Operations Research
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An Integer Optimization Approach to Large-Scale Air Traffic Flow Management This paper presents a new integer programming (IP) model for large-scale instances of the air traffic flow management (ATFM) problem. The model covers all the phases of each flight—i.e., takeoff, en route cruising, and landing—and solves for an optimal combination of flow management actions, including ground-holding, rerouting, speed control, and airborne holding on a flight-by-flight basis. A distinguishing feature of the model is that it allows for rerouting decisions. This is achieved through the imposition of sets of “local” conditions that make it possible to represent rerouting options in a compact way by only introducing some new constraints. Moreover, three classes of valid inequalities are incorporated into the model to strengthen the polyhedral structure of the underlying relaxation. Computational times are short and reasonable for practical application on problem instances of size comparable to that of the entire U.S. air traffic management system. Thus, the proposed model has the potential of serving as the main engine for the preliminary identification, on a daily basis, of promising air traffic flow management interventions on a national scale in the United States or on a continental scale in Europe.
Operations Research - Tập 59 Số 1 - Trang 211-227 - 2011
A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem In this paper, we analyze a generalization of a classic network-flow model. The generalization involves the replacement of deterministic demand with stochastic demand. While this generalization destroys the original network structure, we show that the matrix underlying the stochastic model is dual network. Thus, the integer program associated with the stochastic model can be solved efficiently using network-flow or linear-programming techniques. We also develop an application of this model to the ground-holding problem in air-traffic management. The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.
Operations Research - Tập 51 Số 1 - Trang 167-171 - 2003
The Price of Fairness In this paper we study resource allocation problems that involve multiple self-interested parties or players and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a “fair” allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We focus on two well-accepted, axiomatically justified notions of fairness, viz., proportional fairness and max-min fairness. For these notions we provide a tight characterization of the price of fairness for a broad family of problems.
Operations Research - Tập 59 Số 1 - Trang 17-31 - 2011
The Air Traffic Flow Management Problem with Enroute Capacities Throughout the United States and Europe, demand for airport use has been increasing rapidly, while airport capacity has been stagnating. Over the last ten years the number of passengers has increased by more than 50 percent and is expected to continue increasing at this rate. Acute congestion in many major airports has been the unfortunate result. For U.S. airlines, the expected yearly cost of the resulting delays is currently estimated at $3 billion. In order to put this number in perspective, the total reported losses of all U.S. airlines amounted to approximately $2 billion in 1991 and $2.5 billion in 1990. Furthermore, every day 700 to 1100 flights are delayed by 15 minutes or more. European airlines are in a similar plight. Optimally controlling the flow of aircraft either by adjusting their release times into the network (ground-holding) or their speed once they are airborne is a cost effective method to reduce the impact of congestion on the air traffic system. This paper makes the following contributions: (a) we build a model that takes into account the capacities of the National Airspace System (NAS) as well as the capacities at the airports, and we show that the resulting formulation is rather strong as some of the proposed inequalities are facet defining for the convex hull of solutions; (b) we address the complexity of the problem; (c) we extend that model to account for several variations of the basic problem, most notably, how to reroute flights and how to handle banks in the hub and spoke system; (d) we show that by relaxing some of our constraints we obtain a previously addressed problem and that the LP relaxation bound of our formulation is at least as strong when compared to all others proposed in the literature for this problem; and (e) we solve large scale, realistic size problems with several thousand flights.
Operations Research - Tập 46 Số 3 - Trang 406-422 - 1998
Modeling of Transport Risk for Hazardous Materials The transport of hazardous materials is an important strategic and tactical decision problem. Risks associated with this activity make transport planning difficult. Although most existing analytical approaches for hazardous materials transport account for risk, there is no agreement among researchers on how to model the associated risks. This paper provides an overview of the prevailing models, and addresses the question “Does it matter how we quantify transport risk?” Our empirical analysis on the U.S. road network suggests that different risk models usually select different “optimal” paths for a hazmat shipment between a given origin-destination pair. Furthermore, the optimal path for one model could perform very poorly under another model. This suggests that researchers and practitioners must pay considerable attention to the modeling of risks in hazardous materials transport.
Operations Research - Tập 46 Số 5 - Trang 625-642 - 1998
Process Location and Product Distribution with Uncertain Yields We present a framework to analyze the process location and product distribution problem with uncertain yields for a large multinational food processing company. This problem consists of selecting the location of processes, the assignment of products, and the distribution of production quantities to markets in order to minimize total expected costs. It differs from the traditional facility location problem due to characteristics that are inherent to process industry sectors. These include significant economies of scale at high volumes, large switchover times, and production yield uncertainty. We model the problem as a nonlinear mixed-integer program. A challenging aspect of this problem is that the objective function is neither convex nor concave. We develop an exact approach to linearize the objective function. We present heuristics to solve the problem and also construct lower bounds based on a reduction of the constraint set to evaluate the quality of the solutions. This framework has been used to make process choice and product allocation decisions at the food processing company, and the estimated annual cost savings are around 10%, or $50 million. In addition, the insights from the model have had a significant strategic and organizational impact at this company. Our framework and conclusions are relevant to other industrial sectors with similar characteristics, such as pharmaceuticals and specialty chemical manufacturers.
Operations Research - Tập 60 Số 5 - Trang 1050-1063 - 2012
A Unifying View of Hybrid Simulation/Analytic Models and Modeling In this paper we give unifying definitions for both hybrid simulation/analytic models and modeling. We present four classes of hybrid simulation/analytic models and give examples of each class, including numerical results for two of the examples Four usages of hybrid simulation/analytic modeling are also presented with examples.
Operations Research - Tập 31 Số 6 - Trang 1030-1052 - 1983
Network Design and Allocation Mechanisms for Carrier Alliances in Liner Shipping Many real-world systems operate in a decentralized manner, where individual operators interact with varying degrees of cooperation and self motive. In this paper, we study transportation networks that operate as an alliance among different carriers. In particular, we study alliance formation among carriers in liner shipping. We address tactical problems such as the design of large-scale networks (that result from integrating the service networks of different carriers in an alliance) and operational problems such as the allocation of limited capacity on a transportation network among the carriers in the alliance. We utilize concepts from mathematical programming and game theory and design a mechanism to guide the carriers in an alliance to pursue an optimal collaborative strategy. The mechanism provides side payments to the carriers, as an added incentive, to motivate them to act in the best interest of the alliance while maximizing their own profits. Our computational results suggest that the mechanism can be used to help carriers form sustainable alliances.
Operations Research - Tập 58 Số 6 - Trang 1726-1742 - 2010
Allocation of Cost Savings in a Three-Level Supply Chain with Demand Information Sharing: A Cooperative-Game Approach We analyze the problem of allocating cost savings from sharing demand information in a three-level supply chain with a manufacturer, a distributor, and a retailer. To find a unique allocation scheme, we use concepts from cooperative game theory. First, we analytically compute the expected cost incurred by the manufacturer and then use simulation to obtain expected costs for the distributor and the retailer. We construct a three-person cooperative game in characteristic-function form and derive necessary conditions for the stability of each of five possible coalitions. To divide the cost savings between two members, or among three supply chain members, we use various allocation schemes. We present numerical analyses to investigate the impacts of the demand autocorrelation coefficient, ρ, and the unit holding and shortage costs on the allocation scheme.
Operations Research - Tập 57 Số 1 - Trang 200-213 - 2009
Car-Following and Steady-State Theory for Noncongested Traffic Car-following and continuum theories have been shown by other investigators to describe a number of aspects of the complex phenomenon of vehicular traffic flow in both quantitative and qualitative terms. It is the purpose of this paper to suggest a variation in these theories in an effort to make them more accurate for traffic densities less than optimum. The theory as modified for noncongested traffic may help to describe quantitatively the sudden change of state occurring in a traffic stream going from a relatively free-flowing condition to a crawling stop-and-go condition and back again.
Operations Research - Tập 9 Số 1 - Trang 66-76 - 1961
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