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Personne# Prem Kumar

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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.

2015We consider the assignment of gates to arriving and departing flights at a large hub airport. This problem is highly complex 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. Some of the cost components in the objective function of the basic assignment model include notional penalty for not being able to assign a gate to an aircraft, penalty for the cost of towing an aircraft with a long layover, and penalty for not assigning preferred gates to certain turns. One of the major contributions of this paper is to provide mathematical model for all these complex constraints that are observed at a real airport. Further, we study the problem in both planning and operations modes simultaneously, and such an attempt is, perhaps, unique and unprecedented. For planning mode, we sequentially introduce new additional objectives to our gate assignment problem that have not been studied in the literature so far(i) maximization of passenger connection revenues, (ii) minimization of zone usage costs, and (iii) maximization of gate plan robustnessand include them to the model along with the relevant constraints. For operations mode, the main objectives studied in this paper are recovery of schedule by minimizing schedule variations and maintaining feasibility by minimal retiming in the event of major disruptions. Additionally, the operations mode models must have very, very short run times of the order of a few seconds. These models are then applied to a functional airline at one of its most congested hubs. Implementation is carried out using Optimization Programming Language, and computational results for actual data sets are reported. For the planning mode, analyst perception of weights for the different objectives in the multi-objective 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 is studied. The final results indicate that it is possible to apply this model to even large real-life problems instances to optimality within short run times with clever formulation of conventional continuous time assignment model. Copyright (c) 2013 John Wiley & Sons, Ltd.

Michel Bierlaire, Prem Kumar, Francesco Piu

The Locomotive Assignment Problem (LAP) is a class of planning and scheduling problems solved by assigning a fleet of locomotives to a network of trains. In the planning versions of the LAP, the type of consist (a group of linked locomotives) assigned to each train in a given schedule is determined. We introduce an optimization model (called consists selection) that precedes the planning LAP solution and determines the set of consist types. This selection leads to solutions that are characterized by potential savings in terms of overall fueling cost and are easier to handle in the routing phase. © 2015 Elsevier Ltd.