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This paper studies a two-dimensional two-stage guillotine cutting stock problem which includes determination of how the items should be cut from stock panels in an optimal way, by developing and applying different solution approaches. An integer programming model with new features is proposed. A random key based genetic algorithm is utilized to obtain feasible solutions, and by applying a local search within the algorithm, a hybrid structure is acquired. Besides, a novel two-stage math-heuristic solution method is proposed. In the first stage of this method, a relaxation of the problem is solved; in the second, this solution is improved. The time to obtain the results of the developed two-stage math-heuristic solution approach is significantly lower than the other methods given in the article. Optimal solution values were obtained in 26 of 30 test problems taken from the literature with the proposed mathematical model, in 14 with mathematical programming based heuristic method, and in 16 with a random key based genetic algorithm. [ABSTRACT FROM AUTHOR]

The aim of this study is to provide a balanced distribution of air traffic controller workload (ATCW) across airspace sectors taking into account the complexity of airspace sectors and the factors affecting ATCW, both objective and perceived. Almost all the studies focusing on the airspace sectorisation problem use heuristic or metaheuristic algorithms in dynamic simulation environments instead of a mathematical modelling approach. The paper proposes a multi-objective mixed integer mathematical model for airspace sectorisation. The model is applied to the upper, en-route level of Turkish airspace. Geographical information systems (GIS) are used to advantage for airspace analysis. The multi-objective model developed in this paper is scalarised by using the conic scalarisation method. For solving the scalarised problem, the CPLEX and DICOPT solvers of GAMS software are implemented. Finally, the optimal sector boundaries of Turkish airspace are defined. [ABSTRACT FROM AUTHOR]