A heuristic method to solve the location and machine selection problem in a two-dimensional continuous area

摘要

In this paper, a heuristic method is developed to solve the location and machine selection problem in a two-dimensional continuous area. In this method, a two-step algorithm is proposed in which the choosing sequence of the machines is determined in the first step and machines are located in the second step. Initially, the problem is formulated as a nonlinear mixed integer programming (MIP) model. This model is then modified to determine the location of machines step by step. Some small, medium and large-sized problems are designed and solved by both branch-and-bound (B&B) and the proposed method to verify the efficiency and effectiveness of the proposed method and the results obtained are compared. Computational results show that the proposed method can provide high quality solutions in a very reasonable time in comparison to B&B method, particularly in the case of medium-to-large sized problems.