# Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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### To which area does constraint programming belong?

The problem I solved is a flow-shop scheduling problem with parallel machines. I solved it with the IBM ILOG CPLEX Optimization framework. There I used the constraint programming (CP). The question ...
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### Reduction of Unnecessary Parameters and Variables in an MIP

Let's observe an example constraint: $\sum \limits^E_{e\ \in \ A_a \ \cap \ B_b \ \cap \ C_c} x_{e,a,b,c} \geq n_{a,b,c} \; \; \; \forall a \in A,b \in B,c \in C$ with $e \in E$ an element and $A_a$ ...
714 views

### 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 ...
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### OR-backed serious games

A "serious game" is a game (usually a simulation) designed for a primary purpose other than pure entertainment. Games like the beer game or the fresh connection can be considered serious games serving ...
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### Optimal value exceeds actual value for a minimization problem [closed]

I am solving a nonlinear numerical optimization problem in Pyomo using Scip as a solver. The goal is to minimize a certain objective function. For certain input conditions, I notice that the solver ...
327 views

### Benchmark problems for scenario-based stochastic optimization

$\newcommand{\E}{\mathbb{E}}$I am working on numerical algorithms for solving convex large-scale multistage scenario-based problems and I am looking for some standard benchmarks problems. I have so ...
4k views

### What instances can be solved today by modern solvers (pure LP)?

I have found a PowerPoint presentation in which the presentor Hall claims instances could be of the size of 108 in variables and constraints to be solved today. I assume that he meant sparse problems. ...
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### Geometric interpretation of a Linear problem with bounded variables

I have a question of how to make a geometric interpretation of this problem \begin{eqnarray} \mbox{max} & z = 3x_1+x_3 \\ s.a: & \\ & \begin{array}{cc} x_1+2x_2+x_3+x_4& =...
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### Variable bounds in column generation

Consider the set covering problem \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} ...
137 views

### Strategic planning based on average values

If you have strategic planning problems like hub location problems, the input data often consists of average values for shipping volumes etc. When planning capacities, it is risky to ignore the ...
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### Is it possible (or straightforward) to define many secondary problems in bilevel programming?

I am new to bilevel programming. I was wondering whether it is possible (or straightforward) to formulate a bilevel problem in which there are many secondary-level problems? An example might be a ...
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### Minimizing a project costs through nonlinear optimization

I have a project and I want to minimize the costs. I am are responsible for the inspection of 1000 miles of sewer grid in Canada. My goal is to provide time high quality inspection reports. I tried to ...
352 views

### KKT inequality conditions

Let's say I have an objective function $$f(x_1,x_2, \cdots, x_n)$$ and $N$ constraints $$x_i \ge 0.$$ I am trying to solve it with KKT conditions. Now the objective function becomes f(x_1,x_2,...
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### As an Operations Research professional, how is your time divided when working on an optimization project?

When working on an optimization project, what is the typical time division (in percentage) between the various tasks that you have to work on: Problem understanding/definition (figuring out what is ...
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### Python PuLP - Unable to Model Non-Square Matrix

I am having issues with setting up constraints using both input arrays from excel and variable arrays within PuLP. It appears the model only works with square matrices and my final code has a matrix ...
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### Guidelines for Linear Optimization approaches?

When solving a Linear Optimization model (or Linear Program), there are a lot of solution approaches. Just to name a few: Primal Simplex Dual Simplex Ellipsoid Method (as if) ...
328 views

### How to handle real-world (soft) constraints in an optimization problem?

Cross-posted at Stats.SE (aka Cross Validated) I am working on a problem which involves optimizing for minimum power consumption in a large compressor network interconnected through pipelines (think ...
397 views

### How to determine if a given problem seems to be a good fit to be solved using combinatorial Benders decomposition

Combinatorial Benders decomposition is a mathematical programming technique consisting into dividing a problem into a master problem and a sub problem. The master problem is solved to optimality (or ...
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### Why the optimal value that minimizes a function does not satisfy condition?

I have found a solved example of A Stochastic Two-Period Model with No Setup Cost in the book Operational Research by Hillier, 7th edition, that has a lot of complicated calculations to arrive to the ...
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### Difference between lazy callbacks and using lazy constraints directly

I'm trying to use lazy constraints to solve an optimization problem. In some software such as CPLEX or GUROBI, they have some tools to handle them directly (in the original model) or using callback ...