We consider the assignment of gates to arriving and departing flights at a large hub airport. It is considered to be a highly complex problem even in planning stage when all flight arrivals and departures are assumed to be known precisely in advance. There are various considerations that are involved while assigning gates to incoming and outgoing flights (such a flight pair for the same aircraft is called a turn) at an airport. Different gates have restrictions, such as adjacency, last-in-first-out gates and towing requirements, which are known from the structure and layout of the airport. When optimizing the gate assignment costs, we consider different, and often, conflicting objectives such as maximization of gate rest time between two turns, minimization of the cost of towing an aircraft with a long layover, minimization of overall costs that includes penalization for not assigning preferred gates to certain turns, among others.One of the major contributions of this paper is to mathematically model all these features that are observed in the real-life. Further we also attempt to study the problem in both planning and operations mode, which has rarely been accomplished in the literature. For planning, we sequentially introduce different objectives to our gate assignment problem -such as maximization of connection revenues, minimization of zone usage at airport and maximization of schedule reliability -and include them to the model along with the relevant constraints. For operations, the main consideration is recovery of schedule by minimizing schedule variations and maintaining feasibility in the event of major disruptions. Additionally the operations models must have very, very short run times, in the order of a few seconds.These models are then applied to a real airline at one of its most congested hubs. Implementation is done using OPL and computational results for actual data sets are reported. For the planning mode, analyst perception of weights for the different objectives in the multiobjective model is used wherever actual dollar value of the objective coefficient is not available. The results are also reported for large, reasonable changes in objective function coefficients. For the operations mode, flight delays are simulated and the performance of the model studied. The final results indicate that it is possible to solve even large instances of real-life problems to optimality within short run times with conventional continuous time assignment model.
Even though rail transportation is one of the most fuel efficient forms of surface transportation, the cost of fuel constitutes one of the major categories of very high operating costs for railroad companies. In the United States, unlike in Europe, fueling cost is, by far, the highest single operating cost. For larger companies with several thousands of miles of rail network, the fuel bills often run into several billions of dollars annually. The railroad fueling problem considered in this paper has three distinct cost components. Fueling stations charge a location-dependent price for the fuel in addition to a fixed contracting fee over the entire planning horizon. In addition, the railroad company must also bear incidental and notional costs for each fueling stop. This paper proposes a mixed-integer linear program model that determines the optimal strategy for contracting and fuel purchase schedule decisions that minimize overall costs under certain reasonable assumptions. The model is tested on large, real-life problem situations. The mathematical model is further refined by introduction of several feasible mixed-integer program (MIP) cuts. The paper compares the efficiency of different MIP cuts to reduce the run time. Although the scale of the problem was expected to diminish the model performance, run time and memory requirements were observed to be fairly reasonable. It, thus, establishes that exact workable methods should be considered for actual implementation of this problem at railroad companies, in addition to heuristic approaches. This paper has given us a reasonable satisfaction that we have successfully demonstrated the capability to solve a dynamic version of the locomotive refueling problem where the capacity of the fueling yards vary across days during the planning horizon.
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