Modelling constraints in Choco solver

Question

I'm playing around with choco solver to solve some task scheduling problems.

I have several jobs and possible slots (where a job can be executed). There are some constraints like:

• There could only one job per slot (C.1)
• A job needs a certain time t and slot has an available duration d. The job must fit into the that available duration: t<=d (C.2)

So, basically expressed with some basic/pseudo classes:

class Job {
    int id;
    int time;
}

class Slot {
    int id;
    int duration;
}

Currently, I'm able to allocate a slot for each job, assuming that id of a job and a slot are consecutively numbered

int jobCount = 5;  // 5 jobs with ids from 0 to 4
int slotCount= 20; // 20 jobs with ids from 0 to 19
Model model = new Model("Example");
IntVar[] jobs = model.intVarArray("Job", jobCount, 0, slotCount, false);
// all jobs must have different slots (C.1)
model.allDifferent(jobs).post();

// solving - details omitted, because I think it is not relevant...
Solution solution = model.getSolver().findSolution();
// assign the jobs to the slots like (pseudo-code): 
// foreach i in jobs.length do 
//     job = getJobForId(i);
//     getSlotForId(jobs[i]).setJob(job);

This is working as expected. But now I want to model the other constraints as well. But I'm stucking on how to combine the job/slot with the times/durations, because the time and duration is a dependent variable.

At a first step, I modeled two additional variables for times and durations:

int[] slotDurations = {10, 20, 10, 40, ..., 20} // 20 durations (d)
IntVar[] durations = model.intVarArray("Time", slotCount, slotDurations);

int[] jobTimes = {5, 16, 30, 2, 17} // 5 times (t)
IntVar[] times = model.intVarArray("Time", jobCount , jobTimes);

Now, I need to express the constraint that the time should fit into the duration (C.2).

Is it possible to define a constraint like this (not working/valid pseudo-code):

for(int i=0;i<jobCount;i++){
    times[i].le(durations[jobs[i]]).post();
}

or is the model totally wrong?!

Maybe someone has a solution or an idea?!

Answer 1

If you say that there can be only one job per slot, then it is natural to select slot as your IntVarArray, as so:

 IntVar[] slots = model.intVarArray("Slot", slotCount, 0, jobCount, false);
 int[] jobTimes = {0, 5, 16, 30, 2, 17};  //6(!) items; see explanation below.
 int[] slotDurations = {10, 20, 10, 40, ..., 20}; //20 items

Here, slots points to the items in jobTime. If you have more slots than jobs, then take care with the allDifferent constraint: You will end up having no solutions. In that case, use a modified constraint, such as allDifferentExcept0 so that the solver can select a valid item. Then, jobTimes[0] must be an entry satisfying all slots (say, 0).

Then you are very close. All you need to do is to introduce an intermediate IntVarvariable, say shadowTime, which represents the times in the order given by slots, like so:

IntVar[] shadowTime = model.intVarArray("shadowTime", slotDurations.length, 0, jobTimes.length, false); //has the jobTimes in the order indicated by slots.
for(int i=0;i<slotCount;i++){
    model.element(shadowTime[i], jobTimes, slots[i]).post();
    //this is similar to what you wanted to achieve with 'durations[jobs[i]]' in your code
}

Then you can add the constraint C.2 in the same loop:

//within in the above loop:
{    
    ...
    model.arithm(shadowTime[i], "<", slotDurations[i]).post();
}

You can then enumerate all solutions as described in the manual (while (solver.solver(){...}).