Solving a Real Problem in Plastic Industry: A Case in Trim-loss Problem


In this paper, a cutting plane model is presented for solving a problem in a cast polypropylene (CPP) plastic film manufacturer. The company produces plastic rolls from plastic pellets with widths ranging from 3 050 mm to 3 250 mm. The plastic rolls are trimmed according to customer’s orders. In prior to the trimming process, the production planning and inventory control (PPIC) department scheduled the machines and arranged the plastic trim compositions manually. In this work, the plastic trimming problem is solved by applying the trim loss model. Since trimmed loss problem is an NP-hard problem. In this case, the permutations are selected in advance so that the total length is feasible to the machine length. The computation is carried out using visual basic for application (VBA). The model outcomes are then used for optimizing the machine scheduling process. Modified earliest due date is proposed to schedule in which machines customer’s orders should be done. The machines scheduling represents the company conditions and the cutting production can be scheduled for daily basis.

Keywords: cutting plane; cutting stock; earliest due date; machine scheduling; non-polinomial-hard problem.

[1] Delorme M, Lori M, Martello S. Bin packing and cutting stock problems: Mathematical models and exact algorithms. European Journal of Operation Research 2016; 255(1):1–20.

[2] Furin F, Malaguti E. Models for the two-dimensional two-stage cutting stock problem with multiple stock size. Computers & Operation Research 2013; 40(8):1953–1962. science/article/pii/S0305054813000749

[3] Kallrath J, Rebennack S, Kallrath J, Kusche R. Solving real-world cutting stock-problems in the paper industry: mathematical approaches, experience, and challenges. European Journal of Operation Research 2014; 238(1):374–389. S0377221714002562

[4] Cui Y, Song X, Chen Y, Cui YP. New model and heuristic solution approach for a one-dimensional cutting stock problem with usable leftovers. Journal of the Operational Research Society 2017; 68(3):269–280.

[5] Tanir D, Ugurly O, Guler A, Nuriyev U. One-dimensional cutting stock problem with divisible items [Online] from (2016). [Accessed on 10 August 2018]

[6] Rietz J, Dempe S. Large gaps in one-dimensional cutting stock problems. Journal Discrete Applied Mathematics, 2008;156(10): 1929–1935. S0166218X07004295

[7] Belov G. Problems, Models and algorithms in one and two-dimensional cutting. [PhD Dissertation]. TU. Dresden, Germany (2004). pp. 33–37. pdf

[8] Bazaraa M, Jarvis JJ, Sherali HD. Linear programming and network flows. John Wiley&Sons, Inc: Hoboken; (2005). pp. 9–10. 20and%20network%20flows%202005&f=false

[9] Pinedo ML. Scheduling theory, algorithms, and systems. Springer Science and Business Media: New York (2008). pp. 44–46.

[10] Demir HI, Kokcam AH, Simsie F, Uygun Ö. Solving process planning, weighted earliest due date scheduling and weighted due date sssignment using simulated annealing and evolutionary strategies. International Journal of Industrial and Manufacturing Engineering, 2017;11(9):1547–1554. http://waset. org/publications/10007844