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SPEC CPU2000 Benchmark Description File

Benchmark Name


Benchmark Author

Dr. Andreas Loebel
Konrad-Zuse-Zentrum Berlin (ZIB)
Takustr. 7
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

Benchmark Description

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 minimized.

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 arithmetic.

Input Description

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 cost.

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 polynomial.

The benchmark requires about 100 and 190 megabyte for a 32 and a 64 bit architecture, respectively.

Output Description

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.

Programming Language

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

  #ifndef _PROTO_
  #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: */

  #ifdef _PROTO_
  long resize_prob( network_t *net )
  long resize_prob( net )
    network_t *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

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

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