This paper considers a facility moving along a route of straight line to serve several facilities in xy plane. A route is obtained which minimizes the objective function expressed in terms of average rectilinear distance between the service facility and facilities to he served. The forms of the objective functions can be classified into several cases according to the initial and end points of the routes. In some cases, as in the problem of optimal location of new facility, the cordinates of the optimal routes are median of the cordinates of facilities to be served. In others, the optimal routes are obtained after examining the values of objective functions on the boundaries of slopes and intercepts. An overall optimal route is obtained by comparing these routes. The entire procedure has been programmed in BASIC language, and several case examples are given.