A column generation on two-dimensional cutting stock problem with fixed-size usable leftover and multiple stock sizes

Decision making viva genetic algorithm for the utilization of leftovers

“…This shows the efficiency and dominancy of the presented approach in the sense that fulfills the given demand from the nonstandard leftovers. The presented algorithm in this article is a novel approach to this era, because the previous approaches minimized leftovers in the stock by using the cutting concept, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] whereas the proposed one used the combinatorial concept. The maximum utilization of the stock in Reference [56] is up to 99.15%, whereas the presented approach used the stock up to 100%.…”

“…22 A two-dimensional two-stage cutting-stock problem (2D-2CSP) with many stock sizes with fixed-size leftovers is investigated, where a fixed-size usable leftover is an item whose size is defined in advance that could be used later. 23 This way, with fixed-size usable leftovers, they reduced the waste area, therefore helped to make the better cutting patterns. Furthermore, a 3D demand cutting and packing decision process for daily tailored orders of a real-life steel retailer is proposed.…”

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

“…F. Clautiaux et al [34] proposed diving heuristic based on column generation and used dynamic programming to solve pricing problem. Most recently, S. Sumetthapiwat et al [35] proposed a mathematical model which utilized column generation method and integer solution finding strategies to solve one-dimensional cutting stock problem with useable leftover.…”

“…However, the same information is included in terms of reels of paper saved through application of this study. To illustrate the solution procedure, a small real industrial example is solved which is concerned with production planning of grey back paper in master reels of widths 60 to 70 inches and cutting of limited stocked reels of widths 35,30,25,22, and 18 inches, available in stock. The thickness of paper and grade are 1.0 mm and 350 g/m 2 , respectively.…”

“…The over-produced reels are stocked for later usage or negotiated with client and those produced of width less than the minimum acceptable limit are either recycled or utilized in the form of less valuable products than the ordered items. To fill the order, the objective function of the model minimizes the trim loss area in cutting master reels of widths 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, and 60 inches, and stocked reels of widths 35,30,25,22, and 18 inches. The obtained optimal solution comprises of four non-integer decision variables as presented in Table 4.…”