Past, present and future of large scale transshipment computer codes and applications

Abstract Three generations of computers have elapsed since the first satisfactory method for solving transportation and transshipment problems was devised. During this time many computational advances have taken place in developing computer codes to solve these problems. For example, recent breakthroughs in the solution and human engineering aspects of transshipment problems have made it possible to solve problems in only a few minutes that require many hours of computing time with commercial LP packages. Additionally the computer memory requirements of new methods have enabled the solution of vastly larger problems than previously imagined possible (50,000 equations and 62 million variables). Enhancing the significance of these developments, new ways have been discovered for modelling broad classes of real world problems as transshipment or transshipment-related problems. The primary purpose of this paper is to summarize these events and to do some crystal ball gazing to provide what we believe to be “best estimates” of future trends.

[1]  J. Munkres ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[2]  Darwin Klingman,et al.  Double-Pricing Dual and Feasible Start Algorithms for the Capacitated Transportation (Distribution) Problem , 1972 .

[3]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[4]  Darwin Klingman,et al.  NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems , 1974 .

[5]  D. R. Fulkerson,et al.  An Out-of-Kilter Method for Minimal-Cost Flow Problems , 1960 .

[6]  Merrill M. Flood,et al.  A transportation algorithm and code , 1961 .

[7]  Fred W. Glover,et al.  An improved version of the out-of-kilter method and a comparative study of computer codes , 1974, Math. Program..

[8]  Stephen Glicksman,et al.  Coding the transportation problem , 1960 .

[9]  Darwin Klingman,et al.  Augmented Threaded Index Method for Network Optimization. , 1974 .

[10]  G. Bennington An Efficient Minimal Cost Flow Algorithm , 1973 .

[11]  F. L. Hitchcock The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[12]  R J Clasen THE NUMERICAL SOLUTION OF NETWORK PROBLEMS USING THE OUT-OF-KILTER ALGORITHM , 1968 .

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

[14]  C. M. Shetty,et al.  Efficient computational devices for the capacitated transportation problem , 1974 .

[15]  D. R. Fulkerson,et al.  A primal‐dual algorithm for the capacitated Hitchcock problem , 1957 .

[16]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[17]  Jack B. Dennis,et al.  A High-Speed Computer Technique for the Transportation Problem , 1958, JACM.

[18]  Darwin Klingman,et al.  The Augmented Predecessor Index Method for Locating Stepping-Stone Paths and Assigning Dual Prices in Distribution Problems , 1972 .

[19]  P. Schweitzer,et al.  AN ALGORITHM FOR COMBINING TRUCK TRIPS , 1972 .

[20]  Robert G. Busacker,et al.  A PROCEDURE FOR DETERMINING A FAMILY OF MINIMUM-COST NETWORK FLOW PATTERNS , 1960 .

[21]  Abraham Charnes,et al.  The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems , 1954 .

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

[23]  Jr. L. Wheaton Smith Current Status of the Industrial Use of Linear Programming , 1956 .

[24]  Darwin Klingman,et al.  A Computational Study of the Effects of Problem Dimensions on Solution Times for Transportation Problems , 1975, JACM.

[25]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

[26]  Ellis L. Johnson,et al.  Networks and Basic Solutions , 1966, Oper. Res..

[27]  A. Gleyzal,et al.  An algorithm for solving the transportation problem , 1955 .

[28]  M. Klein A Primal Method for Minimal Cost Flows with Applications to the Assignment and Transportation Problems , 1966 .

[29]  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.

[30]  Gerald L. Thompson,et al.  Benefit-Cost Analysis of Coding Techniques for the Primal Transportation Algorithm , 1973, JACM.

[31]  Leon Gainen,et al.  Linear programming in bid evaluation , 1954 .