New answers tagged scheduling
1
Besides the useful answers mentioned by community folks, some notations would be considered:
As there are many scheduling environments in the real situation or academic literature you should first determine which kind of scheduling model you have faced. For this, it would be helpful to see the Graham notation to determine (or at least for the benchmark) the ...
2
I'm not sure there is name for your specific problem, but I think it is safe to say that it falls into the umbrella category of job shop scheduling, with the objective of minimizing makespan. If you do a web search for "taxonomy of job shop models" you will find a barely finite number of diagrams and articles on the subject. This paper, for ...
2
I didn't find a way to express the transition constraints so i give a description what this does and mention what it lacks.
using JuMP
using Gurobi #needs Gurobi license but any other MILP solver callable from JuMP should work too## Heading ##
using UnicodePlots
are dependencies. I used UnicodePlots for debugging. It is neat. In Julia dependencies can be ...
4
joni's answer is correct. However, this formulation will not allow you to find an optimal solution for anything more than 10-12 teams, even without any additional typical sports scheduling constraints. If you aren't using a commercial solver, the limit is even lower.
There is an excellent book about round robin scheduling by Dirk Briskorn. It is a must-read ...
5
If I understood you correctly, you could do it like this (assuming that $n$ is even and $m = n-1$)
First, add the binary variables
$$
\begin{align}
h_{is} &= \begin{cases} 1, &\text{if team $i$ plays at home in round $s$ and $s-1$}, \\ 0, &\text{otherwise}, \end{cases} \\\\
%
a_{is} &= \begin{cases} 1, &\text{if team $i$ plays away in ...
1
Since you are open to a heuristic, I wonder if a restricted decision diagram (DD) might work for you. Decision diagrams are similar to dynamic programs in the sense that each node represents a state of the system and each arc represents a decision that results in a new state that is dependent only on the decision and the state at which it is made. The least ...
1
since you deal with a scheduling problem I encourage you to have a look at CPOptimizer scheduling within CPLEX.
See also https://stackoverflow.com/questions/49405659/mip-vs-cp-for-scheduling-problems
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