Lower bounds and reduction procedures for the bin packing problem
Discrete Applied Mathematics - Combinatorial Optimization
Exact Solution of the Two-Dimensional Finite Bon Packing Problem
Management Science
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
INFORMS Journal on Computing
Search Strategies for Rectangle Packing
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
An Exact Algorithm for Higher-Dimensional Orthogonal Packing
Operations Research
Propagation via lazy clause generation
Constraints
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
New filtering for the cumulative constraint in the context of non-overlapping rectangles
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Explaining the cumulative propagator
Constraints
The g12 project: mapping solver independent models to efficient solutions
ICLP'05 Proceedings of the 21st international conference on Logic Programming
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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In this paper we present a model for the carpet cutting problem in which carpet shapes are cut from a rectangular carpet roll with a fixed width and sufficiently long length. Our exact solution approaches decompose the problem into smaller parts and minimise the needed carpet roll length for each part separately. The customers requirements are to produce a cutting solution of the carpet within 3 minutes, in order to be usable during the quotation process for estimating the amount of carpet required. Our system can find and prove the optimal solution for 106 of the 150 real-world instances provided by the customer, and find high quality solutions to the remainder within this time limit. In contrast the existing solution developed some years ago finds (but does not prove) optimal solutions for 30 instances. Our solutions reduce the wastage by more than 35% on average compared to the existing approach.