A new lower bound for the non-oriented two-dimensional bin-packing problem
نویسندگان
چکیده
The two-dimensional discrete bin-packing problem (2BP ) consists in minimizing the number of identical rectangles used to pack a set of smaller rectangles. This problem is NP-complete. It occurs in industry if pieces of steel, wood, or paper have to be cut from larger rectangles. It belongs to the family of cutting and packing (C & P) problems, more precisely Two-Dimensional Single Bin Size Bin-Packing Problems (2SBSBPP), following the typology of Wäscher et al. [10]. A 2BP instance D is a pair (I,B). It is composed of the set I = {1, . . . , n} of items i to pack, and a bin B = (W,H) of width W and height H (W,H ∈ N). For the oriented case (2BP |O), an item i is of width wi and height hi (wi, hi ∈ N). We consider the non-oriented version of the problem (2BP |R), i.e. where the items can be rotated. So we consider the two possible orientations: w i = h 2 i and w 2 i = h 1 i . Before rotation, an item is of size (w i , h 1 i ), otherwise it is of size (w i , h 2 i ). An orientation of the set of items is an application r from I to {1, 2} that associates an orientation r(i) to each item i in I. Many methods [2,4,5,7,9] have been proposed
منابع مشابه
Extending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items
In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...
متن کاملA Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem
In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...
متن کاملNew Lower Bounds for the Three-dimensional Orthogonal Bin Packing Problem
In this paper, we consider the three-dimensional orthogonal bin packing problem, which is a generalization of the well-known bin packing problem. We present new lower bounds for the problem and demonstrate that they improve the best previous results. The asymptotic worst-case performance ratio of the lower bounds is also proved. In addition, we study the non-oriented model, which allows items t...
متن کاملAbstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...
متن کاملA Three-dimensional Bin Packing Algorithm
In this paper an approximation algorithm for the three-dimensional bin packing problem is proposed and its performance bound is investigated. To obtain such a bound a modified bin packing algorithm is considered for a two-dimensional problem with bounded bin and its area utilization is estimated. Finally, a hard example gives a lower bound of the performance bound. '
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Oper. Res. Lett.
دوره 35 شماره
صفحات -
تاریخ انتشار 2002