An Algorithm for Two Dimensional Cutting Stock Problems with Demand

In this paper, two-dimensional cutting stock problem with demand has been studied.In this problem, cutting of large rectangular sheets into specific small pieces should be carried out hence, the waste will be minimized. Solving this problem is important to decrease waste materials in any industry that requires cutting of sheets. In most previus studies, the demand of pieces has not been usually considered. The cutting problems belong to the category of Np-hard problems. So finding a desirable solution in a suitable time is practically impossible and heuristic methods must be used. A meta-heuristic algorithm using SA approach is presented.Then attempt will be made to regulate the SAs parameters. Initial solutions are produced with a rule based algorithm and two internal and main SAs are used that lead to better performance of the algorithm. Due to lack of benchmark or test problems, two procedures for generating random problems is presented and are used to study efficiency of the algorithm. For this purpose, problems about 10 to 50 types of pieces with maximum demands of 2400 are generated and solved using the proposed algorithm. The results indicate that the algorithm capable of finding a solution with less than 6% of waste for problems with 30 types of pieces and total demands of 500.