| Abstract: | We consider a resource allocation problem, where resources of different capacities must satisfy multiple demands. The demand sizes and the resource capacities are limited to sizes that are power‐of‐two integers (i.e., 1, 2, 4, 8, …). The cost of the resources exhibit economies‐of‐scale savings, i.e., the cost per capacity unit is smaller for resources with larger capacity. The problem is to select the minimum‐cost set of resources that satisfies the demands, while each of the demands must be assigned to a single resource and the number of selected resources does not exceed a specified upper bound. We present algorithms that take advantage of the special structure of the problem and provide optimal solutions in a negligible computing effort. This problem is important for the allocation of blocks of Internet Protocol (IP) addresses, referred to as subnets. In typical IP networks, subnets are allocated at a large number of nodes. An effective allocation attempts to balance the volume of excess addresses that are not used versus fragmentation of addresses at nodes to too many subnets with a discontinuous range of addresses. Due to the efficiency of the algorithms, they can readily be used as valuable modules in IP address management systems. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005. |
