A Dynamic Programming Solution to a Problem of Loom Box Sequence Planning

Abstract

A drop box loom has a vertical rack of four boxes on each side of the loom to hold the shuttles. When a weft pick is inserted there is a choice of empty boxes to receive the shuttle. Choosing the empty box to be used at each pick of the pattern is termed "the loom box sequence problem". For reasons of safety and wear and tear, rack movements are minimized; in particular, movements to the opposite end of the rack are to be avoided. A further constraint is that, to repeat, the shuttles must begin and end the sequence in the same boxes.

This problem may be formulated simply in dynamic programming terms, but this leads to a computer storage requirement of 10¹² variables. A practical program using only 16 K storage has been written and the results for a typical problem are presented.