Network freight flow consolidation organizes the commodity flow with special attention to the minimization of the flow costs but the efficiency of transport resources is not addressed. In contrast, vehicle routing targets primarily the maximization of the efficiency of transport resources but the commodity-related preferences are treated as inferior requirements. This article is about the probl...

In classical linear network flow (LNF) problems, a network consists of multiple source and sink nodes, where each node is a sink node or a source node, but not both. Usually, there is only one kind of commodity flow and the goal is to find flow schedules and routes such that all sink nodes’ flow demands are satisfied and the total flow transmission cost is minimized. We develop a capacity expan...

Maximization of flow through the network has remained core issue in the field of optimization. In this paper a new advanced network problem is introduced, i.e., a multi-commodity network with a separator. This network consists of several sub-networks linked through a commodity separator. The objective is to maximize the flow of the commodity of interest from the commodity mixture at the output ...

the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...

This paper considers a multi-port and multi-period container planning problem of shipping companies that use both standard and foldable containers. A company must decide which number of empty containers of each type to purchase and reposition at each port within a defined period to minimize the total purchasing, repositioning, and storage costs. Wedevelop amodel to optimally allocate both folda...

In the k-splittable flow problem, each commodity can only use at most k paths and the key point is to find the suitable transmitting paths for each commodity. To guarantee the efficiency of the network, minimizing congestion is important, but it is not enough, the cost consumed by the network is also needed to minimize. Most researches restrict to congestion or cost, but not the both. In this p...

We consider the following 2-commodity, integer network synthesis problem: Given two n×n, non-negative, symmetric, integer-valued matrices R = (rij) and S = (sij) of minimum flow requirements of 2 different commodities, construct an undirected network G = [N,E, c] on node set N = {1, 2, . . . , n} with integer edge capacities {c(e) : e ∈ E}, such that: (i) for any two pairs (i, j) and (k, l), i ...

In this paper we describe a new algorithm for buffered global routing according to a prescribed buffer site map. Specifically, we describe a provably good multi-commodity flow based algorithm that finds a global routing minimizing buffer and wire congestion subject to given constraints on routing area (wirelength and number of buffers) and sink delays. Our algorithm allows computing the tradeof...

Hop constraint is associated with modern communication network flows. We consider the problem of designing an optimal undirected network with integer-valued edge-capacities that meets a given set of single-commodity, hop-constrained network flow value requirements. We present a strongly polynomial, combinatorial algorithm for the problem with value of hop-parameter equal to three when values of...