72 research outputs found

    Advanced Multi-Stage Local Search Applications to Vehicle Routing Problem with Time Windows: A Review

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    ... This paper presents a survey of the latest research motivated by this recognition. The presentation is focused on multi-stage applications of advanced local search techniques on the VRPTW. Multi-stage algorithms optimize the number of vehicles and travel time independently in order to ensure that the search is directed towards the achievement of the primary objective. Basic features of these algorithms, as well as hybridization strategies are described. For most algorithms, experimental results on Solomon's benchmark test problems are provided and analyze

    Efficient Solution Procedures for Multistage Stochastic Formulations of Two Problem Classes

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    We consider two classes of stochastic programming models which are motivated by two applications related to the field of aviation. The first problem we consider is the network capacity planning problem, which arises in capacity planning of systems with network structures, such as transportation terminals, roadways and telecommunication networks. We study this problem in the context of airport terminal capacity planning. In this problem, the objective is to determine the optimal design and expansion capacities for different areas of the terminal in the presence of uncertainty in future demand levels and expansion costs, such that overall passenger delay is minimized. We model this problem as a nonlinear multistage stochastic integer program with a multicommodity network flow structure. The formulation requires the use of time functions for maximum delays in passageways and processing stations, for which we derive approximations that account for the transient behavior of flow. The deterministic equivalent of the developed model is solved via a branch and bound procedure, in which a bounding heuristic is used at the nodes of the branch and bound tree to obtain integer solutions. In the second study, we consider the project portfolio optimization problem. This problem falls in the class of stochastic programs in which times of uncertainty realizations are dependent on the decisions made. The project portfolio optimization problem deals with the selection of research and development (R&D) projects and determination of optimal resource allocations for the current planning period such that the expected total discounted return or a function of this expectation for all projects over an infinite time horizon is maximized, given the uncertainties and resource limitations over a planning horizon. Accounting for endogeneity in some parameters, we propose efficient modeling and solution approaches for the resulting multistage stochastic integer programming model. We first develop a formulation that is amenable to scenario decomposition, and is applicable to the general class of stochastic problems with endogenous uncertainty. We then demonstrate the use of the sample average approximation method in solving large scale problems of this class, where the sample problems are solved through Lagrangian relaxation and lower bounding heuristics.Ph.D

    Optimal Metering Point Configurations for Optimized Profile Descent Based Arrival Operations at Airports

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    Optimized profile descent (OPD) is an arrival procedure for the Next Generation Air Transportation System, which has been demonstrated to effectively decrease noise, emissions, and fuel costs. Implementation of OPD operations requires effective metering policies because of the increased role of uncertainty in aircraft trajectories during descent. While optimal sequencing and spacing of OPD flights have been studied in the literature, any potential savings resulting from possible changes in metering point configurations have not been addressed. In this paper, we develop models to further increase the value of OPD operations over conventional arrival procedures by optimizing metering point configurations, which include identification of the optimal number and locations of metering points to use during OPD. We derive an algorithmic framework based on implementations of a stochastic dynamic programming model and a nonlinear stochastic integer program to identify best metering point configurations where resulting computational difficulties are addressed through convex approximation and Lagrangian decomposition procedures. We also describe numerical results based on actual traffic information at major U.S. airports, which indicate that the total potential savings in the top 10 major airports could be up to $22 million a year if the proposed policies are implemented. The online appendix is available at https://doi.org/10.1287/trsc.2017.0788 . </jats:p

    Climate change and optimal energy technology R&D policy

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    Public policy response to global climate change presents a classic problem of decision making under uncertainty. Theoretical work has shown that explicitly accounting for uncertainty and learning in climate change can have a large impact on optimal policy, especially technology policy. However, theory also shows that the specific impacts of uncertainty are ambiguous. In this paper, we provide a framework that combines economics and decision analysis to implement probabilistic data on energy technology research and development (R&D) policy in response to global climate change. We find that, given a budget constraint, the composition of the optimal R&D portfolio is highly diversified and robust to risk in climate damages. The overall optimal investment into technical change, however, does depend (in a non-monotonic way) on the risk in climate damages. Finally, we show that in order to properly value R&D, abatement must be included as a recourse decision.R&D portfolio Energy technology Climate change Stochastic programming Public policy
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