Operations Research Stack Exchange
Operations Research Stack Exchange

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What is a "hard problem" in the context of Mixed-integer programming?

As a practical (real-world problems) point of view, it's important we could solve optimization problems as quickly as possible (for instance, to release a daily schedule). Maybe a problem with many variables Or constraints is solved in a few time…
A.Omidi
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Divisibility constraints in integer programming

In the study of a certain pure mathematical problem (related to infinite-dimensional Lie algebras) I found myself in a situation where it would be very desirable to be able to solve an integer programming problem, where one of the constraints is a…
Andrei Smolensky
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4 answers

Best model for precedence constraints within scheduling problem

Suppose I'm modeling a problem where I want to compute the start time bucket for some jobs. All time buckets have equal duration. There are some additional constraints involved but I also have to model some precedence constraints for certain…
JakobS
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Modeling the uncertainty of the input parameters

There are many approaches to deal with the uncertainty such as stochastic programming, robust optimization and fuzzy programming. Finding a suitable approach that is applicable in the real situations can be tricky. I have two main questions: 1- In…
Mehdi
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Does the problem of P vs NP come under the category of Operational Research?

I am enrolled in an Operational Research program. I am also interested in Algorithms, and I wish to know whether "P vs NP" is a common point in both of the fields, so that the effort put in understanding this problem forwards me in both directions.
Vikranth Inti
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How to linearize a constraint with a maximum or minimum in the right-hand-side?

Suppose we have three variables, $x, y, z \in \mathbb R$. How can we linearize constraints with the following structure? $$z \geq \min(x, y)$$ $$z \leq \max(x, y)$$
Michiel uit het Broek
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Warm start CPLEX using google or-tools

I have been trying to use the SetHint python API in google or-tools to warm start MIPs and solve it using CPLEX. It looks like my hints are accepted by the SetHint function but I am not sure whether CPLEX is actually using the warm start, the CPLEX…
Palaniappan Chellappan
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Are there any benefits to using Gurobi's built-in "blended" multi-objective functionality?

The newer versions of Gurobi include a couple of built-in functionalities for multi-objective optimization: blended objectives and hierarchical (lexicographically ordered) objectives. Suppose we wanted to minimize $2x + 3.5y + 7z$. Using the…
dxb
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references on the empirical study on the practice of OR

I am looking for (introductory) references on the empirical studies on the practice of OR. I mean literature that looks at questions like: Which methods are used in practice? How do people interact with the optimization software? What factors…
PSLP
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Optimization models for portfolio optimization

What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms of risk measures or formulations?
Daniel Duque
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What is quadratization?

In the context of discrete optimization, what exactly does it mean to "quadratize" a function? The term seems to be used mainly by operations researchers, in my experience.
Nike Dattani
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Bound on the number of constraints to be generated (lazy constraints)

I am working on a very large optimisation problem. All variables are continuous, the objective is linear and the constraints convex, but I have many such constraints (on the order of $2^n$ — actually, one constraint per possible solution to a given…
dourouc05
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Is Apple's M1 suitable for Operations Research?

I am curious about the performance of Apple's M1 chip solving optimizations models, MIP, LP, and in solutions approach as benders or columns generations. I read that is a spectacular cpu to perform machine learning tasks, and was wondering how good…
orpanter
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How to get the best bound of large LP problems in CPLEX?

When using the C callable library to solve a large LP, how can I get the best bound after calling the method CPXXlpopt? Does it depend on the algorithm used to solve the LP? I need this for cases in which the LP is too large and the Time Limit is…
Orlando Rivera Letelier
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Has the expressibility of 'non-integrality testing' as extension to MILP been studied before?

It turns out that extending MILP with any of the constraints $y=\lfloor x\rfloor$, $y=\lceil x\rceil$, $0 < x$, or $x\notin \mathbb{Z}$ is 'equally hard'. (see my answer here, and below) Expressing strict inequalities exactly in MILP is something…
Discrete lizard
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