT(SMALL(IF(myrange "", ROW(myrange) + COLUMN(myrange)*0.00001),
ROWS(A$1:A1)), "00000.00000"), ".", "C"), FALSE), "")
but CTRL Shift Enter with {} before and after 🙂 😀
Here's a way with pivot table
https://www.bookkempt.com/2018/02/aligning-non-contiguous-data.html
This is brilliant. Bookmarked 🙂
Another possibility.
This assumes that you have a row index 'k' to use in the SMALL function and a column index 'h' to identify the columns of 'myRange'.
If you define 'coord' to refer to
=k+h/10 [assuming h<10]
then it will be possible to recover values later based upon location within 'myRange'. The formula 'nb' that identifies non-blanks by coordinates is given by
= SMALL( IF(myRange"", coord), k )
Finally, to unpick the pieces
= INDEX( myRange, INT(nb), 10*MOD(nb, 1) )
Whilst I am here and making trouble the PQ solution is also a tad over-complicated. All that is needed is to unpivot the entire table and remove the Attribute column.
The advanced editor would show
let
Source = Excel.CurrentWorkbook(){[Name="myRange"]}[Content],
#"Unpivoted Columns" = Table.UnpivotOtherColumns(Source, {}, "Attribute", "Value"),
#"Removed Columns" = Table.RemoveColumns(#"Unpivoted Columns",{"Attribute"})
in
#"Removed Columns"
1.fill the blank cells with 0
2.the requested column value=sum of those mess number column
but this can be used in only one column has value
Chandoo
And if we use the formula SEARCH (100000000, B5: F5)
JC
Another approach with Power Query, it will still work if the number of columns changed:
let
Source = Excel.CurrentWorkbook(){[Name="myrange"]}[Content],
#"Added Custom" = Table.AddColumn(Source, "List", each Record.ToList(_)),
#"Removed Other Columns" = Table.SelectColumns(#"Added Custom",{"List"}),
#"Expanded LIst" = Table.ExpandListColumn(#"Removed Other Columns", "List"),
#"Filtered Rows" = Table.SelectRows(#"Expanded LIst", each ([List] null))
in
#"Filtered Rows"
Cool idea to use Record.ToList as added column. Thanks for sharing this.
Nowadays, you can just use TOCOL on Excel 2024, MS 365, and Web Excel. It has a parameter to ignore blanks/errors/both.