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This paper introduces and illustrates an efficient algorithm, called the sweep algorithm, for solving medium- as well as large-scale vehicle-dispatch problems with load and distance constraints for each vehicle. The locations that are used to make up each route are determined according to the polar-coordinate angle for each location. An iterative procedure is then used to improve the total distance traveled over all routes. The algorithm has the feature that the amount of computation required increases linearly with the number of locations if the average number of locations for each route remains relatively constant. For example, if the average number of locations per route is 7.5, the algorithm takes approximately 75 seconds to solve a 75-location problem on an IBM 360/67 and approximately 115 seconds to solve a 100-location problem. In contrast, the time to solve a problem with a fixed number of locations increases quadratically with the average number of locations per route. The sweep algorithm generally produces results that are significantly better than those produced by GASKELL'S savings approach and are generally slightly better than CHRISTOFIDES AND EILON'S results; however, the sweep algorithm is not as computationally efficient as Gaskell's and is slightly less so than Christofides and Eilon's. [ABSTRACT FROM AUTHOR]

The article examines the problem of managing railroad equipment and personnel in a hypothetical railroad system. The tasks of a hypothetical scheduler are presented, including crew assignments, shift changes, and route assignments. Variables and restraints include crew productivity, overtime pay, and union work regulations. The article states that the number of computations was too great for even an International Business Machines 650 class computer, and that the modified simplex method of A. Charnes and C. E. Lemke was adopted. A set of linear programs is presented and discussed. The additional question facing the scheduler of selecting which traffic to move was approached through an adaptation of the "dual-method" of linear programming, a method developed originally by C. E. Lemke.

Crow-fly distance between the depot and delivery points is usually used when considering the problem of locating a depot. Instead, we assume that vans can only travel along a rectangular system of roads. This leads us to a much simpler solution. [ABSTRACT FROM AUTHOR]

The article presents questions and answers related to geography. One person asks about the common isthmuses. Another person inquires about the shortest route around the world starting from New York City. A question is raised regarding the highest mountain in North America and in the world, and the location of Mount Hercules.