Optimal Carpet Cutting

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.