A column generation scheme for scheduling cutting machines in a clothing industry

This work addresses a scheduling problem arising from an application in a real industrial context, namely task scheduling in the cutting department of a clothing industry. In general, clothes are produced by assembling fabric cutouts. In the cutting department, fabric rolls on a line with a constant speed, and is cut by automated machines arranged along the line. Machines are all identical. A fabric cutout j, j = 1, ..., n, requires a cutting time pj, and must be assigned for cutting to one of the machines. There is a time window [rij, dij] associated with the cutting task j on machine Mi, whose length only depends on the rolling speed of the fabric and on the horizontal working space of each machine. A set-up time occurs when switching from one cutout to another, due to the movement of the cutting head to the next cutout. Cutouts arrive in batches over time. The problem consists in assigning and sequencing cutting tasks of a batch to the minimum number of the machines, in such a way that all cutting tasks are performed within their respective time windows. Based on a set partitioning model, different column generation algorithms are proposed for the problem. The solution of the corresponding separation subproblems is addressed.