The Weber problem in congested regions with entry and exit points

Farham, Mohammad Saleh
Süral, Haldun
İyigün, Cem
The Weber problem is about finding a facility location on a plane such that the total weighted distance to a set of given demand points is minimized. The facility location and access routes to the facility can be restricted if the Weber problem contains congested regions, some arbitrary shaped polygonal areas on the plane, where location of a facility is forbidden and traveling is allowed at an additional fixed cost. Traveling through congested regions may also be limited to certain entry and exit points (or gates). It is shown that the restricted Weber problem is non-convex and nonlinear under Euclidean distance metric which justifies using heuristic approaches. We develop an evolutionary algorithm modified with variable neighborhood search to solve the problem. The algorithm is applied on test instances derived from the literature and the computational results are presented.


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Single Source Capacitated Multi Facility Location Problem (SSCMFLP) is a continuous location-allocation problem such that determining the locations of p facilities in the plane and allocations of n demand points to only one facility by considering the capacity restriction of each facility so as to minimize total transportation cost to satisfy n demand points from p facilities. In addition to Mixed Integer Non-Linear Programming formulation of the problem in the literature, we give a new formulation for the ...
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A planar single facility location problem, also known as the Fermat–Weber problem, is to find a facility location such that the total weighted distance to a set of given demand points is minimized. A variation to this problem is obtained if there is a restriction coming from congested regions. In this study, congested regions are considered as arbitrary shaped polygonal areas on the plane where location of a facility is forbidden and traveling is charged with an additional fixed cost. The traveling fixed cost ...
Citation Formats
M. S. Farham, H. Süral, and C. İyigün, “The Weber problem in congested regions with entry and exit points,” COMPUTERS & OPERATIONS RESEARCH, pp. 177–183, 2015, Accessed: 00, 2020. [Online]. Available: