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...

Original scientific papers This paper mainly addresses a two-dimensional defective stocks guillotine cutting stock problem where stock of different sizes is available. Herein a new heuristic algorithm which is based on tree is proposed to discuss this problem. In particular, such an algorithm consists of two parts: the first part is an initial solution of the cutting stock problem where there a...

Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic method was proposed for such problems. Then, the ...

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...

Selection of feasible cutting patterns in order to minimize the raw material wastage which is known as cutting stock problem has become a key factor of the success in today’s competitive manufacturing industries. In this paper, solving a rectangular shape medium size two-dimensional cutting stock problem is discussed. Our study is restricted to raw materials (main sheets) in a rectangular shape...

We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industr...

A heuristic particle swarm optimization (HPSO) is proposed as a solution to one-dimensional cutting stock problem (1D-CSP), which incorporate genetic operators into particle swarm optimization (PSO). In this paper, a heuristic strategy that is based on the results of analysis of the optimal cutting pattern of particles with successful search processes is described, which process a global optimi...