Adding priority to rows in LpsolveAPI in R

Question

I have an optimised time allocation lp code in R using LpSolverAPI. The code works fine with the given constraints which are :

The time allotted per job must be met The time a worker works cannot exceed the paid work time

But, i need to add a "priority" while the time is allocated to each job. Meaning, there are jobs that need to be completed first/ must be given first priority while allocating workers.

The code i have is below.

The time must be allotted to job4, job2, job3 and finally job1 (as per priority_matrix) If no time is workers are free then lower priority jobs can remain un allocated.

With the below code (without priority) no time is allocated to job 4.

library(lpSolveAPI)

jobs <- c(1,1,1,1)

workermax <- c(8,6,9)
jobmax <- c(6,6,5,6)

priority_matrix <- as.matrix(c(4,2,3,1),ncol = 1, bycol = T)  ##priority of each job
rownames(priority_matrix) <- c("Job1","Job2","Job3","Job4")



scheduler_input2 <- matrix(c(8, 0, 0, 0,6,0,8,0,9,0,6,0), nrow=4 , byrow =T)
obj.vals <- scheduler_input2
colnames(obj.vals) <- c("worker1","worker2","worker3")
rownames(obj.vals) <- c("Job1","Job2","Job3","Job4")


nworkers <- ncol(scheduler_input2)
njobs <- nrow(scheduler_input2) #4
ncol = nworkers*njobs

distribution<- make.lp(ncol=ncol)
set.type(distribution, columns=1:ncol, type = c("integer"))

set.objfn(distribution, obj.vals) 
lp.control(distribution,sense='max')

#cosntraint1
time_per_job <- function (job_index) {
  skill_cols <- (0:(nworkers-1))*njobs + job_index
  add.constraint(distribution, rep(1,nworkers), indices=skill_cols,type="<=", rhs=jobmax[job_index])
}

lapply(1:njobs, time_per_job)

#cosntraint2
max_hrs_by_worker <- function (DA_index) {
  DA_cols <- (DA_index-1)*njobs + (1:njobs) #relevant columns for a given room
  add.constraint(distribution, xt=jobs, indices=DA_cols,type="<=",rhs=workermax[DA_index])
}
lapply(1:nworkers, max_hrs_by_worker)

solve(distribution)

get.objective(distribution)

distribution<-matrix(get.variables(distribution), njobs,nworkers)

Thanks in advance.

score 1 · Answer 1 · answered May 25 '22 at 09:05

The description is not precise enough to give a definite answer. Also, write the problem down in mathematical notation before starting to code. The code is not very easy to read and not at all structure-revealing. This is partly a problem with LpSolveAPI which has a somewhat medieval way to represent optimization models.

If you want to enforce that job2 can only be executed if job4 is executed then introduce binary variables:

 y[j] = 1 if job j is executed
        0 otherwise

and the precedence constraint:

 y[job4] >= y[job2]

Adding priority to rows in LpsolveAPI in R

1 Answers1