It is not true that the Two-Phase methods requires Simplex iterations, it is just the common way to do it. Let's assume we have a linear program with $n$ variables and $m$ constraints. Step 1) ...

As mentioned earlier, all algorithms are constructed using loops and conditional statements, including the algorithms employed by LP/MIP solvers. There are plenty of problems where it is more ...

In general, I think Constraint Programming or Constraint Satisfaction Problems have their roots in Computer Science/Artificial Intelligence communities that may or may not overlap to some extent with ...

In the context of computational complexity theory, a hard problem typically refers to an infinite set of problem instances for which it is widely believed that the worst-case amount of work needed to ...

While it may seem reasonable to think that costs increase when you increase production, the transportation problem only considers the costs of moving things around. As a consequence, increasing ...

Earlier this year I needed a web application to let some Chinese students (with varying English language proficiencies) play around with models for Timetabling and Rolling Stock scheduling. I used an ...

For the at-least variant, it seems you can write down this problem as propositional logic and convert your constraints into Conjunctive Normal Form, which gives you the constraints you need only using ...

Optimality implies that a proof was constructed that proves there does not exist a better solution than the best feasible solution found. A brute force search does indeed give you a (rather long) ...

If you are willing to introduce an additional binary variable and your goal is to have only a single constraint on $y$, you could do the following: Introduce three binary variables $\zeta_{10}$, $\... View answer Accepted answer 5 votes Let us get some additional insights by assuming$d_{ij} \in \{0,1\}$and interpreting the data as a directed graph. For now we assume the number of$i$'s and$j$'s is the same, but I don't think it ... View answer 5 votes If the problem you are solving is in$P$, I guess you can construct a branch-and-bound algorithm that only produces a polynomial number of nodes, since you can use your polynomial time algorithm to ... View answer Accepted answer 4 votes Since you mention that you want to operate two out of three machines, it boils down to a problem where you first pick two machines and then perform a standard$R2||C_{\max}\$ parallel machine ...

While these equations have many interpretations in OR (e.g. robust optimization), in this case I like to understand what happens here using a Game Theory perspective. These two equations can be ...

For the following I did not check in depth the rules related to end-of-period/beginning of period, so this is something you should carefully check for your problem. However, the approach does not ...

It sounds like what you want is to reduce each vector in your matrix to the relevant entries, and take the Cartesian Product of the column vectors. That is definitely not a problem where linear ...