Originally posted by: _Hadi_

Does anyone know that if it is possible and how in CP I can model a problem where a task can be done by one or more resources at the same time. Meaning that at the same time it is possible to perform a task with say 3 resources which it means it can be done faster than the case performing the task with only one resource.

Thanks! 

Originally posted by: Petr Vilím

Hello,

yes, it can be done using interval variables and constraint called alternative. The idea is that a task can be performed in different modes, and depending on the chosen mode (the alternative) the task has different resource requirements and different duration. Have a look on example sched_rcpspmm (in C++ and OPL) or SchedRCPSPMM (in Java and C#) that is delivered together with CP Optimizer.

If you know that some particular resource is used by a task in every mode and always in the same quantity then it is better for the task itself, not the alternatives, to require that particular resource.

Finally, it is also possible to model the problem using constraints on sizeOf and heightAtStart expressions. However I do not recommend that unless the number of alternatives is really big. This model would not propagate well.

Petr

Originally posted by: _Hadi_

Petr, thanks for  your reply. 

About the second option that you mentioned it can be modeled with sizeOf and heightatstart, lets say I have 90 tasks and in general 18 resources. Given task can be done by one or two resources. Do you think this is the case I should use the second approach? 

Can you explain a little bit more that how this can be done with the second approach?

Thanks,

Hadi

Originally posted by: Petr Vilím

Hello Hadi,

If I understand right, given task has only two modes. In mode 1 it use resource A, it mode 2 it uses resource B and C. In this case alternatives and optional intervals is the best approach. Optional interval variable T1 can model mode 1 and another optional interval variable can model mode 2. The task itself is then model by non-optional interval T and there's constraint alternative(T, [T1, T2]).

If there's too many modes then the number of alternatives can be very high. In this case, just to save the memory, there's another way to model the problem. Let say that a task requires 2 units of capacity from any of the 18 resources. It could be 2 capacity units from a single resource or a split: 1 capacity unit from one resource and another 1 capacity unit from another one. This problem can be modeled by pulses with variable height: pulse(T, 0, 2). The task can require such a pulse from all the resources and then total height of those pulses can be constrained using heightAtStart expression:

resourceA = ... + pulse(T, 0, 2) + ...;

resourceB = ... + pulse(T, 0, 2) + ...;

...

heightAtStart(T, resourceA) + heightAtStart(T, resourceB) + ... == 2;

Petr

Originally posted by: _Hadi_

Petr, I think the second approach is what I needed. 

Thank you,

Hadi

Originally posted by: _Hadi_

Pter, I have one more question. 

What I have done is like below: 

forall (t in tasks)

sum (r in resources) sizeOf(task[t][r] * speed[r] ~= task.size

heihgtatStart couldn't find a feasible solution in my case, I also have an intensity function defined for each task. Do you have any thoughts or comments that may say above formulation might be wrong?

Thanks,

Hadi