Um problema de corte com padrões compartimentados

In this paper we will present the application of the Compartmented Knapsack Problem (CKP) in the Cut Problem of Steel Rolls (CPSR), that it is a problem of cut in two stages with restrictions special of grouping of items. The CKP consists of constructing compartments of unknown capacities in a knapsack of known capacity, in view of that items of interest is grouped in subgroups, in mode that, items of a grouping cannot be matched with items of another one. To understand the CKP more good it admits that the knapsack of a alpinist must be composite for an ideal number of compartments with items of four categories (remedies, foods, tools, clothes), however, items of distinct categories cannot be matched to form one same compartment, in addition, is unknown the ideal capacities of each compartment of the knapsack.

[1]  Marcos A. Pereira,et al.  Uma abordagem matematica para o problema de corte e laminação de fitas de aço , 1993 .

[2]  A. I. Hinxman.  The trim-loss and assortment problems: A survey , 1980 .

[3]  Ralph E. Gomory,et al.  A Linear Programming Approach to the Cutting Stock Problem---Part II , 1963 .

[4]  S. Martello,et al.  Algorithms for Knapsack Problems , 1987 .

[5]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[6]  Robert W. Haessler,et al.  Solving the two-stage cutting stock problem , 1979 .

[7]  J. M. Valério de Carvalho,et al.  A Computer Based Interactive Approach To A Two-Stage Cutting Stock Problem , 1994 .

[8]  Ralph E. Gomory,et al.  The Theory and Computation of Knapsack Functions , 1966, Oper. Res..

[9]  Nei Yoshihiro Soma,et al.  A Polynomial Approximation Scheme for the Subset Sum Problem , 1995, Discret. Appl. Math..

[10]  Gerhard Wäscher,et al.  Heuristics for the integer one-dimensional cutting stock problem: A computational study , 1996 .

[11]  Hisatoshi Suzuki.  A generalized knapsack problem with variable coefficients , 1978, Math. Program..

[12]  Fabiano do Prado Marques.  O Problema da Mochila Compartimentada , 2000 .

[13]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[14]  J. Soeiro Ferreira,et al.  A two-phase roll cutting problem , 1990 .

[15]  Nelson Maculan,et al.  An algorithm for determining the K-best solutions of the one-dimensional Knapsack problem , 2000 .

[16]  Edward Y. H. Lin,et al.  A Bibliographical Survey On Some Well-Known Non-Standard Knapsack Problems , 1998 .

[17]  Robert W. Haessler,et al.  Controlling Cutting Pattern Changes in One-Dimensional Trim Problems , 1975, Oper. Res..

[18]  Robert E Johnston,et al.  Bounds for nested knapsack problems , 1995 .

[19]  An LP-based approach to a two-stage cutting stock problem , 1995 .

[20]  Robert W. Haessler.  Technical Note - A Note on Computational Modifications to the Gilmore-Gomory Cutting Stock Algorithm , 1980, Oper. Res..

[21]  Nei Yoshihiro Soma,et al.  A new enumeration scheme for the knapsack problem , 1987, Discret. Appl. Math..

[22]  Hartmut Stadtler,et al.  A one-dimensional cutting stock problem in the aluminium industry and its solution , 1990 .