Trim Loss Optimization by an Improved Differential Evolution

Abstract

The “trim loss problem” (TLP) is one of the most challenging problems in context of optimization research. It aims at determining the optimal cutting pattern of a number of items of various lengths from a stock of standard size material to meet the customers’ demands that the wastage due to trim loss is minimized. The resulting mathematical model is highly nonconvex in nature accompanied with several constraints with added restrictions of binary variables. This prevents the application of conventional optimization methods. In this paper we use synergetic differential evolution (SDE) for the solution of this type of problems. Four hypothetical but relevant cases of trim loss problem arising in paper industry are taken for the experiment. The experimental results compared with those of the other techniques show the competence of the SDE to solve the problem.

A Description of Supply Chain Planning Problems in the Paper Industry with Literature Review

“…The model is a binary nonlinear programming utilizing branch and price algorithm and marginal cost heuristic for solving. Puemsin et al (2012) and Ali et al (2013) provide solution approaches for twodimensional cutting stock problems. The setting is the same as in Westerlund and Isaksson (1998), i.e.…”

“…solving the cutting stock problem for paper converting industry. Puemsin et al (2012) use mixed integer nonlinear programming whereas Ali et al (2013) utilize synergetic differential evolution. Both solution methods provide adequate results.…”

A New Decision Model for Reducing Trim Loss and Inventory in the Paper Industry

“…Gilmore and Gomory [1] presented a delayed pattern generation technique for solving a one-dimensional cutting problem using linear programing. Other methods can also be found in the literature [2][3][4][5][6][7][8][9][10][11][12][13]. Morabito and Arenales [14] considered different objectives (e.g., cutting time and trim loss) in the preparation of the cutting plan.…”