Fuzzy bin packing problem

This paper deals with the fuzzy bin packing problem that is a packing problem of non-rigid rectangles into an open rectangular bin. This problem is different from the conventional bin packing problem, which considers only rigid rectangles. The goal of the fuzzy bin packing problem is to minimize both the height of a packing and the extra cost due to the reduction of each piece. The total cost of the problem is represented as the sum of the height cost and the extra cost due to reductions of the pieces, which is called reduction cost. Because the conventional bin packing problem itself is an NP-hard problem, the presented optimization method assumes that an initial packing for non-reduced pieces has already been found. A closed form solution is presented for fuzzy bin packing problems, in which fuzzy numbers are triangular and the reduction cost is given by a quadratic function.

[1]  Manfred Kunde,et al.  On a Special Case of Uniform Processor Scheduling , 1988, J. Algorithms.

[2]  Hyung Lee-Kwang,et al.  High speed flexible fuzzy hardware for fuzzy information processing , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[3]  E. F. Codd,et al.  Multiprogram scheduling , 1960, Commun. ACM.

[4]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[5]  Micha Hofri.  Two-Dimensional Packing: Expected Performance of Simple Level Algorithms , 1980, Inf. Control..

[6]  Bernard Chazelle,et al.  The Bottomn-Left Bin-Packing Heuristic: An Efficient Implementation , 1983, IEEE Transactions on Computers.

[7]  Frank Thomson Leighton,et al.  A provably efficient algorithm for dynamic storage allocation , 1986, STOC '86.

[8]  Yossi Azar,et al.  On Two Dimensional Packing , 1997, J. Algorithms.

[9]  H. Lee-Kwang,et al.  Ranking fuzzy values with satisfaction function , 1994 .

[10]  Antonio Albano.  A method to improve two-dimensional layout , 1977 .

[11]  Keon-Myung Lee,et al.  Hierarchical partition of nonstructured concurrent systems , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[12]  Edward G. Coffman,et al.  Average-case analysis of cutting and packing in two dimensions , 1990 .

[13]  Antonio Albano,et al.  Optimal Allocation of Two-Dimensional Irregular Shapes Using Heuristic Search Methods , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Brenda S. Baker,et al.  A 5/4 Algorithm for Two-Dimensional Packing , 1981, J. Algorithms.

[15]  Antonio Albano,et al.  NESTING TWO-DIMENSIONAL SHAPES IN RECTANGULAR MODULES , 1976 .

[16]  Keon-Myung Lee,et al.  Fuzzy hypergraph and fuzzy partition , 1995, IEEE Trans. Syst. Man Cybern..

[17]  Ronald L. Rivest,et al.  Orthogonal Packings in Two Dimensions , 1980, SIAM J. Comput..