Varignon Frame
The Varignon frame, named after Pierre Varignon, is a mechanical device which can be used to determine an optimal location of a warehouse for the destribution of goods to a set of shops. Optimal means that the sum of the ''weighted distances'' of the shops to the warehouse should be minimal. The frame consists of a board with n holes corresponding to the n shops at the locations \mathbf x_1, ...\mathbf x_n, n strings are tied together in a knot at one end, the loose ends are passed, one each, through the holes and are attached to weights below the board (see diagram). If the influence of friction and other odds of the real world are neglected, the knot will take a position of equilibrium \mathbf v. It can be shown (see below), that point \mathbf v is the optimal location which minimizes the weighted sum of distances :(1): \ D(\mathbf x)=\sum_^n m_i\, \mathbf x_i-\mathbf x\, . The optimization problem is called Weber problem. Mechanical Problem - Optimization Problem If the holes ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]