We develop a heuristic for a problem motivated by the loading of aircraft or trucks: pack blocks into a bin so that their center-of-gravity is as close as possible to a target point. Our heuristic either produces good solutions or else signals that none is possible. It also works when loading non-homogeneous blocks into a bin of non-zero and possibly nonhomogeneous mass. How should cargo be stowed in an airplane? There are two con icting objectives: to use limited space e ciently by lling the aircraft, and to balance the load so that the aircraft will y more safely, y faster, and use less fuel Chapel, 1948; MACP 55-41, 1987. Although the rst issue has been much-studied under the rubric of bin-packing problems", there has been little work on the issue of balance. We model the problem of balancing the load as that of arranging n blocks" intervals in a 1-dimensional bin so that the center-of-gravity of the packed blocks is as close as possible to a target point p. We assume that the bin is su ciently small that we can treat acceleration due to the gravity of the earth as everywhere uniform and parallel. We ignore gravity other than that of the earth. In addition we assume that the bin is rigid. In this, the simplest formulation, we are interested only in the center-of-gravity of the packed blocks 1
Amiouny et al. REF consider the problem of packing a set of one-dimensional boxes of different weights and different lengths into a flat bin (so they are not allowed to stack these boxes), in such a way that after placing the last box, the center of gravity is as close as possible to a fixed target point.
Balanced Loading
Oper. Res.
Oper. Res.
Computer Science Mathematics