The paper addresses a multi-item, multi-plant lot-sizing problem with transfer costs and capacity constraints. The problem is reformulated according to a multi-commodity flow formalism, and decomposed, through Lagrangean relaxation, into a master facility location problem and a slave minimal cost multi-commodity flow problem. The decomposition framework gives rise in a natural way to the design...

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to tackle a variety of computing tasks, among them computation shortest paths and design efficient networks. For path problem, mathematical model for evolution is available it been shown in computer experiments through analysis that dynamics solves problem. this paper, we generalize network We formulate as...

The competitive market and declined economy have increased the relevant importance of making supply chain network efficient. This has created many motivations to reduce the cost of services, and simultaneously, to increase the quality of them. The network as a tri-echelon one consists of Suppliers, Warehouses or Distribution Centers (DCs), and Retailer nodes. To bring the problem closer to real...

There are many problems related to the design of networks and accommodate demands from different users subject to some constraints on users’ quality of service (QoS) and fairness through the network. The problem of resource allocation and message routing plays a determinant role in the optimization of networks performance. Our work emphasizes the message routing problem in data networks, but it...

The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-desigu problem: given a set of multi-commodity flow demands, find a network subject to certain constraints such that the commodities can be maximally routed. This paper focuses on th...

In this paper we define the multi-commodity connected facility location (MCFL) problem, a natural generalization of the well-known multi-commodity rent-or-buy (MROB) and connected facility location (CFL) network design problems. Like in MROB, we wish to send one unit of flow from a set of sources to a set of sinks. This flow is supported by renting or buying edges. For each bought edge e, we pa...

This paper studies a resource allocation problem in a graph, concerning the joint optimization of capacity allocation decisions and object placement decisions, given a single capacity constraint. This problem has applications in internet content distribution and other domains. The solution to the problem comes through a multi-commodity generalization of the single commodity k-median problem. A ...