J E Beasley

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
Heading line
For each arc (i,j), with i=1, ... ,n+1 and j=1, ... , n
Heading line
For each arc (i,j), with i=1, ... ,n+1 and j=1, ... , n

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