# Yet Another Math Programming Consultant

I am a full-time consultant and provide services related to the design, implementation and deployment of mathematical programming, optimization and data-science applications. I also teach courses and workshops. Usually I cannot blog about projects I am doing, but there are many technical notes I'd like to share. Not in the least so I have an easy way to search and find them again myself. You can reach me at erwin@amsterdamoptimization.com.

## Saturday, March 25, 2023

### Simultaneous equation models and data errors

## Thursday, March 16, 2023

### Algorithm vs. model

From [1]:

We are given a plane defined by Ax+By+Cz-D = 0 where D is significantly larger than A,B,C and GCD(A,B,C) = 1. How would I find all points (x, y, z), where x,y,z are integers and >= 0, that lie on the plane in an efficient manner?

So the poster asks for an algorithm to find \(\color{darkred}x,\color{darkred}y,\color{darkred}z \in \{0,1,2,\dots\}\) such that \[\color{darkblue}A \cdot \color{darkred}x + \color{darkblue}B \cdot \color{darkred}y + \color{darkblue}C \cdot \color{darkred}z = \color{darkblue}D\] Besides the assumptions stated in the question, I'll further assume \(\color{darkblue}A,\color{darkblue}B,\color{darkblue}C,\color{darkblue}D\gt 0\).

## Tuesday, March 14, 2023

### Choosing between NLP solvers: interior point or active set.

One way to categorize (local) nonlinear programming (NLP) solvers is **active set methods** and **interior point solvers**. Some representative large-scale sparse solvers are:

- Active set: CONOPT, SNOPT. These are using SQP algorithms.
- Interior point: IPOPT, Knitro. Note: Knitro also contains an active set algorithm.

## Monday, March 6, 2023

### Some approaches for moving data between MS Access and GAMS

Moving data between different environments is always more difficult than we hope. Here I list some approaches and actually try them out on a small dataset. We hit some bugs along the way and also a few conceptual stumbling blocks (even for this stylized example). We had some issues with Access as well as GAMS Connect.

This question came up in an actual project. My idea was: "Let me show you how this can be done". I am afraid, I got carried away a bit. But it demonstrates that we should not underestimate these, at first sight, menial tasks. When the data set becomes larger, the problems compound. We can't eyeball the data, and statistically, it is more likely we encounter some problems.

## Friday, February 24, 2023

### Another fast MIP model: covering

In [1], the following problem is stated:

- There is a collection of \(n=1,000\) test questions.
- Each question covers a number of skills.
- Given is a requirement for a number of questions for each required skill (e.g., 4 questions about skill 1, 3 questions about skill 2, etc.).
- Create a test with the minimum number of questions that fulfills the requirements.

## Thursday, February 16, 2023

### Assigning jobs to machines without overlap

Here we consider the following problem from [1]:

- We have jobs with a given start time and completion time
- Jobs can be repeated on given days (e.g. job 1 needs to run on Monday, Wednesday, and Friday)
- We want to assign jobs to machines in such a way that there is no overlap
- The objective is to minimize the number of machines needed to execute all jobs

## Wednesday, February 15, 2023

### Supplier selection: an easy MIP

- We want to order items in different quantities from suppliers.
- Suppliers have an available inventory for these items. This can be zero.
- We can split the ordering over different suppliers.
- The cost structure is as follows:
- Shipping cost is a fixed cost per supplier.
- Item cost is a variable per-unit cost.

## Monday, February 13, 2023

### Populating SQLite databases

GAMS has three easy ways to populate a SQLite database:

- Using the tool
**gdx2sqlite**. This tool populates a SQLite database with data from a GDX file. This means we first have to export GAMS data to a GDX file. As there is quite some file I/O going on here (writing GDX file, reading GDX file, writing database), I would expect this to be slower than the next method. - The new GAMS-
**connect**facility. This does not use intermediate files, and directly copies records from in-memory data. This should be the fastest. - Old fashioned
**CSV**files. We first export data as a GDX file, and then use**gdxdump**to convert the data to a CSV file. Then sqlite can import the CSV file, and populate the database. There is much file I/O here, so this should be slow.

## Saturday, January 28, 2023

### Tiny non-convex quadratic model brings solvers to their knees

Here is a very small geometric problem:

Given \(n\) points in 2d space, find the smallest triangle that contains all these points.

Find the smallest triangle containing all points. |

This looks like a simple problem. Somewhat to my surprise, my attempt here does not bear that out.

## Tuesday, January 24, 2023

### Export GAMS GDX file to different Python formats (CSV,Feather,Pickle)

**GAMS user**can run the GAMS script, without knowing Python or having Python installed. (GAMS comes with its own somewhat barebones Python, which is used inside the GAMS script). On the other hand, the

**Python user**will not need to have GAMS installed to read the generated data files. This is opposed to Python packages and tools that can interact with GDX files directly. You can see a few in the PyPI directory [1]. Those will require both a GAMS system and a Python environment.