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Forestry management under uncertainty

ANNALS OF OPERATIONS RESEARCH 2011年第1期190卷 17-39页

作者： Alonso-Ayuso, Antonio Escudero, Laureano F. Guignard, Monique Quinteros, Martin Weintraub, Andres Univ Rey Juan Carlos Dept Estadist & Invest Operat Madrid Spain Univ Penn Wharton Sch Dept Operat & Informat Management Philadelphia PA 19104 USA Univ Los Andes Fac Ingn Santiago Chile Univ Chile Dept Ingn Ind Santiago Chile

The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period the planner must decide which cells to cut and what access roads to build in order to maximize expected net profit. We have previously developed deterministic mixed integer linear programming models for this problem. The main contribution of the present work is the introduction of a multistage stochastic integer programming model. This enables the planner to make more robust decisions based on a range of timber price scenarios over time, maximizing the expected value instead of merely analyzing a single average scenario. We use a specialization of the Branch-and-Fix Coordination algorithmic approach. Different price and associated probability scenarios are considered, allowing us to compare expected profits when uncertainties are taken into account and when only average prices are used. The stochastic approach as formulated in this work generates solutions that were always feasible and better than the average solution, while the latter in many scenarios proved to be infeasible.

关键词： Forest planning Scenario tree stochastic integer programming Branch-and-fix coordination

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An exact approach for solving integer problems under probabilistic constraints with random technology matrix

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ANNALS OF OPERATIONS RESEARCH 2010年第1期177卷 127-137页

作者： Beraldi, Patrizia Bruni, Maria Elena Univ Calabria Dipartimento Elettron Informat & Sistemist I-87030 Arcavacata Di Rende CS Italy

This paper addresses integer programming problems under probabilistic constraints involving discrete distributions. Such problems can be reformulated as large scale integer problems with knapsack constraints. For their solution we propose a specialized Branch and Bound approach where the feasible solutions of the knapsack constraint are used as partitioning rules of the feasible domain. The numerical experience carried out on a set covering problem with random covering matrix shows the validity of the solution approach and the efficiency of the implemented algorithm.

关键词： stochastic integer programming Probabilistic constraints Branch and bound method

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ON STRUCTURE AND STABILITY IN stochastic PROGRAMS WITH RANDOM TECHNOLOGY MATRIX AND COMPLETE integer RECOURSE

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MATHEMATICAL programming 1995年第1期70卷 73-89页

作者： SCHULTZ, R Konrad-Zuse-Zentrum für Informationstechnik Berlin Berlin Germany

For two-stage stochastic programs with integrality constraints in the second stage, we study continuity properties of the expected recourse as a function both of the first-stage policy and the integrating probability measure. Sufficient conditions for lower semicontinuity, continuity and Lipschitz continuity with respect to the first-stage policy are presented. Furthermore, joint continuity in the policy and the probability measure is established. This leads to conclusions on the stability of optimal values and optimal solutions to the two-stage stochastic program when subjecting the underlying probability measure to perturbations.

关键词： stochastic integer programming PARAMETRIC integer programming CONTINUITY STABILITY WEAK CONVERGENCE OF PROBABILITY MEASURES

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Study on multi-objective optimization of flow allocation in a multi-commodity stochastic-flow network with unreliable nodes

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2008年第1-2期28卷 185-198页

作者： Liu, Qiang Zhao, Qingzhen Zang, Wenke Shandong Econ Univ Sch Informat Management Jinan 250014 Shandong Peoples R China Shandong Normal Univ Sch Management & Econ Jinan 250014 Shandong Peoples R China Shandong Normal Univ Sch Math Sci Jinan 250014 Shandong Peoples R China

A long distance transportation problem was abstracted to a resource flow allocation problem upon a stochastic-flow network with unreliable nodes. The objectives were the probability that transmission was successful and transportation cost. In order to solve constructed model, a multi-objective genetic algorithm was propounded. Tested by examples, the algorithm well solved the flow allocation problem in a stochastic-flow network.

关键词： stochastic-flow network Multi-objectivegenetic algorithm stochastic integer programming Minimal path

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Rates of convergence in stochastic programs with complete integer recourse

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SIAM JOURNAL ON OPTIMIZATION 1996年第4期6卷 1138-1152页

作者： Schultz, R Konrad-Zuse-Zentrum I. D-14195 Berlin Takustrasse 7 Germany

The stability of stochastic programs with mixed-integer recourse and random right-hand sides under perturbations of the integrating probability measure is considered from a quantitative viewpoint. Objective-function values of perturbed stochastic programs are related to each other via a variational distance of probability measures based on a suitable Vapnik-Cervonenkis class of Borel sets in a Euclidean space. This leads to Holder continuity of local optimal values. In the context of estimation via empirical measures the general results imply qualitative and quantitative statements on the asymptotic convergence of local optimal values and optimal solutions.

关键词： stochastic integer programming parametric integer programming Holder continuity stability variational distance of probability measures Vapnik-Cervonenkis class law of the iterated logarithm

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Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations

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COMPUTATIONAL MANAGEMENT SCIENCE 2018年第3-4期15卷 325-349页

作者： van der Laan, Niels Romeijnders, Ward van der Vlerk, Maarten H. Univ Groningen Dept Operat POB 800 NL-9700 AV Groningen Netherlands

We derive bounds on the expectation of a class of periodic functions using the total variations of higher-order derivatives of the underlying probability density function. These bounds are a strict improvement over those of Romeijnders et al. (Math Program 157:3-46, 2016b), and we use them to derive error bounds for convex approximations of simple integer recourse models. In fact, we obtain a hierarchy of error bounds that become tighter if the total variations of additional higher-order derivatives are taken into account. Moreover, each error bound decreases if these total variations become smaller. The improved bounds may be used to derive tighter error bounds for convex approximations of more general recourse models involving integer decision variables.

关键词： stochastic integer programming Convex approximations Error bounds

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stochastic survivable network design problems

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Electronic Notes in Discrete Mathematics 2013年 41卷 245-252页

作者： Ljubić, Ivana Mutzel, Petra Zey, Bernd Department of Statistics and Operations Research University of Vienna Vienna Austria Department of Computer Science TU Dortmund Dortmund Germany

In this paper we introduce survivable network design problems under a two-stage stochastic model with fixed recourse and finitely many scenarios. We propose a new cut-based formulation based on orientation properties which is stronger than the undirected cut-based model. We use a two-stage branch&cut algorithm for solving the decomposed model to provable optimality. In order to accelerate the computations, we suggest a new cut strengthening technique for the decomposed L-shaped optimality cuts that is computationally fast and easy to implement. © 2013 Elsevier B.V.

关键词： Benders decomposition Branch-and-cut stochastic integer programming stochastic survivable network design

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Optimal Nursing Home Shift Scheduling: A Two-Stage stochastic programming Approach 16

Optimal Nursing Home Shift Scheduling: A Two-Stage Stochasti...

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16th IEEE International Conference on Automation Science and Engineering (CASE)

作者： Jiang, Shujin Li, Mingyang Hyer, Kathryn Kong, Nan Purdue Univ W Lafayette IN 47907 USA Univ S Florida Tampa FL 33620 USA

ISBN: (纸本)9781728169040

In this paper, we study a nursing home staff schedule optimization problem under resident demand uncertainty. We formulate a two-stage stochastic binary program accordingly, with objective to minimize the total labor cost (linearly related to work time) incurred by both regular registered nurses (RRNs) and part-time nurses (PTNs). As a significant constraint, we balance RRNs' total amount of work time with residents' total service need for every considered shift. Besides, we restrict feasible shift schedules based on common scheduling practice. We conduct a series of computational experiments to validate the proposed model. We discuss our optimal solutions under different compositions of residents in terms of their disabilities. In addition, we compare the total labor costs and an RRN scheduling flexibility index with the given optimal solution under different combinations of RRNs and PTNs. Our analysis offers an operational approach to set the minimum number of nurses on flexible shift schedules to cover uncertain the service needs while maintaining a minimum labor cost.

关键词： Nurse scheduling stochastic integer programming demand scenario generation Minimum Data Set (MDS)

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UAV-assisted Wireless Power Charging for Efficient Hybrid Coded Edge Computing Network

UAV-assisted Wireless Power Charging for Efficient Hybrid Co...

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IEEE International Conference on Communications (ICC)

作者： Ng, Jer Shyuan Ng, Wei Chong Lim, Wei Yang Bryan Xiong, Zehui Niyato, Dusit Leung, Cyril Miao, Chunyan Alibaba Grp Singapore Singapore Alibaba NTU JRI Singapore Singapore SUTD Singapore Singapore Nanyang Technol Univ SCSE Singapore Singapore Nanyang Technol Univ LILY Res Ctr Singapore Singapore Univ British Columbia ECE Vancouver BC Canada

ISBN: (数字)9781538683477

ISBN: (纸本)9781538683477

With the ubiquitous sensing enabled by the Internet-of-Things (IoT), massive amount of data is generated every second, transforming the way we interact with the world. To manage big data and enable analytics at the edge of the network, large amount of computation power is required to perform the computation intensive tasks. However, the energy-constrained IoT devices are not able to perform the computation tasks without compromising the quality-of-service of the applications. In this paper, we propose a hybrid network in which users can offload their computation tasks to edge servers through coded edge offloading or perform local computation with the wireless power transfer derived from coalitions of unmanned aerial vehicles (UAVs) serving as mobile charging stations. We consider a two-level optimization approach where an optimal UAV coalitional structure that minimizes the network cost is formed. In the performance evaluation, we provide extensive sensitivity analyses to study the performance of the cost minimization approach amid varying network parameters.

关键词： Edge computing coded computation unmanned aerial vehicles stochastic integer programming coalition

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Optimal stochastic Coded Computation Offloading in Unmanned Aerial Vehicles Network

Optimal Stochastic Coded Computation Offloading in Unmanned ...

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IEEE Global Communications Conference (GLOBECOM)

作者： Ng, Wei Chong Lim, Wei Yang Bryan Ng, Jer Shyuan Sawadsitang, Suttinee Xiong, Zehui Niyato, Dusit Alibaba Grp Hangzhou Peoples R China Alibaba NTU JRI Singapore Singapore Chiang Mai Univ Coll Arts Media & Technol Chiang Mai Thailand Singapore Univ Technol & Design Singapore Singapore Nanyang Technol Univ Sch Comp Sci & Engn Singapore Singapore

ISBN: (纸本)9781728181042

Today, modern unmanned aerial vehicles (UAVs) are equipped with increasingly advanced capabilities that can run applications enabled by machine learning techniques, which require computationally intensive operations such as matrix multiplications. Due to computation constraints, the UAVs can offload their computation tasks to edge servers. To mitigate stragglers, coded distributed computing (CDC) based offloading can be adopted. In this paper, we propose an Optimal Task Allocation Scheme (OTAS) based on stochastic integer programming with the objective to minimize energy consumption during computation offloading. The simulation results show that amid uncertainty of task completion, the energy consumption in the UAV network is minimized.

关键词： Unmanned Aerial Vehicles Coded Distributed Computing stochastic integer programming Task Allocation

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