a b s t r a c tIn this paper, we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem. The capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities, which depend on flow volumes on the arcs. By combining a column and row generation technique and a strong formulation including forcing constraints, this heuristic derives high quality results, and computational effort can be reduced considerably. The capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem.

A heuristic for solving manufacturing process and equipment selection problems M. CHEN ² In a dynamic manufacturing environment, machines and machining process selection based on current part mix may need to be revised if part mix has changed or new machine tools have become available and economical. However, the costs of acquiring new machines and revising manufacturing process may exceed the bene® ts derived from such expansion or revision. The problem of selecting the best machining process and equipment in a dynamic manufacturing environment is studied in this paper. An integer programming model and a heuristic algorithm were developed to solve the problem of multiple time periods. Lagrangian relaxation was used to generate lower bounds of the integer programming model for testing the optimality of the heuristic solution. Numerical examples are presented to illustrate the model and the solution technique.