TY - JOUR
T1 - Commentary on facility location in the presence of congested regions with the rectilinear distance metric
AU - Sarkar, Avijit
AU - Batta, Rajan
AU - Nagi, Rakesh
N1 - Funding Information:
This work was supported by the National Science Foundation, via Grant DMI -9800429. This support is gratefully acknowledged. The authors also wish to acknowledge the help of the Editor-in-chief, whose comments significantly improved the paper's exposition.
PY - 2004/12
Y1 - 2004/12
N2 - This paper is a commentary on the work of Butt and Cavalier (Socio-Econ. Plann. Sci. 31(2) (1997) 103), a paper that was published in an earlier issue of this journal. With the aid of an example problem, we demonstrate that the set of gridlines proposed by them to find the rectilinear least cost path between two points in the presence of convex polygonal congested regions is inadequate. We proceed to prove its adequacy for the case of rectangular congested regions in which the edges of the rectangles are parallel to the travel directions. In wake of the difficulties of the general problem, we consider a specific example of a convex quadrilateral congestion region and a pair of external origin and destination points. Finally, we revisit the example shown in Butt and Cavalier's paper and present a mixed integer linear programming formulation that determines the optimal locations of the entry and exit points for this example.
AB - This paper is a commentary on the work of Butt and Cavalier (Socio-Econ. Plann. Sci. 31(2) (1997) 103), a paper that was published in an earlier issue of this journal. With the aid of an example problem, we demonstrate that the set of gridlines proposed by them to find the rectilinear least cost path between two points in the presence of convex polygonal congested regions is inadequate. We proceed to prove its adequacy for the case of rectangular congested regions in which the edges of the rectangles are parallel to the travel directions. In wake of the difficulties of the general problem, we consider a specific example of a convex quadrilateral congestion region and a pair of external origin and destination points. Finally, we revisit the example shown in Butt and Cavalier's paper and present a mixed integer linear programming formulation that determines the optimal locations of the entry and exit points for this example.
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U2 - 10.1016/S0038-0121(03)00025-9
DO - 10.1016/S0038-0121(03)00025-9
M3 - Comment/debate
AN - SCOPUS:3543132540
SN - 0038-0121
VL - 38
SP - 291
EP - 306
JO - Socio-Economic Planning Sciences
JF - Socio-Economic Planning Sciences
IS - 4
ER -