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This paper develops a new polynomially bounded shortest path algorithm, called the partitioning shortest path (PSP) algorithm, for finding the shortest path from one node to all other nodes in a network containing no cycles with negative lengths. This new algorithm includes as variants the label setting algorithm, many of the label correcting algorithms, and the apparently computationally superior threshold algorithm.

This paper presents six new variants of the polynomially bounded Partitioning Shortest Path (PSP) algorithm for finding the shortest path from one node to all other nodes in a network. Three of these variants, one for negative arc lengths, but without negative cycles, and two for nonnegative arc lengths, augment the PSP algorithm to maintain a property called sharp by Shier and Witzgall. The other three variants augment the PSP algorithm to maintain a property called near-sharp for nonnegative arc lengths. Extensive computational testing is presented on one of the sharp variants for nonnegative arc lengths and two of the near-sharp variants. The empirical results based on 4500 test problems with 90 different configurations and three different network topologies indicate that these new algorithms have excellent computational performance characteristics. Based on total solution times for the 4500 test problems, these new algorithms out-perform all other algorithms tested. In addition, one of the near-sharp algorithms strictly dominates all others on all problem topologies tested.shortest path algorithms

Many real-world applications have profited from netform innovations in both modeling and solution strategies. Practical experience shoves that advances in netform modeling and solution strategies overcome many of the difficulties in conceptual design and problem solving of previous approaches to system optimization. Moreover, they provide the type of technologies required of truly useful decision-planning tools, technologies that facilitate modeling, solution, and implementation. The ultimate test and worth of computer-based planning models, however, depends on their use by practitioners. In this tutorial, we show how certain algebraic models can be viewed graphically using netform modeling and describe several large practical problems we have solved. Some of our insights can make it easier for practitioners to take advantage of these technologies.

This paper first presents a brief reveiw of the multicriteria problems faced by the United States Army, Navy, and Marine Corps in making enlisted personnel assignment decisions. Then for the most complex of these military assignment problems, the Marine Corps problem, a new modeling and solution approach is presented with computational results for a problem having eleven criteria and approximately 10,000 constraints and 780,000 variables. Other contributions of this paper include: (a) New insights into the effects on model structure and solution efficiency of handling preemptive multiple criteria sequentially versus simultaneously. (b) Derivation of an excellent convex proportional fill function. (c) Providing multicriteria researchers with a class of large-scale test problems.preemptive multicriteria, assignment, networks, manpower