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...

This short note presents a formal description of a fast and robust shortest path algorithm. Modeled on an algorithm of Pape (1974), it requires less memory store than most algorithms and at the same time permits arc lengths to range between -[chi] and +[chi]. It is described in a machine...

This paper considers a distribution model with upper and lower bounds on the number of units shipped from an origin or to a destination. Our problem differs from the classical distribution model in which the node shipping amounts are, by contrast, specified exactly. This generalization of the...

This paper describes a procedure for determining if constrained network problems (i.e., network problems with additional linear constraints) can be transformed into equivalent pure network problems by a linear transformation involving the node constraints and the extra constraints. These results...

This paper contains a new and very successful application of mathematical programming in the petroleum industry. Specifically, the paper describes the design and implementation of a model and computer system to address the complex short-term planning and operational issues associated with the...