Multi-commodity Problem Research Articles

Parallel Implementations Of A Branch-And-Bound Algorithm For Multicommodity Location With Balancing Requirements

AbstractWe present two parallel branch-and-bound algorithms for the multicommodity location problem with balancing requirements. The first algorithm implements a master-slave approach in order to perform a parallel exploration of the search tree. The second algorithm decomposes the problem in order to compute the lower bounds in parallel. We realized implementations of these algorithms on a PC-based network of Transputers. Experimental results are reported and analyzed.

The Solution of Multiperiod Network Models with Bundle Constraints by Aggregation

We present a new network aggregation/disaggregation approach for solving a multiperiod, network model with bundle (Generalized Upper Bounding) side constraints. The model describes production planning and distribution problems. Instead of solving the original multicommodity problem, we transform it so that a pair of single-commodity network flow problems can be solved. The original network is aggregated and the resulting problem is solved. Its solution determines a disaggregated problem that yields a feasible, near optimal solution to the original problem. We describe the determination of theoretical a priori and a posteriori bounds. We also introduce a very tight “computational” error bound. The implementation of the algorithm was tested against MPSX/370, and the specialized code for solving networks with side constraints NETSIDE. The proposed solution method was found to be much more efficient with negligible error.

A Parallel Projection for the Multicommodity Network Model

We present an application of parallel computing techniques to the solution of a quadratic programme that arises in the resource-directive decomposition method for multicommodity problems. A sequential algorithm for the quadratic programme is discussed, and its extension to a parallel implementation is given. Computational testing of the sequential and parallel algorithms was done on the Sequent Symmetry S81 parallel computer located in the Parallel Processing Laboratory at Southern Methodist University. On several large test problems the parallel version achieved a speed-up of 10 with 12 processors.

A Parallel Projection for the Multicommodity Network Model

We present an application of parallel computing techniques to the solution of a quadratic programme that arises in the resource-directive decomposition method for multicommodity problems. A sequential algorithm for the quadratic programme is discussed, and its extension to a parallel implementation is given. Computational testing of the sequential and parallel algorithms was done on the Sequent Symmetry S81 parallel computer located in the Parallel Processing Laboratory at Southern Methodist University. On several large test problems the parallel version achieved a speed-up of 10 with 12 processors.

A special spatial equilibrium problem

In this paper, we study a special single-commodity spatial equilibrium problem. We show how the problem is related to a shortest-path problem and develop a simple algorithm for its solution. We also discuss an extension of the single-commodity problem to a multicommodity problem.

Probabilistic Demands and Costs in Facility Location Problems

When deterministic assumptions in ‘classical’ location problems are relaxed some new theoretical and algorithmic problems arise. In this paper, the definition of medians is generalized to the cases: (1) when generated demands and travel costs are random, and (2) when the demand induced at the facilities is random because of competition. Under a particular set of assumptions, the well-known theorems on ‘optimality of node locations' hold for the underlying ‘probabilistic networks’. For case (1) the model is shown to be a generalization of the probabilistic and deterministic median location problems on networks. The relationship of the model to a multicommodity location problem is also pointed out. Additionally, within the framework of the problem formulation, certain parallels with multiobjective location problems are drawn. For case (2), the competitive median location problem is formulated, and some results presented. For the special structure of probabilistic tree networks some interesting localization properties for the 1-median and 2-median are discussed.

A Note on Warszawski's Multi-Commodity Location Problem

This note shows two easily incorporated improvements in computing the lower bounds for Warszawski's branch and bound algorithm for the multi-commodity location problem. The lower bounds become relatively stronger, thereby making the branch and bound algorithm more efficient.

A generalized upper bounding algorithm for multicommodity network flow problems

AbstractAn algorithm for solving min‐cost or max‐flow multicommodity flow problems is described. It is a specialization of the simplex method, which takes advantage of the special structure of the multicommodity problem. The only nongraph or nonadditive operations in a cycle involve the inverse of a working basis, whose dimension is the number of currently saturated arcs. Efficient relations for updating this inverse are derived.