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.
638 questions
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How to solve this riddle with a MIP?
On a square grid, a loop passes through each cell exactly once. For certain rows and columns, the maximum number of consecutive cells traversed by the path in that row or column is bounded by the tag ...
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Workforce scheduling MIP problem size reduction
A workforce scheduling problem MIP formulation
Decision variable $x_{ij} = 1$ if shift $i$ is assigned to worker $j$, $0$ otherwise.
Objective is a sum of multiple objectives
Maximize demand coverage
...
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GAMSPy conditional assignment not working as expected
In the online course "Effortless Modeling in Python with GAMSPy" by Bluebird Optimization, Lesson 17 introduces the anatomy of conditional statements, including the point that the operator <...
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How to linearize min/max function of a large number of values as a constraint?
Assuming I have 100 variables $r_1 \dots r_{100}$ which can be positive or negative and I try to find the minimum of all of them in a MILP problem and bind that to a variable $y$.
$$y = \min_{i \in \{...
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Modeling a condition in a worker shift assignment problem MIP
In a worker shift assignment problem, let's suppose there are some unassigned shifts for a day (e.g., morning 8 to 11 is an unassigned shift that any qualified worker can take) and some additional ...
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Addressing loopholes in the assignment of medical residents to hospitals
We have a medical residency program and residents are assigned to a different "main" hospital to work in every year. Each resident is assigned to one hospital and each hospital is assigned N ...
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Indicator constraint
Assuming $x_1, x_2, x_3$ are binaries, what implementation is preferable?
$x_1 + x_2 + x_3 \le 1$
or as indicator constraint
$IF \quad x_1=1 \quad THEN \quad x_2 + x_3 = 0, $
$IF \quad x_2=1 \quad ...
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Heuristic for personnel scheduling with rotating shifts and balanced weekend/weekday staffing
I have the following question or problem. I have a patient-to-therapist scheduling problem in which patients $p$ are assigned to different therapists $t$ for treatment. Each therapist has a certain ...
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MIP model for minimum spanning tree
In this post, Erwin Kalvelagen explores how the minimum spanning tree problem can me modeled with different MIPs. The models are based on Optimal Trees (Magnanti, Wolsey).
In the flow formulation II, ...
- 486
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Graph crossing minimization problem
I would like to formulate the graph crossing minimization problem as a MI(N)LP (it's ok if it is non linear) : given a graph $G(V,E)$, what is the minimum number of edge crossings in any drawing of $G$...
- 486
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Computational tool to polyhedra from binary vertices with no extra integer solutions creating extra integer or real dimension if necessary
All logical operations acting can be expressed as IP constraints. But it's not obvious that just because one can build everything out of existing logical constraint and other linear constraints that ...
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Are there existing formats to express symmetries between variables in (MI)LP
LP and MILPs can have symmetries which can complicate solving them.
Existing file formats such as .MPS, .lp, .nl or serializing the matrices A and the vectors b,c are stadard ways to store and ...
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How to prove a model is better than another one
Recently, I developed a linear MIP model for a problem that was originally proposed about ten years ago using a non-linear formulation (specifically, involving binary variables multiplied by ...
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Which of the formulations here is better for a MIP solver?
Problem:
Objective 1: maximize resource-shift assignments ($\sum_{ij} x_{ij}$) where $x_{ij}$ is 1 if resource $i$ is assigned to shift $j$.
Objective 2: minimize the multiple assignments to the same ...
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Trying to get simple tests for indicator function builders to work
I've been trying to build a model using Pyomo GDP constructs, however for some reason, it seems that logical operators cannot be mixed with relational expressions yet.
I am trying to implement these ...
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