Abstract: In an interval graph G = (V,E) the distance between two vertices u, v is de£ned as the smallest number of edges in a path joining u and v. The eccentricity of a vertex v is the maximum among distances from all other vertices of V . The diameter (δ) and radius (ρ) of the graph G is respectively the maximum and minimum among all the eccentricities of G. The center of the graph G is the set C(G) of vertices with eccentricity ρ. In this context our aim is to establish the relation ρ = δ 2 for an interval graph and to determine the center of it.
Abstract: A manufacturing inventory model with shortages with
carrying cost, shortage cost, setup cost and demand quantity as
imprecise numbers, instead of real numbers, namely interval number
is considered here. First, a brief survey of the existing works on
comparing and ranking any two interval numbers on the real line
is presented. A common algorithm for the optimum production
quantity (Economic lot-size) per cycle of a single product (so as
to minimize the total average cost) is developed which works well
on interval number optimization under consideration. Finally, the
designed algorithm is illustrated with numerical example.