# Questions tagged [modeling]

For questions related to the process of converting a real-world problem into a mathematical model. Can include questions related to linearization, logical constraints, tightness of formulations, and so on.

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### partitioning hub assignment models

When solving large-scale hub assignment models (1000+ candidate hubs and 1000+ demand nodes), it is possible that parts of a cost matrix are not connected to one another. A typical workflow would be: ...
150 views

### Does dispersion really matter?

Context: Given a counting process $\{N(t),\,t\ge 0\}$ which tracks the number of events (arrivals) by time $t$, the index of dispersion (for counts) is the variance-to-mean ratio of the cumulative ...
413 views

### How to linearize a constraint with a maximum of binary variables times some coefficient in the right-hand-side

I have the following constraint that I'd like to linearize: $P$ is a given set $b_p \in \{0,1\} , \forall p \in P$ a binary variable associated with each element of $P$ $c_p \in \mathbb{R}^+$, a ...
240 views

### Connectivity of two nodes in an arbitrary undirected graph

Is there an efficient way to model the connectivity of two nodes in an arbitrary undirected graph? I would like to have a binary variable representing this connectivity: 1 if there exists a path ...
317 views

### Tightness of an LP relaxation without using objective function

How can we measure the tightness of a linear programming relaxation for a mixed integer linear program without using the objective value? I would like to get a measure in terms of the feasible set and ...
1k views

### Modeling floor function exactly

Suppose we want to enforce a constraint $$y=\lfloor{x}\rfloor$$ where $x$ is some continuous variable. One option is to use $$x-1\leq{y}\leq{x},\quad y\in\mathbb{Z},$$ which fails on the edge case ...
228 views

### How to fit a Beta distribution to three estimates from an “expert”?

I'm modeling a process time, $X$, for a simulation study and have an "expert" estimate of the minimum, $\hat a$, the most likely (mode), $\hat m$, and the maximum, $\hat b$. I'd prefer to avoid the ...
144 views

### Conditional Controls in MIP Models

Innocently cross-posted at Mathematics SE I am developing a model that operates in the realm of mixed integer programming, although I am fairly unfamiliar with this area of mathematics at the moment. ...
339 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 ...
498 views

### Dealing with non-overlapping constraints

Let us consider the following problem: Let $T$ be a set of tasks. Each task $t \in T$ has a duration $d_t$ and a target start time $s_t$. No two tasks can be executed in parallel. The objective is to ...
124 views

### What are best practices for coding up MIP models? [closed]

When coding an application involving a MIP, what are the best practices I should follow? In particular, I mean: Domain-specific language (GAMS, AMPL) or General purpose (Python, C#)? Structure of the ...
211 views

### How to decide to write an objective function?

I'm working on this problem: In the Njaba river basin, the available water was allocated for the purposes of consumption, irrigation, and electric power supply among three communities. The water ...
204 views

### Symmetry-breaking ILP constraints for square binary matrix

Setup I have a binary $N \times N$ matrix. The objective is to minimize the number of ones in the matrix, subject to various constraints. This leads to symmetries by rotating 90 degrees and/or ...
431 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 ...
916 views

### In an integer program, how can I “activate” a constraint only if a decision variable has a certain value?

Suppose we have the constraint $$a_1x_1 + \cdots + a_nx_n \gtreqless b,$$ where $a_i$ and $b$ are constants and $x_i$ are decision variables. Suppose also that we want the constraint to hold if $y=1$ (...