SPEC CPU2000 Benchmark Description File
Dr. Andreas Loebel
Konrad-Zuse-Zentrum Berlin (ZIB)
D-14195 Berlin, Germany
Phone: +49 (0)30 841 85 - 239
Fax: +49 (0)30 841 85 - 269
Secretary: +49 (0)30 841 85 - 208
Benchmark Program General Category
Combinatorial optimization / Single-depot vehicle scheduling
A benchmark derived from a program used for single-depot vehicle scheduling
in public mass transportation. The program is written in C, the benchmark
version uses almost exclusively integer arithmetic.
The program is designed for the solution of single-depot vehicle scheduling
(sub-)problems occurring in the planning process of public transportation
companies. It considers one single depot and a homogeneous vehicle fleet.
Based on a line plan and service frequenciesd, so-called timetabled trips
with fixed departure/arrival locations and times are derived. Each of this
timetabled trip has to be serviced by exactly one vehicle. The links
between these trips are so-called dead-head trips. In addition, there are
pull-out and pull-in trips for leaving and entering the depot.
Cost coefficients are given for all dead-head, pull-out, and pull-in trips.
It is the task to schedule all timetabled trips to so-called blocks such
that the number of necessary vehicles is as small as possible and,
subordinate, the operational costs among all minimal fleet solutions are
For simplification in the benchmark test, we assume that each pull-out and
pull-in trip is defined implicitly with a duration of 15 minutes and a cost
coefficient of 15.
For the considered single-depot case, the problem can be formulated as a
large-scale minimum-cost flow problem that we solve with a network simplex
algorithm accelerated with a column generation. The core of the benchmark
181.mcf is the network simplex code "MCF Version 1.2 -- A network
simplex implementation", For this benchmark, MCF is embedded in the
column generation process.
The network simplex algorithm is a specialized version of the well known
simplex algorithm for network flow problems. The linear algebra of the
general algorithm is replaced by simple network operations such as finding
cycles or modifying spanning trees that can be performed very quickly. The
main work of our network simplex implementation is pointer and integer
The input file contains line by line
the number of timetabled and dead-head trips (first line),
for each timetabled trip its starting and ending time,
for each dead-head trip its starting and ending timetabled trip and its
Worst case execution time is pseudo-polynomial in the number timetabled and
dead-head trips and in the amount of the maximal cost coefficient. The
expected execution time, however, is in the order of a low-order
The benchmark requires about 100 and 190 megabyte for a 32 and a 64 bit
The benchmark writes to two output files, inp.out and mcf.out. inp.out
contains log information and a checksum, mcf.out contains check output
values describing an optimal schedule computed by the program.
ANSI C, mathematical library (libm) required.
Known portability issues
The header source file "prototyp.h", which is (indirectly)
required by all modules, contains the lines
#if defined(__STDC__) || defined(__cplusplus) || defined(WANT_STDC_PROTO)
#define _PROTO_( args ) args
#define _PROTO_( args )
All C functions (subroutines) are defined in the original program with and
without function prototypes, e.g.:
/* function defined externally: */
extern long suspend_impl _PROTO_(( network_t *, cost_t, long ));
/* function defined in this module: */
long resize_prob( network_t *net )
long resize_prob( net )
In the SPEC version, -DWANT_STDC_PROTO is set as a required compilation
flag in the master Makefile 181.mcf/src/Makefile. This has the effect that
all compilers, predefining __STDC__ or not, use ANSI C prototyping. This is
intended for reasons of compatibility and standard adherence.
Other information, WWW Resources
Background information about the vehicle scheduling problem can be found in
the author's Ph.D. thesis "Optimal Vehicle scheduling in public
transit", which is available via WWW at the author's homepage or at ftp://ftp.zib.de/pub/zib-publications/books/Loebel.disser.ps.
The work horse in the benchmark 181.mcf is the code "MCF Version 1.2
-- A network simplex implementation", which is available for academic
use free of charge via WWW at www.zib.de.
An excellent text book about the network simplex algorithm and network flow
in general is Ahuja, Magnanti, and Orlin: "Network Flows: Theory,
Algorithms, and Applications", Prentice-Hall, Inc., Englewood Cliffs,
New Jersey, 1993.
Last Updated: 14 October 1999