A hybrid heuristic to reduce the number of different patterns in cutting stock problems
Computers and Operations Research - Anniversary focused issue of computers & operations research on tabu search
In situ column generation for a cutting-stock problem
Computers and Operations Research
A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem
Computers and Operations Research
Computers and Operations Research
Strips minimization in two-dimensional cutting stock of circular items
Computers and Operations Research
A CAM system for one-dimensional stock cutting
Advances in Engineering Software
General properties of staircase and convex dual feasible functions
WSEAS Transactions on Information Science and Applications
Theoretical investigations on maximal dual feasible functions
Operations Research Letters
Cutting stock with no three parts per pattern: Work-in-process and pattern minimization
Discrete Optimization
A Column-Generation Based Tactical Planning Method for Inventory Routing
Operations Research
Solution approaches for the cutting stock problem with setup cost
Computers and Operations Research
Using the primal-dual interior point algorithm within the branch-price-and-cut method
Computers and Operations Research
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The cutting stock problem is that of finding a cutting of stock material to meet demands for small pieces of prescribed dimensions while minimising the amount of waste. Because changing over from one cutting pattern to another involves significant setups, an auxiliary problem is to minimise the number of different patterns that are used. The pattern minimisation problem is significantly more complex, but it is of great practical importance. In this paper, we propose an integer programming formulation for the problem that involves an exponential number of binary variables and associated columns, each of which corresponds to selecting a fixed number of copies of a specific cutting pattern. The integer program is solved using a column generation approach where the subproblem is a nonlinear integer program that can be decomposed into multiple bounded integer knapsack problems. At each node of the branch-and-bound tree, the linear programming relaxation of our formulation is made tighter by adding super-additive inequalities. Branching rules are presented that yield a balanced tree. Incumbent solutions are obtained using a rounding heuristic. The resulting branch-and-price-and-cut procedure is used to produce optimal or approximately optimal solutions for a set of real-life problems.