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.
Related
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 want to create a dynamic array that returns me X values based on given probabilities. For instance:
Imagine this is a gift box and you can open the box N times. What I want is to have N random results. For example, I want to get randomly 5 of these two rarities but based on their chances.
I have this following formula for now:
=index(A2:A3,randarray(5,1,1,rows(A2:A3),1). And this is the output I get:
The problem here is that I have a dynamic array with the 5 results BUT NOT BASED ON THE PROBABILITIES.
How can I add probabilities to the array?
Here is how you could generate a random outcome with defined probabilities for the entries (Google Sheets solution, not sure about Excel):
=ARRAYFORMULA(
VLOOKUP(
RANDARRAY(H1, 1),
{
{0; OFFSET(C2:C,,, COUNTA(C2:C) - 1)},
OFFSET(A2:A,,, COUNTA(C2:C))
},
2
)
)
This whole subject of random selection was treated very thoroughly in Donald Knuth's series of books, The Art of Computer Programming, vol 2, "Semi-Numerical Algorithms". In that book he presents an algorithm for selecting exactly X out of N items in a list using pseudo-random numbers. What you may not have considered is that after you have chosen your first item the probability array has changed to (X-1)/(N-1) if your first outcome was "Normal" or X/(N-1) if your first outcome was "Rare". This means you'll want to keep track of some running totals based on your prior outcomes to ensure your probabilities are dynamically updated with each pick. You can do this with formulas, but I'm not certain how the back-reference will perform inside an array formula. Microsoft's dynamic array documentation indicates that such internal array references are considered "circular" and are prohibited.
In any case, trying to extend this to 3+ outcomes is very problematic. In order to implement that algorithm with 3 choices (X + Y + Z = N picks) you would need to break this up into one random number for an X or not X choice and then a second random number for a Y or not Y choice. This becomes a recursive algorithm, beyond Excel's ability to cope in formulas.
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 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”)
I am trying to build an excel file to take soil lab test results and organize and assign them preliminary labels.
A sample test will include pH, SAR/ESP, and EC readings. Based on those readings I want to assign the results the label Normal, Saline, Saline-Sodic, or Sodic.
Each label has an associated range of values for each criteria, simplest way to visualize what Im looking for is a a graph with two axis (SAR/ESP vs EC) with 4 quadrants. 3 of the quadrants refer to the same pH range.
I have a simple if then setup going right now that basically assigns each result all the possible labels based on each category then assigns it the label that comes up the most. However this is slow and ugly. Is there a way to consolidate this so that when I import a table where each row is a test I can have one column calculating this?
For example ph is evaluated:
=IF($I$2<=8.5,"A B D","C")
With A = Saline, B = Saline-Sodic, C= Sodic, D = Normal.
Then SAR is evaluated:
=IF($I$3<=13,"A D","B C")
etc.
Then:
=COUNTIF($B$9:$B$12,"A*")
Iterated for each label.
The labels are then counted:
=INDEX(Table1[Column1],MATCH(MAX(Table1[Column3]),Table1[Column3],0))
Working properly: