Investigating some heuristic solutions for the two-dimensional cutting stock problem

Abstract

In this study, the two-dimensional cutting stock problem (2DCSP) is considered. This is a problem that occurs in the cutting of a number of smaller rectangular pieces or items from a set of large stock rectangles. It is assumed that the set of large objects is sufficient to accommodate all the small items. A heuristic procedure is developed to solve the two-dimensional single stock-size cutting stock problem (2DSSSCSP). This is the special case where the large rectangles are all of the same size. The major objective is to minimize waste and the number of stock sheets utilized. The heuristic procedures developed to solve the 2DSSSCSP are based on the generation of cutting pattern. The Wang algorithm and a specific commercial software package are made use of to generate these patterns. The commercial software was chosen from a set of commercial software packages available in the market. A combinatoric process is applied to generate sets of cutting patterns using the Wang algorithm and the commercial software. The generated cutting patterns are used to formulate an integer linear programming model which is solved using an optimization solver. Empirical experimentation is carried out to test the heuristic procedures using data obtained from both small and real world application problem instances. The results obtained shows that the heuristic procedures developed produce good quality results for both small and real life problem instances. It is quite clear that the heuristic procedure developed to solve the 2DSSSCSP produces cutting patterns which are acceptable in terms of waste generated and may offer useful alternatives to approaches currently available. Broadly stated, this study involves investigating available software (commercial) in order to assess, formulate and investigate methods to attempt to benchmark software systems and algorithms and to employ ways to enhance solutions obtained by using these software systems.