A High-Speed Computer Technique for the Transportation Problem
Journal of the ACM (JACM)
An Investigation of Real-Time Solution of the Transportation Problem
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Journal of the ACM (JACM)
A Code for the Transportation Problem of Linear Programming
Journal of the ACM (JACM)
Linear Programming Computational Procedures for Ordinal Regression
Journal of the ACM (JACM)
Pivot Strategies for Primal-Simplex Network Codes
Journal of the ACM (JACM)
Real World Applications of Network Related Problems and Breakthroughs in Solving Them Efficiently
ACM Transactions on Mathematical Software (TOMS)
A note on computational studies for solving transportation problems
ACM '73 Proceedings of the ACM annual conference
Addressing capacity uncertainty in resource-constrained assignment problems
Computers and Operations Research
Code development and computation testing on network problems
ACM SIGMAP Bulletin
A practitioner's guide to the state of large scale network and network-related problems
AFIPS '76 Proceedings of the June 7-10, 1976, national computer conference and exposition
Addressing capacity uncertainty in resource-constrained assignment problems
Computers and Operations Research
Performance analysis of classification techniques using different parameters
ICDEM'10 Proceedings of the Second international conference on Data Engineering and Management
A comparison of pivot selection rules for primal simplex based network codes
Operations Research Letters
Solution of large dense transportation problems using a parallel primal algorithm
Operations Research Letters
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A computer code for the transportation problem that is even more efficient than the primal-dual method is developed. The code uses the well-known (primal) MODI method and is developed by a benefit-cost investigation of the possible strategies for finding an initial solution, choosing the pivot element, finding the stepping-stone tour, etc. A modified Row Minimum Start Rule, the Row Most Negative Rule for choice of pivot, and a modified form of the Predecessor Index Method for locating stepping-stone tours were found to perform best among the strategies examined. Efficient methods are devised for the relabeling that is involved in moving from one solution to another. The 1971 version of this transportation code solves both 100 × 100 assignment and transportation problems in about 1.9 seconds on the Univac 1108 Computer, which is approximately the same time as that required by the Hungarian method for 100 × 100 assignment problems.An investigation of the effect on mean solution time of the number of significant digits used for the parameters of the problem indicates that the cost parameters have a more significant effect than the rim parameters and that the solution time “saturates” as the number of significant digits is increased. The Minimum Cost Effect, i.e. the fact that total solution time asymptotically tends to the time for finding the initial solution as the problem size is increased (keeping the number of significant digits for the cost entries constant), is illustrated and explained. Detailed breakup of the solution times for both transportation and assignment problems of different sizes is provided. The paper concludes with a study of rectangular shaped problems.