An evaluation of mathematical programming and minicomputers

Abstract The availability of efficient mathematical software on minicomputers could greatly increase the use of operations research techniques in industry and government. The objective of this paper is to demonstrate the feasibility of implementing a particular class of mathematical programming algorithms, namely shortest path algorithms, on “typical” minicomputers. Two distinct shortest path algorithms were tested on four computer systems using a common set of test problems. Computational results are presented which verify the feasibility of implementing these algorithms in a minicomputer environment, and also show the relative efficiency of each algorithm to be the same when tested on a minicomputer as when tested on a large-scale computer system.

[1]  Stuart E. Dreyfus,et al.  An Appraisal of Some Shortest-Path Algorithms , 1969, Oper. Res..

[2]  Abraham Charnes,et al.  Past, Present and Future of Development, Computational Efficiency, and Practical Use of Large Scale Transportation and Transhipment Computer Codes , 1973 .

[3]  Fred Glover,et al.  A Computation Study on Start Procedures, Basis Change Criteria, and Solution Algorithms for Transportation Problems , 1974 .

[4]  Robert B. Dial,et al.  Algorithm 360: shortest-path forest with topological ordering [H] , 1969, CACM.

[5]  U. Pape,et al.  Implementation and efficiency of Moore-algorithms for the shortest route problem , 1974, Math. Program..

[6]  Darwin Klingman,et al.  Implementation and Computational Study on an In-Core, Out-of-Core Primal Network Code , 1976, Oper. Res..

[7]  Fred W. Glover,et al.  Real World Applications of Network Related Problems and Breakthroughs in Solving Them Efficiently , 1975, TOMS.

[8]  Bruce L. Golden,et al.  Technical Note - Shortest-Path Algorithms: A Comparison , 1976, Oper. Res..

[9]  T. R. White,et al.  Practical Applications of Linear Programming to Shell's Distribution Problems , 1976 .

[10]  Fred W. Glover,et al.  Implementation and computational comparisons of primal, dual and primal-dual computer codes for minimum cost network flow problems , 1974, Networks.

[11]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[12]  Gerald G. Brown,et al.  Design and Implementation of Large-Scale Primal Transshipment Algorithms , 1976 .

[13]  Jeffery L. Kennington,et al.  Solving the Pipe Network Analysis Problem Using Optimization Techniques , 1978 .

[14]  B. Golden.  Shortest-Path Algorithms: A Comparison , 1975 .

[15]  Darwin Klingman,et al.  Enhancements of Spanning Tree Labeling Procedures for Network Optimization. , 1979 .

[16]  Fred Glover,et al.  Technical Note - Equivalence of the 0-1 Integer Programming Problem to Discrete Generalized and Pure Networks , 1980, Oper. Res..

[17]  F. Glover,et al.  A computational analysis of alternative algorithms and labeling techniques for finding shortest path trees , 1979, Networks.

[18]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.