9 votes

Julia JuMP successive optimization

Your question has a two-part answer: how JuMP handles successive solves, and how the solvers handle successive solves. How JuMP handles successive solves Recall that JuMP is a modeling layer, not an ...
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  • 3,253
7 votes

Quadratically constrained convex optimization

For all things convex, Mosek's modeling cookbook and conic modeling cheatsheet have you covered. In your case, see the section on convex quadratic sets.
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  • 3,253
6 votes
Accepted

Fleet Management: How to allocate vehicles between departments

If the use of vehicles by departments is deterministic (which I find very unlikely), then scenarios 2 and 3 can be approached as integer programming models. You might be able to do that with random ...
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  • 28.8k
5 votes

Fleet Management: How to allocate vehicles between departments

Based on what you described in the question, the problem you are facing is a variant of the vehicle routing problem. If you have faced some uncertainty, as Prof. Rubin mentioned too, the simulation ...
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  • 5,705
5 votes

Lin-Kernighan TSP edge choice

In Section 5.3 of K. Helsgaun, General k-opt submoves for the Lin-Kernighan TSP heuristic. Mathematical Programming Computation, 1(2-3):119-163 (2009). it is demonstrated how the feasibility of a k-...
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4 votes
Accepted

Lin-Kernighan TSP edge choice

It might help to refer to Figure 3(a) in the Lin-Kernigan paper. Assume that you started out with the tour oriented so that the nodes were visited in the order $$t_1 \rightarrow t_2 \rightarrow \dots \...
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  • 28.8k
4 votes

How to input this LP model of a buffer allocation problem in Gurobi?

You correctly identified that this a linear program. You could either specify this problem in the .lp file format see the Gurobi documenation and consult the syntax rules if you have questions or you ...
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3 votes
Accepted

How to solve assignment problem with additional constraints?

You can create additional "group agents" that represent combinations of actual agents (for instance, $P_{17}$ might be the pairing of $P_1$ and $P_2$) and/or additional "combo tasks&...
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  • 28.8k
3 votes

Julia JuMP successive optimization

I am not familiar with Julia, but you can search for callback and lazycut which allows you ...
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2 votes
Accepted

How to formulate cumulative sum of LpVariable in Pulp Python

This is one way you can formulate/model the problem: $$ \begin{align*} x_{i,t} &\in R^{+} \text{ variable denoting amount of raw material $i$ processed/out in time $t$}\\ q_{i,t} &\in R^{+} \...
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  • 959
2 votes

Quadratically constrained convex optimization

Since $\boldsymbol\Sigma$ is PSD, there exists $\boldsymbol Q$ s.t. $\boldsymbol Q^\top\boldsymbol Q=\boldsymbol \Sigma$ (by Cholesky, or eigendecomposition). Then $\boldsymbol w^\top\boldsymbol \...
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  • 166
2 votes

How to solve assignment problem with additional constraints?

This sounds like a special case of the parallel assignment problem in which the preemption (this is a standard notation in the scheduling theory) would be allowed. I am not aware of how this problem ...
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  • 5,705
1 vote

How to input this LP model of a buffer allocation problem in Gurobi?

Using a dynamic approach like simulation optimization is still one of the best ways to tackle such a problem instead of applying an LP/MIP. Based on what you mentioned, the problem you have faced ...
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  • 5,705
1 vote

Interchange upper- and lower-level decision variables in bi-level programming

This is probably not a very interesting case, but assume the following two things. First, $$g(x,y)\le 0 \implies G(x,y) \le 0 \quad \forall x\in X;\forall y\in Y.$$ Second, $F$ "tracks" $f$ ...
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  • 28.8k
1 vote

Passing exact number of allocations as constraint to pyomo in a sourcing problem

I will first formalize the described problem in mathematical notations, I think it is more suitable, rather than a piece of code, for providing a better understanding. So, let $B$ be the brands set; $...
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1 vote

Common problems/puzzles that can creatively be solved with linear programming?

You can formulate construction of latin squares as an (integer) linear programming problem. Extending that, you can get sudokus this way. I have some code for the latin square part, which I will dig ...
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