The multiperiod two‐dimensional non‐guillotine cutting stock problem with usable leftovers

Abstract

A mixed integer linear programing model for the two‐dimensional non‐guillotine cutting problem with usable leftovers was recently introduced by Andrade et al. The problem consists in cutting a set of ordered items using a set of objects of minimum cost and, within the set of solutions of minimum cost, maximizing the value of the usable leftovers. Since the concept of usable leftovers assumes they can potentially be used to attend new arriving orders, the problem is extended to the multiperiod framework in this work. In this way, the decision at each instant does not minimize in a myopic way the cost of the objects required to attend the orders of the current instant; but it aims to minimize the overall cost of the objects up to the considered time horizon. Some variants of the proposed model are analyzed and numerical results are presented.

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%.…”

“…16,17 The 2D guillotine CSP is presented in which the objective is the minimization of the number of large plates that are used to cut a list of small rectangles. [18][19][20] A linear mixed-integer programming model for the 2D nonguillotine cutting problem with usable leftovers was recently introduced by Birgin et al 21 This problem described a set of ordered materials while using a set of minimum cost, and inside the solutions of minimum cost, the value of the usable leftovers is maximized. A 2D-CSP is transformed into an integer linear program where the policy variables are the number of beams to cut under to a set of feasible patterns.…”

An improved heuristic-dynamic programming algorithm for rectangular cutting problem

“…. Add the above function (14) to the left and right edges of defects; similarly, the same is true for the function (15).…”

“…Martin M. et al (2019) [12] propose a compact integer linear programming (ILP) model for the problem based on the discretization of the defective object and develop a Benders decomposition algorithm and a constraintprogramming (CP) based algorithm as solution methods. For the non-guillotine cutting problem, Gonçalves and Wäscher (2020) [13] combine a MIP model with a new hybrid algorithm to solve it and Birgin et al (2020) [14] propose a mixed integer linear programing model for the problem with usable leftovers. Velasco and Eduardo (2019) [15] study the constrained two-dimensional guillotine cutting problem for obtaining upper bounds.…”

Constrained two‐dimensional guillotine cutting problem: upper‐bound review and categorization

“…In this work, we focus on the unstaged guillotine C2DC, both weighted and unweighted, with fixed orientation of the pieces. The interest in this problem is also motivated by the fact that it arises as a subproblem in the basic cutting stock problem (CSP) and in more complex variants, for example, using leftovers (Andrade et al., ; Chen et al., ) and/or in a multiperiod perspective (Birgin et al., ). A discussion about the CSP is beyond the scope of this paper.…”