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A hub-and-spoke railway system is an efficient way of handling freight transport by land. A modern rail–rail train yard consists of huge gantry cranes that move the containers between the trains. In this context, we consider a rail–rail transshipment yard scheduling problem (TYSP) where the containers arrive to the hub and need to be placed on a train that will deliver them to their destination. In the literature, the problem is decomposed hierarchically into five subproblems, which are solved separately. First, the trains have to be grouped into bundles in which they visit the yard. Next, the trains have to be assigned to tracks within these bundles, namely parking positions. Then the final positions for the containers on trains have to be determined. Next, the container moves that need to be performed are assigned to the cranes. Finally, these moves have to be sequenced for each crane for processing. In this paper, an integrated MILP model is proposed, which aims to solve the TYSP as a single optimization problem. The proposed formulation also enables us to define more robust and complex objective functions that include key characteristics from each of the above-mentioned subproblems. The strength of our proposed formulation is demonstrated via computational experiments using the data from the literature. Indeed, the results show that the TYSP can be solved without the use of decomposition techniques and more insight can be obtained from the same input data used to solve particular single decomposed subproblems.
We consider the problem of assigning flights to airport gates. We examine the general case in which an aircraft serving a flight may be assigned to different gates for arrival, parking, and departure processing. The objectives can be divided into deterministic and stochastic goals. The former include maximization of the total assignment preference score, a minimal number of unassigned flights during overload periods, and minimization of the number of tows. A special focus lies on the stochastic objectives, which aim at minimizing the expected number of any kind of constraint violations, i.e. not respecting gate closures, violation of shadow restrictions (a situation in which gate assignments may cause blocking of neighboring gates) or of tow time restrictions and classical gate conflicts in which two aircraft are assigned to the same gate and are at the airport at the same time. We show that the minimization of expected gate conflicts can be modeled in a graph theoretical approach using the clique partitioning problem (CPP). We furthermore show that the classical (deterministic) flight gate assignment problem, which can also be modeled using a CPP, can be integrated such that a simple though powerful model emerges, which no longer needs including a dummy gate, which is often used in practical gate assignment models. As constraint violations cannot fully be prevented, recovery strategies become necessary. We present a procedure for recovery planning that has proved its practical relevance at numerous airports. Finally, in an extensive numerical study we test our results on practical data, which contain a statistical analysis of flight arrival and departure times. The tests include a detailed comparison of current robustness measures and state-of-the-art approaches found in literature.