i m a total beginner in Choco Solver. I want to make a simple shift scheduler.
i have set integer variables like this
IntVar day1 = model.intVar("day1", new int[] {0,1,2,3,4,5});
where 0 , 1,...5 is a reference ID to an employee.
I have a total of 30 variables,(one for every day of the month) since this a monthly based shift schedule.
I have set up constraints, that do not allow e.g. not be on shift for two days in a row.
My question is,
how can i set up a constraint, such that each employer has a minimum of 5 shifts ie. each value in the domain appears at least 5 times in all 30 variables ?
Thank you!
There are several ways of doing this. Give a look at model.globalCardinality and model.count, these constraints enable to count the number of times a value is used by a set of variables.
http://choco-solver.org/apidocs/org/chocosolver/solver/constraints/IConstraintFactory.html
For instance, model.count(3, vars, model.intVar(5,10)).post(); means that between 5 and 10 variables in vars should be equal to 3, so employee 3 should do between 5 and 10 shifts.
Related
I have a dataset (a view) that has a numeric field "WR_EST_MHs". If that field exceeds a certain number of man hours (120 or 60, depending on 2 other fields' values), I need to split it out into constiuent records and spread those hours over future weeks.
The OH_UG_Key and 1kMCM_Flag fields determine the threshold for splitting. For example, if the OH_UG = 1 AND 1kMCM_Flag = 'N' and the WR_EST_MHs > 120, then spread the WR_EST_MHs value over as many records as is necessary, in 120 MH increments, changing only the WRSchedDate and WRSchedDate_Key fields (advancing each by one week).
Each OH_UG / 1kMCM_Flag / WR_EST_MHs scenario is as follows:
This is an example of what I need to do:
I thought that something like this might work, but I haven't worked with levels before:
with cte as
2 (Select * from "STJOF"."vfactScheduledWAWork"
5 )
6 select WR_Key, WP_Key, WRShedDate, DistSA_Key_Hash, CrewHQ_Key_Hash, Priority_Key_Hash, JobType_Key_Hash, WRStatus_Key_Hash, PerfBy_Key, OHUG_Key, 1kMCM_Flag, WR_EST_MHs
7 from cte cross join table(cast(multiset(select level from dual
8 connect by level >= WR_EST_MHs / 120
9 ) as sys.odcinumberlist))
10 order by WR_Key;
I also thought this could be done with a "tally table" which I have a little experience with. I really don't know where to begin on this one.
So I would say that a "Tally Table" will work if it is applied correctly. (Or, in this case, a tally view.)
First, break the logic for the hour breakout into a function so we don't have case when everywhere like so:
CREATE OR REPLACE FUNCTION get_hour_breakout(in_ohug_key IN NUMBER, in_1kmcm_flag in varchar2, in_tot_hours in number)
RETURN number
IS hours number;
BEGIN
hours:=
case when in_ohug_key=2 and in_1kmcm_flag='N' and in_tot_hours>60 then 60 else
case when in_ohug_key=2 and in_1kmcm_flag='Y' and in_tot_hours>60 and in_tot_hours<=120 then 60 else
case when in_ohug_key=2 and in_1kmcm_flag='Y' and in_tot_hours>120 then 120 else
120
end
end
end;
RETURN(hours);
END get_hour_breakout;
This way, if the hour breakout logic changes, it can be tweaked in one place.
Second, join to a dynamic "tally" view like so:
select wr_key,
WP_Key,
wrscheddate+idxkey.nnn*7 wrscheddate,
to_char(wrscheddate+idxkey.nnn*7,'yyyymmdd') WRSchedDate_Key,
OHUG_Key,
kMCM_Flag,
case when (wr_est_mhs-idxkey.nnn*get_hour_breakout(ohug_key, kmcm_flag, wr_est_mhs))>=get_hour_breakout(ohug_key, kmcm_flag, wr_est_mhs) then get_hour_breakout(ohug_key, kmcm_flag, wr_est_mhs) else wr_est_mhs-idxkey.nnn*get_hour_breakout(ohug_key, kmcm_flag, wr_est_mhs) end wr_est_mhs
from yourView inner join (SELECT ROWNUM-1 nnn
FROM ( SELECT 1 just_a_column
FROM dual
CONNECT BY LEVEL <= 52
)
) idxkey on vwrk.wr_est_mhs/get_hour_breakout(ohug_key, kmcm_flag, wr_est_mhs) > idxkey.nnn
By using the connect by level we, in effect, generate a bunch of zero indexed rows, then by joining to it with the hours divided by the breakout greater than the feed number we get a few rows for each group.
For example, if the function returns 120 and the hours are 100 you get a single row, so it stays 1 to 1. If the function returns 120 and the hours are 500, however, you get 5 rows because 500/120=4.1666666…, which in the join gives rows 4,3,2,1,0. Then the rest is simple math to determine the number of hours per breakout.
This could also be improved by moving the function call into the lower view so it is only used once per row. And the inline tally view could be made into it's own view, depends on the maintainability you need to build into it.
I have a big dataset (around 100k rows) with 2 columns referencing a device_id and a date and the rest of the columns being attributes (e.g. device_repaired, device_replaced).
I'm building a ML algorithm to predict when a device will have to be maintained. To do so, I want to calculate certain features (e.g. device_reparations_on_last_3days, device_replacements_on_last_5days).
I have a function that subsets my dataset and returns a calculation:
For the specified device,
That happened before the day in question,
As long as there's enough data (e.g. if I want last 3 days, but only 2 records exist this returns NA).
Here's a sample of the data and the function outlined above:
data = data.frame(device_id=c(rep(1,5),rep(2,10))
,day=c(1:5,1:10)
,device_repaired=sample(0:1,15,replace=TRUE)
,device_replaced=sample(0:1,15,replace=TRUE))
# Exaxmple: How many times the device 1 was repaired over the last 2 days before day 3
# => getCalculation(3,1,data,"device_repaired",2)
getCalculation <- function(fday,fdeviceid,fdata,fattribute,fpreviousdays){
# Subset dataset
df = subset(fdata,day<fday & day>(fday-fpreviousdays-1) & device_id==fdeviceid)
# Make sure there's enough data; if so, make calculation
if(nrow(df)<fpreviousdays){
calculation = NA
} else {
calculation = sum(df[,fattribute])
}
return(calculation)
}
My problem is that the amount of attributes available (e.g. device_repaired) and the features to calculate (e.g. device_reparations_on_last_3days) has grown exponentially and my script takes around 4 hours to execute, since I need to loop over each row and calculate all these features.
I'd like to vectorize this logic using some apply approach which would also allow me to parallelize its execution, but I don't know if/how it's possible to add these arguments to a lapply function.
I have tried to use the R package LPSolve and in particular the lp.transport function to solve a optimisation problem. In my fictitious example below I have 5 office sites that I need to resource with a minimum number of employees and I have set up a cost matrix that determines the distance from each employees home to the office. I want to minimize the total distance traveled to work whilst meeting the minimum number of employees per office.
Initially this was working as I was treating all employees as equal (1). however problems have started to occur when I rate each employee by how efficient they are. For example I now want to say that officeX needs the equivalent of 2 engineers which might be made up of 4 engineers who are 50% efficient or 1 that is 200% efficient. When I do this however the solution found will split a employee across a number of offices, what I need is a additional constraint so impose that a employee can only be at 1 Office.
Anyway hopefully that is enough background here is my example:
Employee <- c("Jim","John","Jonah","James","Jeremy","Jorge")
Office1 <- c(2.58321505105556, 5.13811249390279, 2.75943834864996,
6.73543614029559, 6.23080251653027, 9.00620341764497)
Office2 <- c(24.1757667923894, 19.9990724784926, 24.3538456922105,
27.9532073293925, 26.3310994833106, 14.6856664813007)
Office3 <- c(38.6957155251069, 37.9074293509861, 38.8271000719858,
40.3882569566947, 42.6658938732098, 34.2011184027657)
Office4 <- c(28.8754359274453, 30.396841941228, 28.9595182970988,
29.2042274337124, 33.3933900645023, 28.6340025144932)
Office5 <- c(49.8854888720157, 51.9164328512659, 49.948290261029,
49.4793138594302, 54.4908258333456, 50.1487397648236)
#create CostMatrix
costMat<-data.frame(Employee,Office1, Office2, Office3, Office4, Office5)
#efficiency is the worth of employees, eg if 1 they are working at 100%
#so if for example I wanted 5 Employees
#working in a office then I could choose 5 at 100% or 10 working at 50% etc...
efficiency<-c(0.8416298, 0.8207991, 0.7129663, 1.1406839, 1.3868177, 1.1989748)
#Uncomment next line to see the working version based on headcount
#efficiency<-c(1,1,1,1,1,1)
#Minimum is the minimum number of Employees we want in each office
minimum<-c(1, 1, 2, 1, 1)
#solve problem
opSol <-lp.transport(cost.mat = as.matrix(costMat[,-1]),
direction = "min",
col.signs = rep(">=",length(minimum)),
col.rhs = minimum,
row.signs = rep("==", length(efficiency)),
row.rhs = efficiency,
integers=NULL)
#view solution
opSol$solution
# My issue is one employee is being spread across multiple areas,
#what I really want is a extra constraint that says that in a row there
# can only be 1 non 0 value.
I think this is no longer a transportation problem. However you still can solve it as a MIP model:
I've this following optimization problem. A company produces a product, say Big A. To produce this product, it requires 5 processes. (Please find the detail table below). For each process, there are number of supplier that supply raw material for that particular process. E.g. For process 1, there are 3 supplier 1,2 & 3.
The constrain for the CEO of this company,say C, is that for each process the CEO has to purchase supplies from Supplier 1 first, then for additional supplies from 2nd Supplier and so on.
The optimization problem is C wants 700 units for total material to produce for 1 unit of Big A then how will he do it at minimum cost. How the optimization will change if the amount of units require increases to 1500 units.
I'll be grateful if I get the solution of this answer. But if somebody can suggest me some reference regarding this problem it will be a great help too. I'm mainly using R software here.
Process Supplier Cost Units Cumm_Cost Cumm_Unit
1 1 10 100 10 100
1 2 20 110 30 210
1 3 10 200 40 410
2 1 20 100 20 100
2 2 30 150 50 250
2 3 10 150 60 400
3 1 40 130 40 130
3 2 30 140 70 270
3 3 50 120 120 390
4 1 20 120 20 120
4 2 40 120 60 240
4 3 20 180 80 420
5 1 30 180 30 180
5 2 10 160 40 320
5 3 30 140 70 460
Regards,
I will start by solving the specific problem that you have posted and then will demonsrate how to formulate the problem more abstractively. For simplicity, I will use Excel's Solver add-in to solve the problem, but any configuration of a modeling language (such as AIMMS, AMPL, LINGO, OPL, MOSEL and numerous others) with a solver (CPLEX, GUROBI, GLPK, CBC and numerous others) can be used. If you would like to use R, there exists an lpSolve package that calls the lpSolve solver (which is not the best one in the word to be honest, but it is free of charge).
Note that for "real" (large scale) integer problems, the commercial solvers CPLEX, GUROBI and XPRESS perform a lot better than others. The first completely free solver that performs decently in most tests (including Hans Mittelman's page) is CBC. CBC can be hooked up in excel and solve the built-in solver model without restrictions in the number of constraints or variables, by using this add-in. Therefore, assuming that most CPU is going to be spent by the optimization algorithm, using CBC/OpenSolver seems like an efficient choice.
SPREADSHEET SETUP
I follow some conventions for convenience:
Decision variable cells are marked Green.
Constraints are marked red.
Data are marked grey.
Objective function is marked blue.
First, lets augment the table you presented as follows:
The added columns explained briefly:
Selected?: equals 1 if the (Process, Supplier) combo is allowed to produced a positive quantity, zero otherwise.
Quantity: the quantity produced, defined for each (Process, Supplier) combo.
Max Quantity?: Equals 1 if the Suppliers produces the maximum amount of units for that particular Process.
Quantity UB: equals Units * Selected?. This makes the upper bound either equal to Units, when the Supplier is allowed to produce this Process, or zero otherwise.
Quantity LB: equals Units * Max Quantity?. This is to ensure that whenever the Max Quantity? column is 1, the produced quantity will be equal to Units.
Selection: For the 1st supplier, it equals 0. For the 2nd and 3rd suppliers, it equals the Max Quantity? of the previous supplier (row) minus the Selected? of the current supplier (row).
A screenshot with formulas:
There exist two more constraints:
There must be at least one item produced from each process and
The total number of items should be 700 (or later 1,500).
Here is their setup:
and here are the formulas:
In brief, we use SUMIF to sum the quantities that are specific to each supplier, which we are going to constrain to be more than 1 item for each process.
To finish the spreadsheet setup, we need to calculate the objective function, namely the cost of the allocation. This is easily done by taking the SUMPRODUCT of columns Quantity and Cost. Note that the cumulative quantities are derived data and not very useful in the current context.
After the above steps, the spreadsheet looks like below:
SOLVER MODEL
For the solver model we need to declare
The Objective
The Decisions
The Constraints
The Solver (and tweak some parameters if necessary).
For ease of exposition, I have given each range the name of its header. The solver model looks as follows:
It should all be explanatory, except possibly the Selected >= 0 part. The column selected equals the difference between the binary max Quantity of the previous supplier minus the Selected of the current supplier. Selected >= 0 => max Quantity of previous supplier >= Selected of current supplier. Therefore, if the previous supplier does not produce at max quantity (binary = 0), the current supplier cannot produce.
Then we need to make sure that the solver setting are OK:
and solve the problem.
Solution for req = 700 :
As we see, the model tries to avoid procedures 3 and 5 as much as possible, and satisfies the constraint "at least 1 item per process" by picking up exactly 1 item for processes 3 and 5. The objective function value is 11,710.
Solution for req = 1,500 :
Here we need more capacity, but yet process 3 seems expensive and the model tries to avoid it by allocating whatever is necessary (just 1 unit to supplier 1).
I hope this helps. The spreadsheet can be downloaded here. I include the definition of the mathematical model below, in case you would like to transfer it to another language.
MATHEMATICAL FORMULATION
A formal definition of your problem is as follows.
SETS:
PARAMETERS:
Decisions:
Objective:
Constraints:
Constraint explanation:
C1: A supplier cannot produce anything from a process if he has not been allocated to that process.
C2: If a supplier's maximum indicator is set to 1, then the production variable should be the maximum possible.
C3: We cannot select supplier s for process p if we have not produced the max quantity available from the previous supplier s_[-1].
C4: We need to produce at least 1 item from each process.
C5: the total production from all processes and suppliers should equal the required amount.
Looks like you should look at the simplex algorithm (or some existing implementation of it).
Wikipedia has a fairly nice description of the algorithm, http://en.wikipedia.org/wiki/Simplex_algorithm
I need to create a simple formula for determining the popularity of an item based on votes and age.
Here is my current formula, which needs some work:
30 / (days between post date and now) * (vote count) = weighted vote
Whenever a vost is cast for an item it checks if its weighted vote is > 300. If an item has a weighted vote more than 300 then it is promoted to the front page.
The problem is that this formula makes it very hard for older items to be promoted.
30 / 1 day * 10 votes = 300 (promoted)
30 / 5 days * 15 votes = 90 (not promoted)
30 / 30 days * 30 votes = 30 (not promoted)
30 / 80 days * 40 votes = 15 (not promoted)
How can I alter the formula to make it relatively easier for older items to be promoted (IE. make the above four weighted values fairly close together)?
Just get a graph drawing program (maybe excel, maybe matlab, maybe GNUplot) and experiment with the formula until you feel it looks right.
There's no right or wrong with these things.
Toss a logarithm on the amount of time it's been since the item was posted. Tweak the base and the constants involved. That'll take you most of the way there.