Developing a transfer point location problem considering normal demands distribution

In the scope of center location problem, transfer point location problems (TPLP) are the ones which have been studied more recently to make models more applicable in real world. The contribution of this work is to develop a model in which demand points are weighted and have a normal distribution. As an assumption, there is no transformation directly from a demand point to the service facility location. This means that the transfer point is always engaged. The contribution of work is summarized in two models. In the first model, all the points are considered in an area while in the second one the points are considered in several areas. The problem is to find out the best location for the transfer point so that the maximum expected weighted distance to all demand points through the transfer point is minimized. A mathematical solution is employed when demand points follow normal distribution, with some points of demands being in regions. Then, this model was solved by replacing real number in a real condition. We used Maple software to solve this objective function as well as MATLAB software to solve this model numerically.