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Multiple copies may be made for classes, etc. Charges, if any, for reproduced copies must be just enough to recover reasonable costs of reproduction. Reproduction for commercial purposes is prohibited. This cover page must be included in all distributed copies. Comments and suggestions are welcome, and should be sent to fengtien@umich.edu. v PREFACE(More)
In this paper we briefly review the importance of LP (linear programming), and Dantzig's main contributions to OR (Operations Research), mathematics, and computer science. In [11, 3] gravitational methods for LP have been introduced. Several versions exist. The three main versions discussed there use a ball of (a): 0 radius, (b): small positive radius, and(More)
We describe a variety of interrelated decisions made during daily operations at a container terminal. The ultimate goal of these decisions is to minimize the berthing time of vessels, the resources needed for handling the workload, the waiting time of customer trucks, and the congestion on the roads and at the storage blocks and docks inside the terminal;(More)
The dawn of mathematical modeling and algebra occurred well over 3000 years ago in several countries (Babylonia, China, India,...). The earliest algebraic systems constructed are systems of linear equations, and soon after, the famous elimination method for solving them was discovered in China and India. This effort culminated in the writing of two books(More)
As the flagship of Hutchison Port Holdings (HPH), Hongkong International Terminals (HIT) is the busiest container terminal on the planet. HIT receives over 10,000 trucks and 15 vessels a day, about six million twenty-foot equivalent units (TEUs) a year. HIT makes hundreds of operational decisions a minute. HIT's terminal management system, the productivity(More)
A new IPM (Interior Point Method) for LPs has been discussed in [9, 10] based on a centering step that attempts to maximize the radius of the inscribed sphere with center on the current objective plane, and using descent directions derived without using matrix inversions. The method is a descent method and may be called the sphere method for LP. In contrast(More)