Combinatorial mechanics

Ph.D.John J. Barthold

Rencontre de Beyrouth, 1988

Takieddine-Amiouny Mona, Makdissi Jeanie, Moughaïzel Joseph, Moughaïzel Laure, Nehmé Raja, Amiouny Fouad, Kallab-Bissat Ilham, Saba Yared Nazik, Nasr Nada, Nasr Sami, Accad Évelyne, Collin Françoise. Rencontre de Beyrouth, 1988. In: Les Cahiers du GRIF, n°43-44, 1990. Liban. pp. 81-95

Heuristics for Balancing Turbine Fans

We develop heuristics for a problem that models the static balancing of turbine fans: Load point masses at regularly spaced positions on the periphery of a circle so that the residual unbalance about the center --- which corresponds to the axis of rotation of the fan --- is as small as possible. We prove that our heuristics provide the same worst-case guarantee in terms of residual unbalance as does total enumeration. Furthermore, computational tests show that our heuristics are orders of magnitude faster and not far from optimum on average. The balancing of rotating elements in modern machinery is critical, and is done in some cases by sophisticated balancing machines. The presence of unbalance in a rotating machine results in vibrations and excess stresses on the bearings, both of which shorten its useful life. Static unbalance, the primary source of unbalance in narrow, disc-shaped rotors such as turbine fans, occurs when the center of gravity of the fan does not coincide with the a..

The Airline Container Loading Problem with Pickup and Delivery

This paper considers the loading optimization problem for a set of containers and pallets transported into a cargo aircraft that serves multiple airports. Because of pickup and delivery operations that occur at intermediate airports, this problem is simultaneously a Weight & Balance Problem and a Sequencing Problem. Our objective is to minimize fuel and handling operation costs. This problem is shown to be NP-hard. We resort to a mixed integer linear program. Based on real-world data from a professional partner (TNT Airways), we perform numerical experiments using a standard B&C library. This approach yields better solutions than traditional manual planning, which results in substantial cost savings.Optimization in air transpor