A cutting stock problem is one of the main and classical problems in operations research that is modeled as Lp < /div> problem. Because of its NP-hard nature, finding an optimal solution in reasonable time is extremely difficult and at least non-economical. In this paper, two meta-heuristic algorithms, namely simulated annealing (SA) and tabu search (TS), are proposed and deve...

This paper considers the one-dimensional cutting stock problem with divisible items, which is a new problem in the cutting stock literature. The problem exists in steel industries. In the new problem, each item can be divided into smaller pieces, then they can be recombined again by welding. The objective is to minimize both the trim loss and the number of the welds. We present a mathematical m...

Problems in operations research are often NP complete and optimal solution for larger problems cannot be obtained, therefore heuristic methods have to be used. The boundary between the size of the problem that can be solved optimally and those where heuristic methods should be used is not always clear. To solve this problem we propose a method based on decision trees. The method can be also use...

One dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which has many applications in, e.g., steel, paper and fiber industries. To define an instance of 1D-CSP, we are given sufficient number of stock rolls which have the same length L, and m types of products with given lengths (l1, l2, . . . , lm) and demands (d1, d2, . . . , dm). A cu...

A linear integer minimization problem (IP) has the modiied integer roundup property (MIRUP) if the optimal value of any instance of IP is not greater than the optimal value of the corresponding LP relaxation problem rounded up plus one. The aim of this paper is to investigate numerically whether the MIRUP holds for the one-dimensional cutting stock problem. The computational experiments carried...

A linear integer minimization problem (IP) has the modified integer round-up property (MIRUP) if the optimal value of any instance of IP is not greater than the optimal value of the corresponding LP relaxation problem rounded up plus one. The aim of this paper is to investigate numerically whether the MIRUP holds for the one-dimensional cutting stock problem. The computational experiments carri...

The MAXGAP problem of a linear integer optimization problem P consists in determining the maximum diierence (gap) (P) between the optimal value z (E) of an instance E 2 P and the LP bound z c (E) with respect to all E 2 P. In the case of the one-dimensional cutting stock problem (1D CSP) it is known that (1D CSP) 1 + 5 132 but there is also a conjecture that (1D CSP) 2. In this paper we show th...