Optimal sorting of product into fixed weight packaging

Abstract

Compac Sorting Equipment make very nifty machines for sorting fruit by weight, diameter, colour, density, blemish or even shape. Compac sought solutions to two closely related problems: the boxing problem and the bagging problem.

The boxing problem requires graded fruit to be assigned to outlets where boxes are filled with a specified number of fruit to a minimum weight (and a specified tolerance for underweights). The aim is to maximise the number of boxes packed. The decision must be made after all information is known, but before the fruit passes the first outlet - a few seconds total. Further, information about fruit already packed in a given box is incomplete (we don’t know exactly which fruit ended up in a box).

The bagging problem requires bags to be filled to a minimum weight - no tolerance for underweights, and no constraints on the number of fruit per bag. In this case complete information is available on fruit already assigned to a bag. Again the aim is to maximise the number of bags packed.