# OR-Library

OR-Library is a collection of test data sets for a variety of OR problems.

A full list of the test data sets available in OR-Library can be found
here.

## Network Flow - Single commodity - Concave Costs - Single Source Uncapacitated

There are currently 240 data files.
These files contain the instances of the single source uncapacitated minimum
concave cost network flow problems considered in Fontes, Hadjiconstantinou
and Christofides(2003), "Upper Bounds for Single Source Uncapacitated Minimum
Concave Cost Network Flow Problems", Networks 41, 221-228 and in
D. B. M. M. Fontes, "Optimal Network Design Using Nonlinear Cost Flows",
PhD thesis, The Management School, Imperial College London, UK, 2000.
email: fontes@fep.up.pt
Problems are divided into ten groups (1, 2, ... , 10) containing three problem
instances, of the same type, each. Groups are defined according to the value
of the ratio between variable cost and fixed cost. Problem size varies between
10 and 50 vertices. For problems with 40 and 50 vertices only 5 groups are given.
Overall, there are 240 problem files.
These files are named CCNFP10g1a.txt, CCNFP10g1b.txt, CCNFP10g1c.txt,
CCNFP10g2a.txt, ... , CCNFP10g10c.txt, CCNFP12g1a.txt, ... , CCNFP50g5c.txt.
The first number, which can be 10, 12, 15, 17, 19, 25, 30, 40 or 50 indicates
the number of vertices considered, while the second number refers to problem
groups, which are, as given in the above work. The letters "a", "b", and "c"
allow to distinguish the three instances generated for each problem size and group.

For convenience all of the files have been zipped together and can be found in
the file CCNFPALL
The format of these files is as follows:
Number of vertices (n+1)
For each customer (i=1 to n)
Demand of customer i
Heading line
For each arc (i,j), with i=1, ... ,n+1 and j=1, ... ,n
Aij
Heading line
For each arc (i,j), with i=1, ... ,n+1 and j=1, ... , n
bij
Heading line
For each arc (i,j), with i=1, ... ,n+1 and j=1, ... , n
cij
If an arc does not exist then the corresponding bij=50000000 and aij=cij=0.
The data given has been used for three different types of polynomial concave
cost functions as follows:
1)f(xij)=-aij xij^2+bij xij+cij
2) f(xij)=-aij xij^2+bij xij
3) f(xij)=bij xij+cij
The largest file is CCNFPALL of size 300Kb (approximately).
The entire set of files is of size 7.5Mb (approximately).

Click here
to access these files