One-dimensional Cutting Stock Problem (1d-csp): a Study on Data Dependent Trim Loss
نویسندگان
چکیده
A generalized approach is introduced for getting minimal trim in onedimensional cutting stock problem (1D-CSP) which occurs extensively while manufacturing of different engineering objects. Our study is especially focused on transmission tower manufacturing industry. The concept of computing total trim by using the idea of pre-defined sustainable trim has been explored in previous work of authors. Given m stock lengths , , ... , , the cutting plan consists of cutting of at most two order lengths at a time out of the demanded set of n order lengths , , ... , . Considering the given data, the total trim has been computed corresponding to two different sustainable trims of order one (viz. ) and order two (viz. ). Introducing various values of sustainable trims as knots between and , the total trim has been computed corresponding to each knot, the linear approximation has been constructed which predict the total trim loss at any arbitrary point lying between and .
منابع مشابه
The trim loss concentration in one-dimensional cutting stock problem (1D-CSP) by defining a virtual cost
Nowadays, One-Dimensional Cutting Stock Problem (1D-CSP) is used in many industrial processes and re-cently has been considered as one of the most important research topic. In this paper, a metaheuristic algo-rithm based on the Simulated Annealing (SA) method is represented to minimize the trim loss and also to fo-cus the trim loss on the minimum number of large objects. In this method, the 1D-...
متن کاملAn ACO algorithm for one-dimensional cutting stock problem
The one-dimensional cutting stock problem, has so many applications in lots of industrial processes and during the past few years has attracted so many researchers’ attention all over the world. In this paper a meta-heuristic method based on ACO is presented to solve this problem. In this algorithm, based on designed probabilistic laws, artificial ants do select various cuts and then select the...
متن کاملFlexible Stock Allocation and Trim Loss Control for Cutting Problem in the Industrial - Use Paper Production
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...
متن کاملOn the MAXGAP Problem for Cutting Stock Problems
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...
متن کاملA note on Integer Programming Models for Cutting Stock Problems with Setup Costs
The 1-dimensional Cutting Stock Problem (1-CSP) seeks to fulfill with a minimum trim loss the demand of parts of various lengths by cutting them out from a given stock size. In the Pattern Minimization Problem (1-PMP) one wants an optimal 1-CSP solution that uses a minimum number of distinct cutting patterns. We discuss two formulations of 1-PMP: (1) introduced by Vanderbeck, and (2) obtained b...
متن کامل