AI and OR in management of operations: history and trends

The last decade has seen a considerable growth in the use of Artificial Intelligence (AI) for operations management with the aim of finding solutions to problems that are increasing in complexity and scale. This paper begins by setting the context for the survey through a historical perspective of OR and AI. An extensive survey of applications of AI techniques for operations management, covering a total of over 1200 papers published from 1995 to 2004 is then presented. The survey utilizes Elsevier's ScienceDirect database as a source. Hence, the survey may not cover all the relevant journals but includes a sufficiently wide range of publications to make it representative of the research in the field. The papers are categorized into four areas of operations management: (a) design, (b) scheduling, (c) process planning and control and (d) quality, maintenance and fault diagnosis. Each of the four areas is categorized in terms of the AI techniques used: genetic algorithms, case-based reasoning, knowledge-based systems, fuzzy logic and hybrid techniques. The trends over the last decade are identified, discussed with respect to expected trends and directions for future work suggested.     

Convergence of generalized conjugate partial Fourier integrals

Generalized conjugate partial Fourier integrals are used to find jumps of functions. The rate of convergence is studied and sharp results are obtained.     

Monstrous Branes

 We study D-branes in the bosonic closed string theory whose automorphism group is the Bimonster group (the wreath product of the Monster simple group with ℤ₂). We give a complete classification of D-branes preserving the chiral subalgebra of Monster invariants and show that they transform in a representation of the Bimonster. Our results apply more generally to self-dual conformal field theories which admit the action of a compact Lie group on both the left- and right-moving sectors. Received: 20 February 2002 / Accepted: 17 August 2002 Published online: 19 December 2002 Communicated by R.H. Dijkgraaf     

Cell transfer and monomial positivity

We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generating functions of Stanley's (P,ω)-partitions. T.L. was supported in part by NSF DMS-0600677.     

A Network Simulation of High-congestion Road-traffic Flows in Cities with Marine Container Terminals

Port cities where marine cargo terminals are located are generally near urban areas characterized by high-congestion road traffic. Changes in cargo traffic volumes into a marine terminal, or in the surrounding traffic arteries, which carry this traffic, can significantly affect the terminal's operations. Conversely, activity at the terminal can have an impact on the traffic levels and congestion for a considerable distance from the terminal. This paper demonstrates a methodology useful for studying the impact of road traffic flows on marine container terminals located in highly congested areas. This model was developed at the request of the Virginia Center for World Trade and was used to answer three planning questions in the port of Hampton Roads, Virginia, USA-what would be the impact of: opening a new section of interstate highway, a projected doubling of container traffic at one terminal, and a daily unit train in the vicinity of another terminal. The problem was made more challenging by limited data-collection funds. None the less, the model was deemed valid by a panel of traffic experts and officials from several major state and private agencies involved in marine traffic management. The model results were subsequently a factor in two major decisions related to terminal management.     

Flips and the Hilbert scheme over an exterior algebra

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.     

Wild tiles in ℝ<Superscript>3</Superscript> with spherical boundaries

Wildly embedded tiles in ℝ³ with spherical boundary are discussed. The construction of the topologically complicated, crumpled cube tiles is reviewed. We construct an infinite family of wildly embedded, cellular tiles with Fox-Artin-type wild points. Finally, a condition on the set of wild points on a cellular tile is given to show that certain wild cells cannot be tiles. Several observations are recorded for further investigations. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 203–211, 2005.