The cutting-stock problem is the problem of filling an order at minimum cost for specified numbers of lengths of material to be cut from given stock lengths of given cost. When expressed as an integer programming problem the large number of variables involved generally makes computation infeasible. This same difficulty persists when only an approximate solution is being sought by linear programming. In this paper, a technique is described for overcoming the difficulty in the linear programming formulation of the problem. The technique enables one to compute always with a matrix which has no more columns than it has rows.
[1]
Abraham Charnes,et al.
A MODEL FOR THE OPTIMAL PROGRAMMING OF RAILWAY FREIGHT TRAIN MOVEMENTS
,
1956
.
[2]
Kurt Eisemann,et al.
The Trim Problem
,
1957
.
[3]
G. Dantzig.
Discrete-Variable Extremum Problems
,
1957
.
[4]
Alan S. Manne,et al.
Programming of Economic Lot Sizes
,
1958
.
[5]
Ralph E. Gomory,et al.
An algorithm for integer solutions to linear programs
,
1958
.
[6]
George B. Dantzig,et al.
Decomposition Principle for Linear Programs
,
1960
.