A simple OPT+1 algorithm for cutting stock under the modified integer round-up property assumption

被引：1

作者：

Jansen, Klaus ^{[2
]}

Solis-Oba, Roberto ^{[1
]}

机构：

[1] Univ Western Ontario, Dept Comp Sci, London, ON, Canada

[2] Univ Kiel, Inst Informat, Kiel, Germany

来源：

INFORMATION PROCESSING LETTERS | 2011年 / 111卷 / 10期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Cutting stock; Algorithms; Modified integer round-up property; NUMBER;

D O I：

10.1016/j.ipl.2011.02.009

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present a simple algorithm for the cutting stock problem with objects of a constant number d of different sizes. Our algorithm produces solutions of value at most OPT + 1 in time d(O(d)) (log(7) n + s(3.5)), where OPT is the value of an optimum solution, n is the number of objects, and s is the total number of bits needed to encode the object sizes. This algorithm works under the assumption that the modified integer round-up property of Scheithauer and Terno for the cutting stock problem holds. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：479 / 482

页数：4

共 9 条

[1] THE MODIFIED INTEGER ROUND-UP PROPERTY OF THE ONE-DIMENSIONAL CUTTING STOCK PROBLEM
SCHEITHAUER, G
TERNO, J
[J]. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1995, 84 (03) : 562 - 571
[2] Theoretical investigations on the modified integer round-up property for the one-dimensional cutting stock problem
Scheithauer, G
Terno, J
[J]. OPERATIONS RESEARCH LETTERS, 1997, 20 (02) : 93 - 100
[3] Sufficient conditions for the integer round-up property to be violated for the linear cutting stock problem
Kartak, VM
[J]. AUTOMATION AND REMOTE CONTROL, 2004, 65 (03) : 407 - 412
[4] Sufficient Conditions for the Integer Round-Up Property to Be Violated for the Linear Cutting Stock Problem
V. M. Kartak
[J]. Automation and Remote Control, 2004, 65 : 407 - 412
[5] An OPT+1 Algorithm for the Cutting Stock Problem with Constant Number of Object Lengths
Jansen, Klaus
Solis-Oba, Roberto
[J]. INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION, PROCEEDINGS, 2010, 6080 : 438 - +
[6] Constructing an Instance of the Cutting Stock Problem of Minimum Size Which Does Not Possess the Integer Round-Up Property
Ripatti A.V.
Kartak V.M.
[J]. Journal of Applied and Industrial Mathematics, 2020, 14 (01) : 196 - 204
[7] A POLYNOMIAL ALGORITHM FOR INTEGER PROGRAMMING COVERING PROBLEMS SATISFYING THE INTEGER ROUND-UP PROPERTY
ORLIN, JB
[J]. MATHEMATICAL PROGRAMMING, 1982, 22 (02) : 231 - 235
[8] POLYNOMIAL ALGORITHM FOR INTEGER PROGRAMMING COVERING PROBLEMS SATISFYING THE INTEGER ROUND-UP PROPERTY.
Orlin, James B.
[J]. 1600, (22):
[9] A Polynomial Time OPT+1 Algorithm for the Cutting Stock Problem with a Constant Number of Object Lengths
Jansen, Klaus
Solis-Oba, Roberto
[J]. MATHEMATICS OF OPERATIONS RESEARCH, 2011, 36 (04) : 743 - 753

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