The Line Restriction

Abstract

The line restriction is—as the grid restriction—a restriction on the relative position of the sizes. If the size pattern consists of n sizes and we denote the ith size by (x_i, y_i) (i = 1,..., n) then the line restriction orders

$${x_i} > {x_j}\;and\;{y_i} > {y_j}\quad if\;i > j.$$

(15.1)

Taking for instance n equal to 3, a size pattern chosen according to the line restriction has the following form (see Fig. 15.1). The figure shows that the service areas, except S₁, all have a similar shape. As when using the grid restriction this has the effect that the recursion formulae can be derived easily and have a simple form.