Tuesday, April 1, 2025

Towers of Hanoi: inventory and network formulation

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The towers of Hanoi problem [1] is a famous puzzle demonstrating recursion. The task is to move a stack of disks from one peg to another. We...
1 comment:
Friday, March 21, 2025

Wolf, goat and cabbage problem: MIP and network model

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The Wolf, goat, and cabbage problem can be stated as [1]: A farmer with a wolf, a goat, and a cabbage must cross a river by boat. The boat ...
Tuesday, February 25, 2025

Small MIP, proving optimality is difficult

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This is a simple, smallish MIP model that is difficult to solve to proven optimality. The problem is stated as [1]: I have grid of dimension...
6 comments:
Monday, February 24, 2025

Programming vs Modeling

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I found another interesting GAMS model. Here, I wanted to demonstrate the difference between programming (implementing algorithms in a progr...
Saturday, February 15, 2025

Network models with node capacities

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Min-cost flow network model A standard min-cost flow network model, formulated as a linear programming model, can look like: Model ...
Monday, November 4, 2024

Sorting using a MIP model

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This is not, per se, very useful, but sorting a parameter inside a MIP model is not very easy for MIP solvers. Obviously, if you need a sort...
6 comments:
Saturday, October 26, 2024

PuLP surprises

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Formulating optimization models inside traditional programming languages such as Python is very popular. The main tool the developers use to...
Tuesday, October 22, 2024

Non-convex Quadratic Integer Programming

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Here, I want to revisit a particular model from [1]: Model 3: Quadratic Preemptive Model \[\begin{align}\max\>&\color{darkred}z_{mode...
Thursday, October 17, 2024

Equity in optimization models

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In optimization models, we often use an aggregate measure in the objective function, such as total profit, the sum of tardiness of jobs, and...
Wednesday, October 16, 2024

GAMS 48 tests

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Some minor quibbles.  gdx2sqlite The latest version of GAMS contains a replacement of gdx2sqlite . This dumps a GDX file into a SQLite datab...