T. Westerlund et J. Isaksson, SOME EFFICIENT FORMULATIONS FOR THE SIMULTANEOUS SOLUTION OF TRIM-LOSS AND SCHEDULING PROBLEMS IN THE PAPER-CONVERTING INDUSTRY, Chemical engineering research & design, 76(A6), 1998, pp. 677-684
A production optimization problem concerned with the paper-converting
industry is considered in the present paper. The problem can be writte
n as a cost minimization or as a profit maximization problem. The prob
lem is to produce a set of product paper reels from larger raw paper r
eels such that certain specifications are satisfied, while the overall
objective function is minimized/maximized. In this formulation, both
the widths and lengths of the different raw paper used are utilized as
variables. The lengths as well as the ordered amounts of the product
paper reels are allowed to vary within certain specified limits. In ad
dition to the trim-loss constraints, constraints for the simultaneous
sequential scheduling of the cutting machines is also included, giving
time constraints for the cutting machines in the considered formulati
on. The income from the product paper and overproduction as well as co
sts derived from the raw paper used, machine time, format changes as w
ell as knife changes are all included in the objective function. A num
erical example from the paper-converting industry under consideration
is included to illustrate the proposed procedure.