Simultaneous scheduling and location (ScheLoc): the planar ScheLoc makespan problem
Tóm tắt
While in classical scheduling theory the locations of machines are assumed to be fixed we will show how to tackle location and scheduling problems simultaneously. Obviously, this integrated approach enhances the modeling power of scheduling for various real-life problems. In this paper, we introduce in an exemplary way theory and three polynomial solution algorithms for the planar ScheLoc makespan problem, which includes a specific type of a scheduling and a rather general, planar location problem, respectively. Finally, a report on numerical tests as well as a generalization of this specific ScheLoc problem is presented.
Tài liệu tham khảo
Carrizosa, E., Hamacher, H. W., Klein, R., & Nickel, S. (2000). Solving nonconvex planar location problems by finite dominating sets. Journal of Global Optimization, 18(2), 195–210.
Durier, R., & Michelot, C. (1985). Geometrical properties of the Fermat–Weber problem. European Journal of Operational Research, 20, 332–343.
Hamacher, H. W., & Hennes, H. (2007). Integrated scheduling and location models: single machine makespan problems. Studies in Locational Analysis, 16, 77–90.
Hennes, H. (2005). Integration of scheduling and location models. Aachen: Shaker Verlag.
Hopcroft, J., & Tarjan, R. (1974). Efficient planarity testing. Journal of the ACM, 21(4), 549–568.
Kalcsics, J., Nickel, S., Puerto, J., & Tamir, A. (2002). Algorithmic results for ordered median problems. Operations Research Letters, 30, 149–158.
Megiddo, N. (1984). Linear programming in linear time when the dimension is fixed. Journal of the Association for Computing Machinery, 31(1), 114–127.
Minkowski, H. (1967). Gesammelte Abhandlungen—Band 2. New York: Chelsea Publishing Company.
Mulmuley, K. (1994). Computational geometry: an introduction through randomized algorithms. Englewood Cliffs: Prentice Hall.
Nickel, S., & Puerto, J. (2005). Location theory: a unified approach. Berlin: Springer.
Puerto, J., & Fernández, F. R. (2000). Geometrical properties of the symmetrical single facility location problem. Journal of Nonlinear and Convex Analysis, 1(3), 321–342.
Rodríguez-Chía, A. M., Nickel, S., Puerto, J., & Fernández, F. R. (2000). A flexible approach to location problems. Mathematical Methods of Operations Research, 51(1), 69–89.
Thisse, J. F., Ward, J. E., & Wendell, R. E. (1984). Some properties of location problems with block and round norms. Operations Research, 32, 1309–1327.
Ward, J. E., & Wendell, R. E. (1985). Using block norms for location modeling. Operations Research, 33, 1074–1090.
Weißler, A. (1999). General bisectors and their application in planar location theory. Aachen: Shaker Verlag.