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2

you could try constraint programming / scheduling within CPLEX and use noOverlap to model the time matrix. In OPL that gives using CP; execute { cp.param.timelimit=10; } {string} nodes={"O","A","B","C","D","E","T"}; tuple edge { key string o; key string d; int time; } {edge} ...

2

I think your third constraint should be + 1, not - 1, on the right hand side. As stated, it says you enter destination nodes one time fewer than you exit them. You want to enter one time more. Fixing that will make the optimal solution feasible, but it will not make the model correct. There still remains the possibility of a solution that is not a contiguous ...

3

If the set $S$ of nodes to be visited is not too large, you can solve $|S|$ shortest path problems with additional constraints imposing a visit to some nodes. With your example, $|S|=|\{A,C \}|=2$ so it is not too bad. 1/ Find the shortest path from $O$ to $A$, while imposing a visit to node $C$. 2/ Then find the shortest path from $O$ to $C$, while ...

4

To be clear, you have a set $S$ of nodes of a graph $G=(V,A)$, with $S\subseteq V$, which must be visited. There is a special node $O$, which must be the starting point of a tour. A tour visiting the nodes in $S$ starting from $O$ (but not returning to $O$) at minimum length must be found? If that is the case, I think the easiest way is to compute an all-...

5

Shameless plug: I recently gave a webinar on diagnosing infeasibility. Here's what your example looks like in SAS: proc optmodel; var A >= 0; var B >= 0; max z = 20*A + 30*B; con c1: A <= 60; con c2: B <= 50; con c3: A+2*B >= 220; solve with lp / iis=true; expand / iis; quit; The resulting IIS contains all three ...

4

There are certainly different ways of achieving what you want. Here is how I would proceed: Start by predefining the set of all possible schedules which satisfy your constraints $2,3,4,6$. Although there are many, I believe that with your constraints, it may be not too difficult to derive them somewhat automatically. Here is a subset of them in the table ...

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