The Euclidean distance Capacitated LocationAllocation Problem in the Presence of k Connections

In the wide range of facility location theory, the capacitated facility location-allocation problems are recently paid attention by many researchers who are working in the field ofoperations research. This paper considers a capacitated locationallocation problem in the presence of k connections on thehorizontal line barrier. The main aim of this paper is to locate a set of new facilities in the plane among a set of existing facilities and to allocate an optimal number of existing facilities to each new facility in order to satisfy their demands such that the summation of the weighted Euclidean barrier distances from newfacilities to existing facilities is minimized. The proposed problem is designed as a mixed-integer nonlinear programming model. Inaddition a lower bound problem based on the forbidden region is also presented. To show the efficiency of the model, a numerical example is provided and the results are graphically compared two cases of with and without passages on the line barrier. It is worth noting that the global optimal solution is obtained

Keywords:

Location-aUocation problem , connection , mixed integer nonlinear programming