×

Contour line construction for a new rectangular facility in an existing layout with rectangular departments. (English) Zbl 1114.90061

Summary: In a recent paper, S. Savas, R. Batta and R. Nagi [Finite-size facility placement in the presence of barriers to rectilinear travel, Oper. Res. 50, No. 6, 1018–1031 (2002)] consider the optimal placement of a finite-sized facility in the presence of arbitrarily shaped barriers under rectilinear travel. Their model applies to a layout context, since barriers can be thought to be existing departments and the finite-sized facility can be viewed as the new department to be placed. In a layout situation, the existing and new departments are typically rectangular in shape. This is a special case of the paper of Savas et al. (loc. cit.). However the resultant optimal placement may be infeasible due to practical constraints like aisle locations, electrical connections, etc. Hence there is a need for the development of contour lines, i.e. lines of equal objective function value. With these contour lines constructed, one can place the new facility in the best manner. This paper deals with the problem of constructing contour lines in this context. This contribution can also be viewed as the finite-size extension of the contour line result of R. L. Francis [Note on the optimum location of new machines in existing plant layouts, J. Ind. Eng. 14, No. 2, 57–59 (1963)].

MSC:

90B80 Discrete location and assignment
Full Text: DOI

References:

[1] Batta, R.; Ghose, A.; Palekar, U., Locating facilities on the manhattan metric with arbitrarily shaped barriers and convex forbidden regions, Transportation Science, 23, 1, 26-36 (1989) · Zbl 0672.90044
[2] Bindschedler, A. E.; Moore, J. M., Optimum location of new machines in existing plant layouts, Journal of Industrial Engineering, 12, 41-48 (1961)
[3] Dearing, P.; Hamacher, H. W.; Klamroth, K., Dominating sets for rectilinear center location problems with polyhedral barriers, Naval Research Logistics, 49, 7, 647-665 (2002) · Zbl 1037.90044
[4] Dearing, P.; Segars, R., An equivalence result for single facility planar location problems with rectilinear distance and barriers, Annals of Operations Research, 111, 89-110 (2002) · Zbl 1041.90026
[5] Dearing, P. M.; Klamroth, K.; Segars, R., Planar location problems with block distance and barriers, Annals of Operations Research, 136, 117-143 (2005) · Zbl 1114.90056
[6] Drezner, Z.; Klamroth, K.; Schöbel, A.; Wesolowsky, G. O., The weber problem, (Drezner, Z.; Hamacher, H. W., Facility Location: Applications and Theory (2004), Springer-Verlag), 1-36, (Chapter 1) · Zbl 1041.90023
[7] Francis, R. L., Note on the optimum location of new machines in existing plant layouts, Journal of Industrial Engineering, 14, 2, 57-59 (1963)
[8] Francis, R. L.; McGinnis, L. F.; White, J. A., Facility Layout and Location: An Analytical Approach (1992), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[9] Frieß, L.; Klamroth, K.; Sprau, M., A wavefront approach to center location problems with barriers, Annals of Operations Research, 136, 35-48 (2005) · Zbl 1114.90058
[10] Klamroth, K., Single Facility Location Problems with Barriers (2002), Springer-Verlag · Zbl 1027.90055
[11] Larson, R. C.; Sadiq, G., Facility locations with the manhattan metric in the presence of barriers to travel, Operations Research, 31, 4, 652-669 (1983) · Zbl 0521.90045
[12] Nandikonda, P.; Batta, R.; Nagi, R., Locating a 1-center on a manhattan plane with “arbitrarily” shaped barriers, Annals of Operations Research, 123, 157-172 (2003) · Zbl 1036.90047
[13] A. Sarkar, R. Batta, R. Nagi, Placing a finite size facility with a center objective on a rectilinear plane with barriers, European Journal of Operational Research, in press, doi:10.1016/j.ejor.2005.08.029; A. Sarkar, R. Batta, R. Nagi, Placing a finite size facility with a center objective on a rectilinear plane with barriers, European Journal of Operational Research, in press, doi:10.1016/j.ejor.2005.08.029 · Zbl 1127.90046
[14] Savas, S.; Batta, R.; Nagi, R., Finite-size facility placement in the presence of barriers to rectilinear travel, Operations Research, 50, 6, 1018-1031 (2002) · Zbl 1163.90623
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.