Which algorithm can I use to allocate human resources?

I have to manage shifts of a variable number of people inside several rooms for a week.

Every shift must be at least 1h long and the number of hours per person for the week should be nearly the same for everyone.

Every person could ask for specific shifts and this could be accepted if a suitable solution can be found.

I could have other constraints, but let's face this very basic situation.

Now the questions:

• Which algorithm should I study and use?

• Is there some free library I can use for this purpose?

• Is there something I can use for C#?

Since Vince asked me to publish my solution, I decided to write this long post.

Please bear in mind that this code is really really basic and absolutely not optimized, written as fast as possible to perform some test.

Credits for Hungarian algorithm code must be done to vivet.

PURPOSE

I need to create shifts for M workers (variable number each week) on N slots (usually 50 each week, but sometimes some slot could be unavailable).

Each worker can suggest slots he wants to take and others he can't absolutely take and, if possible, these requests should be taken in account.

GENERAL IDEA

Given that creating costs matrix for Hungarian solver can be a pain, I decided (just a quick solution) I can create text files for each worker to report his request and one file for unavailable slots.

All these files must be in the same folder.

FILES STRUCTURE

A single text file must have as many rows as daily slots (usually 10) and as many columns as working days (usually 5).

Each cell must contain a preconfigured char:

• O means worker really needs that slot assigned

• o means worker would like to have the slot assigned

• - means no preference on that slot (it's the default naturally)

• x means worker would like not to have the slot assigned

• X means worker can't work on that particular slot

A sample could be

X x - - O
X x - - O
- - - - O
- - - - -
- - - - -
- - - o -
- - - o -
- - - - -
- - - - -
x x x x x

Unavailable slots file must have a well defined name (always the same) and its content will have the same structure of workers files. Naturally each cell having a value different than - means that slot is not available to workers.

CODE

Source code can be found here.

Unfortunately .NET Fiddle uses framework 4.5, so program can't be compiled and run online due to the fact I use a newer framework (4.7.1).

Also consider my real code is organized into several files!

It works and it's fast, so I'm completely satisfied with this part.

A STEP FURTHER

First problem solved, pretty good. But now I have to face the next one: I have several locations to assign workers shifts to and these locations share the same working hours.

A first attempt was to raise the number of columns on each file: cols 1-10 are for the 1st venue, cols 11-20 for the 2nd and so on.

Code works without any change and Hungarian algorithm processes data in a while, good; but, as expected, I end having overlapping shifts for the same workers on multiple venues (it's random, but always happens).

I could solve this problem by computing 1st venue, then changing each worker requests denying slots already given in the 1st venue before computing the 2nd one; not exactly the best way I'm sure, just an idea I had, and I'm not sure I can always find a solution.

OTHER OPTIMIZATIONS

I could also think about adding other rules (e.g. if possible worker should have max 2 ranges in a day (avoiding for example solutions having slots 0, 2, 4, 6 and 8 and preferring slots 0-2, 6-8 instead) and limits, but this goes too far from the starting question, so it will be something I'm asking in future and I'm quite sure it could need some more complex algorithm or libraries (e.g. ORTools by Google) I'm searching/studying.

StackExchange Computer Science Q#105897, answer score: 7