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.

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.

We give heuristics to sequence blocks on a beam, like books on a bookshelf, to minimize simultaneously the maximum deflection and the maximum bending moment of the beam. For a beam with simple supports at the ends, one heuristic places the blocks so that the maximum deflection is no more than 16/9 √ 3 ≈ 1.027 times the theoretical minimum and the maximum bending moment is within 4 times the minimum. Another heuristic allows maximum deflection up to 2.054 times the theoretical minimum but restricts the maximum bending moment to within 2 times the minimum. Similar results hold for beams with fixed supports at the ends.

A general approximation procedure is proposed for the problem of determining optimal angles of wrap for filament wound cylinders that are under pressure, axial, or torsional loads, or under any combination of these loads. For the special cases of open-ended and close-ended cylinders under a pure pressure load, optimal solutions are presented.