USING MATHEMATICAL-PROGRAMMING HEURISTICS IN A MULTICRITERIA NETWORK FLOW CONTEXT

In this paper, we propose a local search procedure to test the robustn ess of a specific 'satisfying point' neighbourhood. It consists of the following steps: (1) build an indifference area around the satisfying point in the criteria space by using thresholds (this takes into acco unt the possible uncertainty, vagueness and/or inaccuracy of data); (2 ) find some points in the satisfying point neighbourhood and the corre sponding solutions in the decision variables space; (3) test the quali ty of these solutions from the point of view of user preference. The i ndifference area is defined by adding constraints to the network model . This approach, which allows us to verify the adequacy of the model, has been applied to a set of multicriteria network flow problems. A he uristic method, based on Lagrangian duality and subgradient techniques , exploits the combinatorial structure of network flow problems in ord er to find certain feasible points.