I have a very detailed excel model to calculate the profitability of a project, that we can call P.
The model has been simplified to compute from 3 unrelated variables. I would like to automatically create a table that shows how inputs A, B and C might vary in order to produce a pre-defined level of profitability, P. For instance, if A = 4 & B = 30, then C must = 2 in order for P to equal 20%. Likewise, if A = 5 & B = 25, then C must = 3 in order for P to equal 20%. A and B should be tested at sensible increments, perhaps 8 intervals each.
A laborious (not scalable) equivalent would be to manually define A and B, then goal-seek C to our pre-defined level of P - we'd then repeat for each combination of A and B at the given intervals and record in a two-way table.
I believe a conventional two-way data table would be pratical if the model sitting behind the inputs were greatly simplified, unfortunately this isn't possible.
Thanks to anyone that can lend a hand. Kind regards.
I think the best way to approach this will be with a VBA macro and the prebuilt GoalSeek Function something like this (p is in cell D1) :
Range(”D1”).GoalSeek Goal:=20 _
ChangingCell:=Range(“C1”)
Related
I want to calculate the Gross Value Added for different countries and industries using multi-regional input-output (MRIO) tables. However, I struggle to find a good explanation of how this is done based on the data available. The definition of the GVA (Gross Value Added) is the output of a country/industry less the intermediate consumption, and it is related to the GDP by:
GVA = GDP + subsidies - taxes
So far, I have used the "extensions" or "satellite accounts" that provide the Value Added (VA) disaggregated across different flows, i.e. example from Exiobase in the picture. The VA is the sum of all 12 to my understanding. However, based on the definition of the GVA, I have subtracted 1-3 since these are taxes (so GVA = sum of line 4-12). To me, this seems like the correct approach, but I have not succeeded in finding an explanation that could confirm/disprove. I also become uncertain due to the naming of the extension, i.e. "value added" sounding like "gross value added". Does anyone know the correct way of doing this?
Finally, in MRIO x is termed "gross output" being the total output to final demand + intermediate consumption:
x = Ax + y (Ax = intermediate, y = demand)
or
x = (I-A)^-1 * y = L*y (L = Leontif inverse/requirement matrix)
Does this mean that I can also derive the GVAs from x by subtracting the intermediate consumption? In my mind, this will just leave me with "y", but there might be a another smart way?
Thanks in advance!
From what I understand, yes you can !
You have to differentiate Z = Ax summed along its rows or along its columns
x - rowSum(Z) is the GVA.
x - colSum(Z) is the total final demand.
Regarding Exiobase, I don't have a real answer.
I found that summing all lines of the VA (keeping lines 1-3), I get "quasi" the same results as subtracting the row sum of Z to x.
Which is stange...
Given an NxM array of positive integers, how would one go about selecting integers so that the maximum sum of values is achieved where there is a maximum of x selections in each row and y selections in each column. This is an abstraction of a problem I am trying to face in making NCAA swimming lineups. Each swimmer has a time in every event that can be converted to an integer using the USA Swimming Power Points Calculator the higher the better. Once you convert those times, I want to assign no more than 3 swimmers per event, and no more than 3 races per swimmer such that the total sum of power scores is maximized. I think this is similar to the Weapon-targeting assignment problem but that problem allows a weapon type to attack the same target more than once (in my case allowing a single swimmer to race the same event twice) and that does not work for my use case. Does anybody know what this variation on the wta problem is called, and if so do you know of any solutions or resources I could look to?
Here is a mathematical model:
Data
Let a[i,j] be the data matrix
and
x: max number of selected cells in each row
y: max number of selected cells in each column
(Note: this is a bit unusual: we normally reserve the names x and y for variables. These conventions can help with readability).
Variables
δ[i,j] ∈ {0,1} are binary variables indicating if cell (i,j) is selected.
Optimization Model
max sum((i,j), a[i,j]*δ[i,j])
sum(j,δ[i,j]) ≤ x ∀i
sum(i,δ[i,j]) ≤ y ∀j
δ[i,j] ∈ {0,1}
This can be fed into any MIP solver.
I’ve used Excel in the past but the calculations including the Poisson-Distribution took a while, that’s why I switched to SQL. Soon I’ve recognized that SQL might not be a proper solution to deal with statistical issues. Finally I’ve decided to switch to Matlab but I’m not used to it at all, my problem Is the following:
I’ve imported a .csv-table and have two columns with values, let’s say A and B (110 x 1 double)
These values both are the input values for my Poisson-calculations. Since I wanna calculate for at least the first 20 events, I’ve created a variable z=1:20.
When I now calculated let’s say
New = Poisspdf(z,A),
it says something like non-scalar arguments must match in size.
Z only has 20 records but A and l both have 110 records. So I’ve expanded Z= 1:110 and transposed it:
Znew = Z.
When I now try to execute the actual calculation:
Results = Poisspdf(Znew,A).*Poisspdf(Znew,B)
I always get only a 100x1 Vector but what I want is a matrix that is 20x20 for each record of A and B (based on my actual choice of z=1:20, I only changed to z=1:110 because Matlab told that they need to match in size).
So in this 20x20 Matrix there should always be in each cell the result of a slightly different calculation (Poisspdf(Znew,A).*Poisspdf(Znew,B)).
For example in the first cell (1,1) I want to have the result of
Poisspdf(0,value of A).*Poisspdf(0,value of B),
in cell(1,2): Poisspdf(0,value of A).*Poisspdf(1,value of B),
in cell(2,1): Poisspdf(1,value of A).*Poisspdf(0,value of B),
and so on...assuming that it’s in the Format cell(row, column)
Finally I want to sum up certain parts of each 20x20 matrix and show the result of the summed up parts in new columns.
Is there anybody able to help? Many thanks!
EDIT:
Poisson Matrix in Excel
In Excel there is Poisson-function: POISSON(x, μ, FALSE) = probability density function value f(x) at the value x for the Poisson distribution with mean μ.
In e.g. cell AD313 in the table above there is the following calculation:
=POISSON(0;first value of A;FALSE)*POISSON(0;first value of B;FALSE)
, in cell AD314
=POISSON(1;first value of A;FALSE)*POISSON(0;first value of B;FALSE)
, in cell AE313
=POISSON(0;first value of A;FALSE)*POISSON(1;first value of B;FALSE)
, and so on.
I am not sure if I completely understand your question. I wrote this code that might help you:
clear; clc
% These are the lambdas parameters for the Poisson distribution
lambdaA = 100;
lambdaB = 200;
% Generating Poisson data here
A = poissrnd(lambdaA,110,1);
B = poissrnd(lambdaB,110,1);
% Get the first 20 samples
zA = A(1:20);
zB = B(1:20);
% Perform the calculation
results = repmat(poisspdf(zA,lambdaA),1,20) .* repmat(poisspdf(zB,lambdaB)',20,1);
% Sum
sumFinal = sum(results,2);
Let me know if this is what you were trying to do.
I'm a total beginner with CPLEX and OPL, so maybe you can help me with the coding of a mixed integer programming model.
In my case: I have an optimization function including a parameter transportation cost which are specific for the starting point (Hubs h), the destination (DCs i), the transported good (Products k) and the mode of transportation (TransportOptions r) used.
I wrote it like this:
float transportC_Hub_DC[Hubs][DCs][Products][TransportOptions] = ...;
//transport cost of one unit of gook k vor starting point h to destination i using transportation option r
I would like to fill this array with its multiple dimensions from an excel spread sheet. At the moment my spreadsheet has the four indexes in separate columns and the specifice transportation cost in another column. It looks like this:
Excel Datasheet
My problem is that I do not know how to make the programme understand how the transportation cost data are ordered. How does the programme know that in the first cell of the column "transportation cost" is the cost for the specific combination of the different indexes? So how do I tell the programme that I used h=1, i=1, k=1, r=1 in the first cell and h=1, i=1, k=1, r=2 in the second cell and not h=1, i=1, k=2, r=1 in the second cell? What do I have to write in the model or the data file in CPLEX to make this clear?
See technote http://www-01.ibm.com/support/docview.wss?rs=0&context=SSCMS55&uid=swg21401340&loc=en_US&cs=utf-8&cc=us&lang=all
The idea is to read a tuple set and then turn your tuple set into a 4D array.
I'm very confused on how to use Microsoft Excel to simulate a "problem", but I've been assured that it's possible.
I have the equation
v(t) = (mg/c)(1-e^((-c/m)(t)))
And I know the values of m, g, k, and c.
m = 170
g = 32 ft/s^2
k = 2.5 lb/ft
c = 1.2 lb/ft/s
So my formula changes into
v(t) = (170*32/1.2)(1-e^((-1.2/170)(t)))
v(t) = (453.33)(1-e^((-.00705)(t)))
The problem is about a bungee jumper, and this is one function that I should use to find velocity, and another that is used for x (distance), but if I can learn how to properly implement this one, I should be able to easily figure out the other one.
I need to somehow implement this in Excel, as a spreadsheet simulation. I have no idea how to implement this in Excel, and I don't know the formulas to do it. I know I could just go through the formula manually and just substitute variables in for t (i.e., .5, 1, 1.5, 2, 2.5, ...), but I know there's supposed to be some way for Excel to do it for me. Additionally, I'm not sure how to simplify the powers and the "e" in my formula, and I actually don't know if I need it if I can just sub in variables like I think I can. Any help would be greatly appreciated.
EDIT: The other state equation, x(t), is below
x(t) = (mg/c)(t) + ((m^2 * g) / c^2))e^((-c/m)(t) - (m^2 * g / c^2))
This formula as mentioned in the OP:
v(t) = (453.33)(1-e^((-.00705)(t)))
needs a little adaptation, as suggested by #Tim Williams, to be suitable for Excel:
=453.33*(1-EXP(-.00705*t)
Excel does not multiply letters by numbers but will attempt to interpret t above as a named range (which may contain one or more numbers) before objecting. So t may be the name given to a range starting .5 and stepping .5 up to and including 10 (may easily be created with Fill , Series…).
If the above formula is then placed in the same row as 0.5 and copied down to suit the results should be as required.
It may however be worth noting that naming a range as a single letter is not best practice and for accuracy, convenience and versatility the constants (eg re gravity) and the variables (eg mass) would be better fed as parameters to the formula.