The cutting stock problem in a hardboard industry: a case study

Abstract This paper deals with the problem of cutting rectangular plates into smaller ones in a Brazilian hardboard industry. The problem is to determine the best patterns to be cut by an automated machine composed of a set of circular saws, devices to move and hold the plates, and loading and unloading stations. This machine involves unusual constraints such as bounds on the number of item types and the difference between the largest and the smallest length of the items in the cutting pattern, as well as usual constraints such as availability of longitudinal and transversal saws, orthogonal and two-staged guillotine cuttings without trimming, among others. A particular two-phase column generation procedure is described for the cutting stock formulation of the hardboard industry. Each phase of the procedure is modeled as an integer program and solved by two alternative methods: The first is based on dynamic programming and the second is a simple extension of the implicit enumeration procedure proposed in Gilmore and Gomory [1] . The application of the methodology is illustrated solving several random examples in a microcomputer as well as an actual problem derived of the hardboard industry under consideration.