Robert Schwarz
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Branching rules in commercial MIP solvers
Accepted answer
16 votes

Tobias Achterberg's thesis includes a review of MIP solver technology from around 2009, including branching decisions and node selection.

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Are Python and Julia used for optimization in industry?
14 votes

Staffjoy was an early user of Julia and JuMP for their start up providing workforce scheduling. They also release all of their internal software as open-source after they shut-down. See for example ...

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Recommended books/materials for practical applications of Operations Research in industry
13 votes

The AIMMS Optimization Modeling book is freely available and very accessible. There are lots of worked examples going from problem description to example data and model formulation.

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Dedicated solver for convex problems
12 votes

Are you formulating your model with nonlinear expressions that just happen to be convex? Or can you provide conic normal forms, maybe using a modeling tool based on displicined convex programming? In ...

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What are Operations Research applications for 'good causes'?
11 votes

A new webinar series was just started: Analytics for a Better World. The first two presentations cover health care (ventilator distribution for COVID-19) and the poverty (food distribution).

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What are the reasons OR industry projects fail?
11 votes

One obstacle in finding champions within the client company is that with OR solutions, there is a fear of automating decisions, which might make some people's job redundant. Or at least this ...

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Is using gradient descent for MIP a good idea?
10 votes

I think that this article is not about using gradient descent to solve MIP problems. It seems to me that they are explicitly enumerating all possible value combinations for the discrete decisions and ...

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How can I estimate the monetary savings of a operation research application?
9 votes

I think this is easiest for applications where cost reduction is an explicit goal of the model. Let's say a company is in the delivery business and uses some specific method / heuristic to assess ...

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How to formulate a MIP that can minimize the costs with a combination of subsets given a set?
8 votes

You can introduce a binary variable $x_s \in \{0,1\}$ for each of your sets. Then, for every element $e$, you add an inequality that implies that exactly one set containing it may be selected: $\sum_{...

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Allocating credit card points
7 votes

That sounds like you could formulate it as MIP. You have a fixed set of planned purchases, right? Each of them ($p$) will yield a constraint of the form $x_p + c_p \cdot y_p = t_p$, where $x_p$ is ...

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Application of complex numbers in Linear Programming?
7 votes

Not quite Linear Programming, but if you are willing to generalize to Convex Programming, I have stumbled over some modeling systems (for disciplined convex programming) that support optimization with ...

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Extreme point and extreme ray of a network flow problem
Accepted answer
6 votes

I believe this result (with proof) is contained in the text book "Network Flows" by Ahuja, Magnati and Orlin. In particular, chapter 11 is on the Network Simplex algorithm and Theorems 11.2 ...

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How are indicator constraints implemented?
Accepted answer
6 votes

You can have a look at SCIP's implementation in cons_indicator. They say that: An indicator constraint is given by a binary variable $z$ and an inequality $ax \le b$. It states that if $z=1$ then $ax ...

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What are Operations Research problems which occur in everyday life?
6 votes

Hanging up laundry to dry is a form of online bin packing. I usually pick largest items first and pick a "line" with the smallest remaining capacity ("best fit"?)/

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Parallel nonlinear solvers
6 votes

I think that there exist multiple solvers based on ADMM. If the variables can be partitioned in two sets in a way that the problem decomposes for one set fixed, then every other iteration can be ...

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Tightness of an LP relaxation without using objective function
6 votes

If (for small dimensions) it is feasible to enumerate the vertices of the polyhedron of the relaxation, as well as the actual feasible set, one could try to find a vertex with the highest distance to ...

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Branch and bound algorithm programming code
5 votes

There are several open-source software packages that use branch-and-bound to solve integer programming, for example: GLPK: https://www.gnu.org/software/glpk CBC: https://github.com/coin-or/Cbc

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Modeling the Round (Nearest Integer) function
5 votes

Assuming finite bounds on $x$, this could be modeled with disjunctions on the many cases to which $x$ can be rounded. For example, if $x \in [ 0, 2 ]$, we would have: $$ \begin{cases} x \le 0.5, &...

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Why is there not a feasible solution for a MIP?
5 votes

As an alternative to finding irreducible infeasible subsets (smaller subproblems that are still infeasible) would be to introduce slack variables into your constraints. Then you would replace your ...

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Warm-start SCIP with a solution
5 votes

If you use the SCIP shell, you can simply interrupt the solving process with Ctrl+C, then use the newstart command the clear the tree and start solving again with optimize. This will keep not only the ...

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Are there reusable formulations/heuristics shared with the community?
5 votes

One group at LANL published several collections of model formulations around infrastructure optimization (power grid, gas pipelines, etc.): https://lanl-ansi.github.io/software/ The formulations are ...

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Paper suggestions on local search algorithms
4 votes

I'm not an expert in the field, but the paper An effective implementation of the Lin-Kernighan traveling salesman heuristic by Keld Helsgaun was mentioned in another question before.

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Finding an Objective Function for Assigning Employees to Sequence Dates
4 votes

I think that if you don't want to introduce additional variables, you will have to use products of them, to give additional value to, say, $x_1 \cdot x_2$. Since theses are all binary variables, you ...

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Examples of machine learning applied to operations research?
4 votes

There is a paper Learning Fast Optimizers for Contextual Stochastic Integer Programs where they develop a "learnable local solver" to solve problems where the MIP solvers did not scale. I have not ...

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How to exploit known solution in MILP
3 votes

You can also submit the solution to the MILP solver. The solver should then use the bound from it automatically. Further, it might use the solution values for various improvement heuristics (e.g. ...

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How can we understand which solution approach is suitable for our mathematical problem?
2 votes

I guess that depends on the application and the constraints and expectations that the end users have. For example, do users work with the model interactively, trying different parameter choices and ...

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Model conversion as fast as gurobipy and solved by open source solvers
2 votes

Do you need a Python library in particular? If you are happy using Julia, you should give JuMP a try. It will give you high-level modeling with fast model generation and connection to most solvers. In ...

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Modeling the Round (Nearest Integer) function
2 votes

As an alternative solution, I propose to add an auxiliary integral variable $y \in \mathbb{Z}$ that should play the role of the rounded $x$. For your example of the inequality, I would add: $$ \begin{...

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Optimization models for portfolio optimization
2 votes

I'm no expert on the topic, but I found the textbook Optimization Methonds in Finance really accessible. The authors teach optimization modeling and solving motivated by applications in finance, ...

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Optimization Problem Libraries
1 votes

There is also: GasLib, with gas network instances based on perturbed real-world data.

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