mends the use of travel time values for congested periods that are 2.5 times the value of time estimates during uncongested periods (7). Kawamura investigated differences in value of time among operators and trucking industry segments; findings from Kawamura’s research show that freight carriers have a value of time that is several times higher than that of passenger vehicles and that there is ...

When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in speed at which LP can be solved, as it linear constraints and variables. The conventional approach to improve solve time relaxation Mixed Integer Programming (MIP) model that encodes such instance aggregate all have same origin or destination. However, bound result...

Most existing facility location models assume that the cost is either a fixed setup or made up of and problem-specific concave submodular term. This structural property plays critical role in developing fast branch-and-price, Lagrangian relaxation, constant ratio approximation, conic integer programming reformulation approaches for these NP-hard problems. Many practical considerations complicat...

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine the number of facilities to be loa...

In classical network flow theory, flow being sent from a source to a destination may be split into a large number of chunks traveling on different paths through the network. This effect is undesired or even forbidden in many applications. Kleinberg introduced the unsplittable flow problem where all flow traveling from a source to a destination must be sent on only one path. This is a generaliza...

We consider the maximization version of the edge disjoint path problem (EDP). In undirected graphs and directed acyclic graphs, we obtain anO( √ n) upper bound on the approximation ratio where n is the number of nodes in the graph. We show this by establishing the upper bound on the integrality gap of the natural multicommodity flow based relaxation. Our upper bound matches to within a constant...

We present a column-generation model and branch-and-price-and-cut algorithm for origin-destination integer multicommodity flow problems. The origin-destination integer multicommodity flow problem is a constrained version of the linear multicommodity flow problem in which flow of a commodity (defined in this case by an origin-destination pair) may use only one path from origin to destination. Br...

closed-loop supply chain network design is a critical issue due to its impact on both economic and environmental performances of the supply chain. in this paper, we address the problem of designing a multi-echelon, multi-product and capacitated closed-loop supply chain network. first, a mixed-integer linear programming formulation is developed to maximize the total profit. the main contribution...