Scheduling Team Meetings

This is a simple problem from [1]:

I'm rusty on constraint optimization and am looking for help in this particular

use case. There are individuals who are each member to several teams. This is a

fixed many-to-many relationship and is determined a-priori. There are 3 time

slots where the teams can be scheduled to conduct a business meeting, but if an

individual is a member of more than one team which are both meeting at a given

time slot, they'll only be able to attend one. The objective is to schedule the

teams into the time slots, minimizing the number of overlaps of individuals.

For beginners, it is often a good idea to split the task in two:

1. Formulate a mathematical model (on a piece of paper)
2. Implement the model in code

GAMS: SMAX and sparsity

This is a discussion about the SMAX function in GAMS and how it behaves for sparse data.

The data structure we were facing was something like:

set

i 'cases' /case1*case100000/

j 'attribute' /j1*j25/

k 'attribute' /k1*k25/

t 'type' /typ1*typ2/

;

parameter p(i,j,k,t) 'positive numbers';

* note: for each i we have only one (j,k)

Plotting NUTS-2 maps from GAMS

 NUTS-2 regions are statistical subnational regions (often provinces), mainly for the EU and UK [1]. 

NUTS hierarchy (from [1])

In [2] we can find mapping information in the form of Shapefiles[3] and related formats. I used the GeoJSON[4] format, and created a Python notebook script to extract a GAMS set from that file. The file is reproduced in the appendix below. The NUTS-2 codes form the set elements, and the name is stored as explanatory text. There is an option to generate Latin names instead of using the native alphabet. The Latin names are also inside the geojson file. E.g. we have: 

EL65  'Πελοπόννησος'

which is in the Greek alphabet. Using the Latin name, this would look like:

EL65  'Peloponnisos'

Linear Programming Nonsense?

1. Inventory balance constraints

I came accross this text [1]:

Inventory Balance Constraint