Solution of large dense transportation problems using a parallel primal algorithm

  • Authors:

  • D. L. Miller;J. F. Pekny;G. L. Thompson

  • Affiliations:

  • Central Research and Development Department, E.I. du Pont de Nemours and Company Inc., Wilmington DE 19898, USA;School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA;Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA 15213, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 1990

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Abstract

We implemented a version of primal transportation algorithm on a 14 processor BBN Butterfly computer and solved a variety of large, fully dense, randomly generated transportation and assignment problems ranging in size up to m = n = 3000. The algorithm alternates between a search and pivot phase. Processors independently locate possible pivots by concurrently searching the reduced cost matrix. Pivots are then performed sequentially by all processors. This parallelization strategy is justified since we have found that the search phase of the algorithm becomes the dominant activity with increasing problem size. The parallel algorithm has the added advantage of being easy to implement. A speedup of approximately 7 was obtained on large problems. The empirical difficulty of solving an n x n transportation problem was proportional to n^a where a varied between 2.0 and 2.2 with increasing shipping amounts.