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)
We establish that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.
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)
We show that the problem of finding a perfect matching satisfying a single equality constraint with 0-1 coefficients in an n × n incomplete bipartite graph, polynomially reduces to a special case of the same problem called the partitioned case. Finding a solution matching for the partitioned case in the incomplete bipar-tite graph, is equivalent to… (More)
In K(n, n) with edges colored either red or blue, we show that the problem of finding a solution matching, a perfect matching consisting of exactly r red edges, and (n − r) blue edges for specified 0 ≤ r ≤ n, is a nontrivial integer program. We present an alternative, logically simpler proof of a theorem in  which establishes necessary and sufficient… (More)