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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11 votes
2 answers
286 views

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: ...
fhk's user avatar
  • 1,069
8 votes
2 answers
190 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 ...
SecretAgentMan's user avatar
11 votes
4 answers
941 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 ...
Renaud M.'s user avatar
  • 2,418
13 votes
5 answers
516 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 ...
Mertcan Yetkin's user avatar
21 votes
5 answers
672 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 ...
Mertcan Yetkin's user avatar
32 votes
8 answers
2k 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 ...
David M.'s user avatar
  • 2,077
11 votes
1 answer
399 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 ...
SecretAgentMan's user avatar
10 votes
1 answer
215 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. ...
GrayLiterature's user avatar
12 votes
3 answers
509 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 ...
chupa_kabra's user avatar
  • 1,485
11 votes
5 answers
1k 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 ...
Renaud M.'s user avatar
  • 2,418
1 vote
1 answer
150 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 ...
Richard's user avatar
  • 3,459
-7 votes
2 answers
269 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 ...
Evan Pk's user avatar
13 votes
1 answer
269 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 ...
Simon's user avatar
  • 1,132
24 votes
4 answers
731 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 ...
Renaud M.'s user avatar
  • 2,418
12 votes
2 answers
3k 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 $y=1$ (...
LarrySnyder610's user avatar
22 votes
5 answers
2k views

How can I best handle symmetries in my MIP?

When dealing with mixed-integer-programs with many symmetric solutions it can take very long until the branch-and-bound-tree search is finished because symmetric optimal solutions cannot be pruned. ...
YukiJ's user avatar
  • 2,023
17 votes
5 answers
744 views

Presolve is cutting down a lot of binary variables. Should I rethink my formulation?

I built my model on Python and am passing it to Gurobi to solve the problem. The presolve phase of Gurobi cuts down ~80% of the integer/binary variables and I am wondering if I should rethink my ...
Abhishiekh Ramesh's user avatar

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