Dear community team,

I'm trying to solve an assignment scheduling problem. I define the problem set as follows:

setof(int) workstation = asSet(1..5);
setof(int) tasks = asSet(1..9);
setof(int) workers = asSet(1..6);​

Now, I need to create a link to define relations between the tasks. Therefore, I try using the tuple concept to do that. 

tuple link{
   {int} task;
};
{link} relations[tasks]=
[{<{1}>}, {<{1}>}, {<{1,2}>}, {<{1,2,3}>}, {<{4,7}>}, {<{6}>}, {<{6}>}, {<{5}>}, {<{8}>}];​

Where "{<{1,2,3}>}" shows the precedence relationship to execute task 4.
Also, I have constraints in the following form.

\begin{equation}\sum_{h \in H} \sum_{i \in I} i . x_{i h j} \leq \sum_{h \in H} \sum_{i \in I} i . x_{i h t} \forall j, t \in N, j<t\end{equation}​

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Best regards
Abbas
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#DecisionOptimization

I am not sure I understand how exactly you want to add those sets into the constraints. Do you mean something like
forall(t in tasks) ...
and then
sum(j in relations[t].task) ...
? Or do you mean something else? If you mean something else then maybe you can give a short example of the constraint that should be generated for the first task, lets say.

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Daniel Junglas
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Dear Daniel,

Many thanks for your response.
Please let's say, I need to define j and t indices over the tasks set on the outer loop. 

  e4: forall(j,t in tasks: j<t)
  	sum(h in workers, i in workstation) i*x[i,h,j] <= 
  		sum(h in workers, i in workstation) i*x[i,h,t];​

But, this constraint should determine refashions between tasks and whose precedence. this is why I defined such a tuple set. Also, I have tried to use the nested set as follows:

setof(int) operations[tasks] = [{1}, {1}, {1,2}, {1,2,3}, {4,7}, {6}, {6}, {5}, {8}];​

 Instead of using tuple and define the constraint in the form:

  e4: forall(j,t in tasks, jj in operations[j], tt in operations[j]: j<t)
  	sum(h in workers, i in workstation) i*x[i,h,jj] <= 
  		sum(h in workers, i in workstation) i*x[i,h,tt];​

But, when the model is solved, the results are not correct. 
I was wondering if, where am I wrong and how can I fix this issue?

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Abbas Omidi
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Original Message:
Sent: Thu April 30, 2020 10:36 AM
From: Daniel Junglas
Subject: Tuple set issue

I am not sure I understand how exactly you want to add those sets into the constraints. Do you mean something like
forall(t in tasks) ...
and then
sum(j in relations[t].task) ...
? Or do you mean something else? If you mean something else then maybe you can give a short example of the constraint that should be generated for the first task, lets say.

------------------------------
Daniel Junglas
------------------------------

hi

{int} tasks=asSet(1..9);
{int} workstation={1,2};
{int} workers={1,2};
setof(int) operations[tasks]=[{1},{1}, {1,2}, {1,2,3}, {4,7}, {6}, {6}, {5}, {8}];



dvar boolean x[workers,tasks,tasks];

subject to
{
  e4: forall(j,t in tasks: j in operations[t])
sum(h in workers, i in workstation)i*x[i,h,j] <= 
sum(h in workers,i in workstation)i*x[i,h,t];}




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ALEX FLEISCHER
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