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Approximations of time-dependent unreliable flow lines with finite buffers

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2016年第3期83卷 295-323页

作者： Goettlich, S. Kuehn, S. Schwarz, J. A. Stolletz, R. Univ Mannheim Sch Business Informat & Math D-68131 Mannheim Germany Univ Mannheim Sch Business D-68131 Mannheim Germany

Flow lines process discrete workpieces on consecutive machines, which are coupled by buffers. Their operating environment is often stochastic and time-dependent. For the flow line under consideration, the stochasticity is generated by random breakdowns and successive stochastic repair times, whereas the processing times are deterministic. However, the release rate of workpieces to the line is time-dependent, due to changes in demand. The buffers between the machines may be finite or infinite. We introduce two new sampling approaches for the performance evaluation of such flow lines: one method utilizes an approximation based on a mixed-integer program in discrete time with discrete material, while the other approximation is based on partial and ordinary differential equations in continuous time and with a continuous flow of material. In addition, we sketch a proof that these two approximations are equivalent under some linearity assumptions. A computational study demonstrates the accuracy of both approximations relative to a discrete-event simulation in continuous time. Furthermore, we reveal some effects occurring in unreliable flow lines with time-dependent processing rates.

关键词： Unreliable flow line Sampling mixed-integer program Conservation laws Piecewise deterministic process

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Facility location design under continuous traffic equilibrium

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2015年第Part1期81卷 18-33页

作者： Ouyang, Yanfeng Wang, Zhaodong Yang, Hai Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA Hong Kong Univ Sci & Technol Dept Civil & Environm Engn Kowloon Hong Kong Peoples R China

This paper presents two modeling approaches for median-type facility location design under elastic customer demand and traffic equilibrium in a continuous space. The first approach, following the continuum approximation scheme, builds upon the special case of an infinite homogeneous plane where traffic equilibrium can be described by an ordinary differential equation. The solution to this homogeneous case, sometimes in a closed form, is then used to develop approximate solutions to more general cases (e.g., those in a heterogeneous space). This model provides a computationally efficient way to obtain managerial insights and near-optimal solutions, especially for large problem instances. We also develop a more traditional discrete location model in the form of a mixed-integer program, which builds directly upon a nonlinear partial differential equation description of customer traffic equilibrium. We develop a Lagrangian relaxation based solution approach with an embedded finite-element method subroutine, to separate and solve the location decisions as well as the traffic equilibrium. Numerical experiments are conducted to illustrate applicability of the proposed models and to compare performance of the two complementing modeling approaches. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Facility location Traffic equilibrium Continuum approximation mixed-integer program Lagrangian relaxation Finite element method

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Planning reliable service facility location against disruption risks and last-mile congestion in a continuous space

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2022年 165卷 123-140页

作者： Wang, Zhaodong Xie, Siyang Ouyang, Yanfeng Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA Meta Inc Menlo Pk CA 94025 USA Cruise LLC 333 Brannan St San Francisco CA 94107 USA

This paper proposes a methodological framework that incorporates probabilistic facility dis-ruption risks, last-mile customers travel path choices, and the induced traffic congestion near the facilities into the consideration of service facility location planning. The customers can be pedestrians, drones, or any autonomous vehicles that do not have to travel via fixed channels to access a service facility. Analytical models are developed to evaluate the expected performance of a facility location design across an exponential number of facility disruption scenarios. In each of these scenarios, customers travel to a functioning facility through a continuous space, and their destination and path choices under traffic equilibrium are described by a class of partial differential equation (PDE). A closed-form solution to the PDE is derived in an explicit matrix form, and this paper shows how the traffic equilibrium patterns across all facility disruption scenarios can be evaluated in a polynomial time. These new analytical results are then incorporated into continuous and discrete optimization frameworks for facility location design. Numerical experiments are conducted to test the computational performance of the proposed modeling framework.

关键词： Facility location Traffic equilibrium Partial differential equation mixed-integer program Reliability

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An analytical approach to the protection planning of a rail intermodal terminal network

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期257卷 511-525页

作者： Sarhadi, Hassan Tulett, David M. Verma, Manish Mem Univ Newfoundland Fac Business Adm St John NF A1C 5S7 Canada McMaster Univ DeGroote Sch Business Hamilton ON L8S 4L8 Canada

Rail-truck intermodal transportation has experienced remarkable growth over the past three decades, and plays a vital role in the freight transportation system in North America. Hence, a crucial issue is to guarantee continuity of service and to minimize the adverse impacts following disruption, natural or man-made. We make the first attempt to develop an analytical framework that could be used by rail intermodal owners to determine the best fortification plan in order to minimize the impact of a worst-case attack. The complexity of the resulting tri-level mathematical model motivated the development of a decomposition-based heuristic solution technique, and the resulting analytical approach was used to solve and analyze problem instances generated using the realistic infrastructure of a railroad operator. (C) 2016 Elsevier B.V. All rights reserved.

关键词： (O) Transportation (T) Logistics mixed-integer program Fortification Decomposition heuristic

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Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2012年第11期63卷 1613-1630页

作者： Camargo, V. C. B. Toledo, F. M. B. Almada-Lobo, B. Univ Sao Paulo Inst Ciencias Matemat & Comp BR-13560970 Sao Carlos SP Brazil Univ Porto P-4100 Oporto Portugal

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance. Journal of the Operational Research Society (2012) 63, 1613-1630. doi:10.1057/jors.2011.159 published online 7 March 2012

关键词： lot sizing and scheduling two-stage production system mixed-integer program time scale

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When to go electric? A parallel bus fleet replacement study

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TRANSPORTATION RESEARCH PART D-TRANSPORT AND ENVIRONMENT 2019年第Jul.期72卷 299-311页

作者： Islam, Adrita Lownes, Nicholas Fehr & Peers Sacramento CA 95833 USA Univ Connecticut Dept Civil & Environm Engn Storrs CT 06269 USA

United States in 2017 emitted about 14.36% of the total global Greenhouse Gas (GHG), 27% of which comes from the transportation sector. In order to address some of these emission sources, alternative fuel technology vehicles are becoming more progressive and market ready. Transit agencies are making an effort to reduce their carbon footprint by adopting these technologies. The overarching objective of this paper is to aid transit agencies make more informed decisions regarding the process of replacing a diesel fleet with alternative-technology buses to minimize GHG emissions. This study investigates the complete course of fleet replacement using a deterministic mixed integer programming. Bus fleet replacement is optimized by minimizing the Life Cycle Cost (LCC) of owning and operating a fleet of buses and required infrastructures while reducing GHG emission simultaneously. Buses operated by Connecticut Department of Transportation (CTDOT) were used as a case-study. Results also show a significant reduction in both cost and emission for optimized replacement schedule vs the unoptimized one. Results also show that a fleet consisting of 79% Battery Electric Bus and 21% Diesel Hybrid Bus yields the least cost solution which conforms to the other operational and environmental constraints. This study also includes various sensitivity tests, that illustrates that although the magnitude of the results may vary depending on the input data, the direction remains the same. The problem formulated in this study can help any transit agencies determine the most optimized solution to their fleet replacement problem under customizable constraints or desired set of outcomes.

关键词： Parallel fleet replacement Optimization mixed-integer program GHG emission Transit Bus

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Robust multi-product newsvendor model with uncertain demand and substitution

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第1期293卷 190-202页

作者： Zhang, Jie Xie, Weijun Sarin, Subhash C. Virginia Tech Dept Ind & Syst Engn Blacksburg VA 24061 USA

This work studies a Robust Multi-product Newsvendor Model with Substitution (R-MNMS), where the demand and the substitution rates are stochastic and are subject to cardinality-constrained uncertainty sets. The goal of this work is to determine the optimal order quantities of multiple products to maximize the worst-case total profit. To achieve this, we first show that for given order quantities, computing the worst-case total profit, in general, is NP-hard. Therefore, we derive the closed-form optimal solutions for the following three special cases: (1) if there are only two products, (2) if there is no substitution among different products, and (3) if the budget of demand uncertainty is equal to the number of products. For a general R-MNMS, we formulate it as a mixed-integer linear program with an exponential number of constraints and develop a branch and cut algorithm to solve it. For large-scale problem instances, we further propose a conservative approximation of R-MNMS and prove that under some certain conditions, this conservative approximation yields an exact optimal solution to R-MNMS. The numerical study demonstrates the effectiveness of the proposed approaches and the robustness of our model. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Stochastic programming Robust Cardinality-constrained uncertainty set mixed-integer program Branch and cut algorithm

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Drawing Subway Maps: A Survey

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COMPUTER SCIENCE-RESEARCH AND DEVELOPMENT 2007年第1期22卷 23-44页

作者： Wolff, Alexander Tech Univ Eindhoven Fac Wiskunde Informat Postbus 513 NL-5600 MB Eindhoven Netherlands

This paper deals with automating the drawing of subway maps. There are two features of schematic subway maps that make them different from drawings of other networks such as flow charts or organigrams. First, most schematic subway maps use not only horizontal and vertical lines, but also diagonals. This gives more flexibility in the layout process, but it also makes the problem provably hard. Second, a subway map represents a network whose components have geographic locations that are roughly known to the users of such a map. This knowledge must be respected during the search for a clear layout of the network. For the sake of visual clarity the underlying geography may be distorted, but it must not be given up, otherwise map users will be hopelessly confused. In this paper we first give a rather generally accepted list of rules that should be adhered to by a good subway map. Next we survey three recent methods for drawing subway maps, analyze their performance with respect to the above rules, and compare the resulting maps among each other and to official subway maps drawn by graphic designers. We then focus on one of the methods, which is based on mixed-integer linear programming, a widely-used global optimization technique. This method guarantees to find a drawing that fulfills a subset of the above-mentioned rules (if such a drawing exists) and optimizes a weighted sum of costs that correspond to the remaining rules. The method can draw even large subway networks such as the London Underground in an aesthetically pleasing manner, similar to maps made by professional graphic designers. If station labels are included in the optimization process, so far only medium-size networks can be drawn. Finally we give evidence why drawing good subway maps is difficult (even without labels).

关键词： Graph drawing Graph labeling Subway map Octilinear layout mixed-integer program NP-hard

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Integrating long-term care insurance purchase decisions with saving and investment for retirement

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INSURANCE MATHEMATICS & ECONOMICS 2007年第3期41卷 362-381页

作者： Gupta, Aparna Li, Lepeng Rensselaer Polytech Inst Troy NY 12180 USA

Risk related to long-term care (LTC) is high for the elderly. Planning for LTC is now regarded as the 'third leg' of retirement planning. In this paper, planning for LTC is integrated with saving and investment decisions for an integrated approach to retirement planning. Optimal LTC insurance purchase decisions are obtained by developing a trade-off between post-retirement I LTC costs and LTC insurance premiums paid and coverage received. Integrating insurance purchase with wealth evolution, consisting of saving and investment decisions, allows addressing affordability issues. Two-way branching models are used for the stochastic health events and asset returns. The problem, formulated as a nonlinearly constrained mixed-integer optimization problem, is solved using a heuristic. Sensitivity analyses are performed for initial health and wealth status. Some important aspects of an individual's behavioral preferences are also addressed in this framework to provide more robust decision Support. (c) 2006 Elsevier B.V. All rights reserved.

关键词： strategy/planning mathematical programming/optimization investment-consumption long-term care insurance mixed-integer program heuristic

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A Collaborative Berth Planning Approach for Disruption Recovery

IEEE OPEN JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS

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IEEE OPEN JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 2022年 3卷 153-164页

作者： Lyu, Xiaohuan Negenborn, Rudy R. Shi, Xiaoning Schulte, Frederik Delft Univ Technol Dept Maritime & Transport Technol NL-2628 CD Delft Netherlands Inst Transport Res German Aerosp Ctr D-12489 Berlin Germany Univ Hamburg Inst Informat Syst D-20146 Hamburg Germany

Traditionally, terminal operators create an initial berthing plan before the arrival of incoming vessels. This plan involves decisions on when and where to load or discharge containers for the calling vessels. However, disruptive unforeseen events (i.e., arrival delays, equipment breakdowns, tides, or extreme weather) interfere with the implementation of this initial plan. For terminals, berths and quay cranes are both crucial resources, and their capacity limits the efficiency of port operations. Thus, one way to minimize the adverse effects caused by disruption is to ally different terminals to share berthing resources. In some challenging situations, terminal operators also need to consider the extensive transshipment connections between feeder and mother vessels. Therefore, in this work, we investigate a collaborative variant of the berth allocation recovery problem which focuses on the collaboration among terminals and transshipment connections between vessels. We propose a mixed-integer programming model to (re)-optimize the initial berth and quay crane allocation plan and develop a Squeaky Wheel Optimization metaheuristic to find near-optimal solutions for large-scale instances. The results from the performed computational experiments, considering multiple scenarios with disruptive events, show consistent improvements of up to 40% for the suggested collaborative strategy (in terms of costs for the terminal operators).

关键词： Cranes Collaboration Planning Resource management Uncertainty Costs Containers Collaborative berth planning disruption recovery mixed-integer program metaheuristic

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