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A stochastic Optimization Model for Designing Last Mile Relief Networks

TRANSPORTATION SCIENCE 2016年第3期50卷 1092-1113页

作者： Noyan, Nilay Balcik, Burcu Atakan, Semih Sabanci Univ Ind Engn Program TR-34956 Istanbul Turkey Ozyegin Univ Dept Ind Engn TR-34794 Istanbul Turkey

In this study, we introduce a distribution network design problem that determines the locations and capacities of the relief distribution points in the last mile network, while considering demand- and network-related uncertainties in the post-disaster environment. The problem addresses the critical concerns of relief organizations in designing last mile networks, which are providing accessible and equitable service to beneficiaries. We focus on two types of supply allocation policies and propose a hybrid version considering their different implications on equity and accessibility. Then, we develop a two-stage stochastic programming model that incorporates the hybrid allocation policy and achieves high levels of accessibility and equity simultaneously. We devise a branch-and-cut algorithm based on Benders decomposition to solve large problem instances in reasonable times and conduct a numerical study to demonstrate the computational effectiveness of the solution method. We also illustrate the application of our model on a case study based on real-world data from the 2011 Van earthquake in Turkey.

关键词： distribution network design post-disaster humanitarian relief accessibility equity stochastic integer programming L-shaped method branch-and-cut

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stochastic Resource Optimization for Wireless Powered Hybrid Coded Edge Computing Networks

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IEEE TRANSACTIONS ON MOBILE COMPUTING 2024年第3期23卷 2022-2038页

作者： Ng, Wei Chong Lim, Wei Yang Bryan Xiong, Zehui Niyato, Dusit Poor, H. Vincent Shen, Xuemin Sherman Miao, Chunyan Nanyang Technol Univ NTU Alibaba Grp Singapore 639798 Singapore Nanyang Technol Univ NTU Alibaba NTU Joint Res Inst Singapore 639798 Singapore Singapore Univ Technol Design Pillar Informat Syst Technol & Design Singapore 487372 Singapore Nanyang Technol Univ Sch Comp Sci & Engn Singapore 639798 Singapore Princeton Univ Dept Elect & Comp Engn Princeton NJ 08544 USA Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

To enable ubiquitous Artificial Intelligence (AI) in the next-generation wireless communications networks, computation-intensive tasks such as data processing and model training have to be performed by energy-constrained end users. In this paper, we present a hybrid coded edge computing network whereby users can choose to complete their computation task through: i) local computation with the wireless power transfer derived from base stations, ii) coded edge offloading, or iii) hybrid computation involving edge offloading and local computation. To minimize the overall network cost, we propose a stochastic resource optimization approach. Given the stochastic nature of wireless charging efficiency and edge servers computation capacities, which can only be observed ex-post , a computation strategy for each user is determined using the two-stage stochastic integer programming (SIP). To address the complexity of the SIP problem which scales with the size of the network, we introduce the efficient computation methods of Benders' decomposition and sample average approximation. Besides, we present a special case of z -stage stochastic offloading optimization that is applicable when the corrective edge offloading action can be executed in multiple stages, e.g., for non-time-sensitive tasks that do not need to be completed by stage two. Finally, we provide extensive sensitivity analyses to evaluate the performance of the proposed cost minimization approach amid varying network parameters. We demonstrate that our approach outperforms deterministic optimization approaches for in-network cost minimization.

关键词： Task analysis Servers Internet of Things Wireless communication stochastic processes Computational modeling Encoding Edge computing resource management network economics multi-tier computing stochastic integer programming

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THE integer L-SHAPED METHOD FOR stochastic integer PROGRAMS WITH COMPLETE RECOURSE

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OPERATIONS RESEARCH LETTERS 1993年第3期13卷 133-142页

作者： LAPORTE, G LOUVEAUX, FV FAC UNIV NOTRE DAME PAIX FAC SCI ECON & SOCIALES B-5000 NAMUR BELGIUM

In this paper, a general branch-and-cut procedure for stochastic integer programs with complete recourse and first stage binary variables is presented. It is shown to provide a finite exact algorithm for a number of stochastic integer programs, even in the presence of binary variables or continuous random variables in the second stage.

关键词： stochastic integer programming L-SHAPED METHOD BRANCH-AND-CUT

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Dynamic capacity acquisition and assignment under uncertainty

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ANNALS OF OPERATIONS RESEARCH 2003年第1-4期124卷 267-283页

作者： Ahmed, S Garcia, R Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-and-bound strategy for the problem. Encouraging preliminary computational results are provided.

关键词： capacity expansion stochastic integer programming decomposition branch-and-bound

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stochastic ONLINE KNAPSACK-PROBLEMS

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MATHEMATICAL programming 1995年第1期68卷 73-104页

作者： MARCHETTISPACCAMELA, A VERCELLIS, C POLITECN MILAN DIPARTIMENTO ECON & PRODI-20133 MILANITALY UNIV ROMA LA SAPIENZA DIPARTIMENTO INFORMAT & SISTEMISTROMEITALY

Different classes of on-line algorithms are developed and analyzed for the solution of {0, 1} and relaxed stochastic knapsack problems, in which both profit and size coefficients are random variables. In particular, a linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value is O(log(3/2) n). An Omega(1) lower bound on the expected difference between the optimum and the solution found by any on-line algorithm is also shown to hold.

关键词： KNAPSACK PROBLEMS ONLINE ALGORITHMS stochastic integer programming

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A mathematical model for maximizing the value of phase 3 drug development portfolios incorporating budget constraints and risk

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STATISTICS IN MEDICINE 2013年第10期32卷 1763-1777页

作者： Patel, Nitin R. Ankolekar, Suresh Antonijevic, Zoran Rajicic, Natasa Cytel Inc Cambridge MA 02139 USA MIT Ctr Biomed Innovat Cambridge MA 02139 USA Maastricht Sch Management NL-6229 EP Maastricht Netherlands Pfizer Inc Specialty Care Business Unit Med Dev Grp New York NY 10017 USA

We describe a value-driven approach to optimizing pharmaceutical portfolios. Our approach incorporates inputs from research and development and commercial functions by simultaneously addressing internal and external factors. This approach differentiates itself from current practices in that it recognizes the impact of study design parameters, sample size in particular, on the portfolio value. We develop an integer programming (IP) model as the basis for Bayesian decision analysis to optimize phase 3 development portfolios using expected net present value as the criterion. We show how this framework can be used to determine optimal sample sizes and trial schedules to maximize the value of a portfolio under budget constraints. We then illustrate the remarkable flexibility of the IP model to answer a variety of what-if' questions that reflect situations that arise in practice. We extend the IP model to a stochastic IP model to incorporate uncertainty in the availability of drugs from earlier development phases for phase 3 development in the future. We show how to use stochastic IP to re-optimize the portfolio development strategy over time as new information accumulates and budget changes occur. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： phase 3 portfolio optimization budget constraints decision analysis stochastic integer programming risk portfolio re-optimization

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A comparison of stochastic programming and bi-objective optimisation approaches to robust airline crew scheduling

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OR SPECTRUM 2011年第1期33卷 49-75页

作者： Tam, Bassy Ehrgott, Matthias Ryan, David Zakeri, Golbon Univ Auckland Dept Engn Sci Auckland 1 New Zealand

A prominent problem in airline crew scheduling is the pairings or Tour-of-Duty planning problem. The objective is to determine a set of pairings (or Tours-of-Duty) for a crew group to minimise the planned cost of operating a schedule of flights. However, due to unforeseen events the performance in operation can differ considerably from planning, sometimes causing significant additional recoverycosts. In recent years there has been a growing interest in robust crew scheduling. Here, the aim is to find solutions that are "cheap' in terms of planned cost as well as being robust, meaning that they are less likely to be disrupted in case of delays. Taking the stochastic nature of delays into account, Yen and Birge (Transp Sci 40:3-14, 2006) formulate the problem as a two-stage stochastic integer programme and develop an algorithm to solve this problem. Based on the contradictory nature of the goals, Ehrgott and Ryan (J Multi-Criteria Decis Anal 11:139-150, 2002) formulate a bi-objective set partitioning model and employ elastic constraint scalarisation to enable the solution by set partitioning algorithms commercially used in crew scheduling software. In this study, we compare the two solution approaches. We improve the algorithm of Yen and Birge (Transp Sci 40:3-14, 2006) and implement both methods with a commercial crew scheduling software. The results of both methods are compared with respect to characteristics of robust solutions, such as the number of aircraft changes for crew. We also conduct experiments to simulate the performance of the obtained solutions. All experiments are performed using actual schedule data from Air New Zealand.

关键词： Airline crew scheduling Robust stochastic integer programming Bi-criteria integer programming

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Farm-level impacts of prolonged drought: is a multiyear event more than the sum of its parts?

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AUSTRALIAN JOURNAL OF AGRICULTURAL AND RESOURCE ECONOMICS 2010年第1期54卷 43-60页

作者： Peck, Dannele E. Adams, Richard M. Univ Wyoming Dept Agr & Appl Econ Laramie WY 82071 USA Oregon State Univ Dept Agr & Resource Econ Corvallis OR 97331 USA

A multiyear discrete stochastic programming model with uncertain water supplies and inter-year crop dynamics is developed to determine: (i) whether a multiyear drought's impact can be more than the sum of its parts, and (ii) whether optimal response to 1 year of drought can increase a producer's vulnerability in subsequent years of drought. A farm system that has inter-year crop dynamics, but lacks inter-annual water storage capabilities, is used as a case study to demonstrate that dynamics unrelated to large reservoirs or groundwater can necessitate a multiyear model to estimate drought's impact. Results demonstrate the importance of analysing individual years of drought in the context of previous and future years of drought.

关键词： crop rotations inter-year dynamics multiyear drought stochastic integer programming

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A branch-and-bound method for multistage stochastic integer programs with risk objectives

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OPTIMIZATION 2008年第2期57卷 277-293页

作者： Heinze, Thomas Schultz, Ruediger Univ Duisburg Essen Dept Math Duisburg Germany

We identify multistage stochastic integer programs with risk objectives where the related wait-and-see problems enjoy similiar separability as in the risk neutral case. For models belonging to this class, we present a solution method combining branch-and-bound with relaxation of non-anticipativity and constraint branching along non-anticipativity subspaces.

关键词： stochastic integer programming multistage models mean-risk models mixed-integer optimization

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B&B frameworks for the capacity expansion of high speed telecommunication networks under uncertainty

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ANNALS OF OPERATIONS RESEARCH 2005年第1期140卷 49-65页

作者： Andrade, R Lisser, A Maculan, N Plateau, G Univ Paris 11 CNRS UMR 8623 LRI F-91405 Orsay France Univ Paris 13 Inst Galilee CNRSUMR 7030 LIPN F-93430 Villetaneuse France Univ Fed Rio de Janeiro COPPE Sistemas BR-21945970 Rio De Janeiro Brazil

The purpose of this paper is to investigate branch and bound strategies and the comparison of branch and cut with pure branch and bound approaches on high speed telecommunication network design under uncertainty. We model the problem as a two-stage stochastic program with discrete first-stage (investment) variables. Two formulations of the problem are used. The first one with general integer investment variables and the second one, a variant of the first model, with 0-1 investment variables. We present computational results for three solution approaches: the integer L-shaped (Benders) decomposition, a branch and bound framework and a disjunctive cutting plane method.

关键词： stochastic integer programming integer L-shaped decomposition branch and bound network design

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