Linear programming and Lagrangian relaxation heuristics for designing a material flow network on a block layout

This paper focuses on the problem of designing a material flow network for a given block layout. For an efficient design of a network, we simultaneously consider locations of input and output points, flow paths, and the smoothness of material flow paths. A mixed integer programming formulation is given for the problem with the objective of minimising the sum of transportation cost, cost related to flow paths, and penalty cost for non-smooth flows, i.e., flows with many turns. We suggest two heuristic algorithms based on the linear programming relaxation and the Lagrangian relaxation techniques. To evaluate performance of the suggested algorithms, a series of computational experiments is performed on well-known problem instances as well as randomly generated test problems. Results show that the suggested algorithms give good solutions in a reasonable amount of computation time.