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Air traffic flow management in Europe has to deal as much with capacity constraints in en route airspace as with the more usual capacity constraints at airports. The en route [...]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2004.09.012 Byline: Guglielmo Lulli (a), Suvrajeet Sen (b) Keywords: Heuristic algorithm; Successive approximation; Stochastic integer programming Abstract: In this paper, we propose a successive approximation heuristic which solves large stochastic mixed-integer programming problem with complete fixed recourse. We refer to this method as the Scenario Updating Method, since it solves the problem by considering only a subset of scenarios which is updated at each iteration. Only those scenarios which imply a significant change in the objective function are added. The algorithm is terminated when no such scenarios are available to enter in the current scenario subtree. Several rules to select scenarios are discussed. Bounds on heuristic solutions are computed by relaxing some of the non-anticipativity constraints. The proposed procedure is tested on a multistage stochastic batch-sizing problem. Author Affiliation: (a) Dipartimento di Matematica Pura ed Applicata, Universita di Padova, 35123 Padova, Italy (b) Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721 USA

Solution for stochastic mixed-integer programming problem is derived using heuristic algorithm.

In this paper, we present a branch-and-price method to solve special structured multistage stochastic integer programming problems. We validate our method on two different versions of a multistage stochastic batchsizing problem (SBSP). One version adopts a recourse formulation, and the other is based on probabilistic constraints. Our algorithmic approach is applicable to both formulations. Our computational results suggest that both classes of problems can be solved using relatively few nodes of a branch-and-price tree. The success of our approach calls for extensions in methodology as well as applications. Key words: stochastic programming; integer programming; batch sizing; branch-and-price algorithm, 1. Introduction Integer requirements on decision variables are indispensable in many operational and planning models. For instance, resource acquisition decisions that represent factors such as fixed charges, changeover costs, and [...]

The research develops a two-level hierarchical architecture for air traffic management problems with related mathematical models. The research further includes a computational analysis that results in both exact and heuristic solutions.