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Comparing Model I and Model II Formulations of Spatially Explicit Harvest Scheduling Models with Maximum Area Restrictions

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FOREST SCIENCE 2016年第1期62卷 28-37页

作者： McDill, Marc E. Toth, Sandor F. St John, Rachel Braze, Janis Rebain, Stephanie A. Penn State Univ Sch Forest Resources University Pk PA 16802 USA Univ Washington Seattle WA 98195 USA Alberta Minist Environm & Sustainable Resource De Edmonton AB Canada US Forest Serv USDA Grand Rapids MI USA

This article investigates whether Johnson and Scheurman's (For. Sci. Monogr. 18, Society of American Foresters, Bethesda, MD 1977) Model II formulation, which can dramatically reduce the size and difficulty of linear programming harvest scheduling models, offers similar potential for efficiency gains in solving spatially explicit harvest scheduling models with area-based adjacency constraints. A total of 150 hypothetical problems and 10 real problems were formulated using Models I and II. The hypothetical problems were distributed (30 each) in five categories: regulated forest problems with four, six, and eight planning periods and overmature forest problems with four and six periods. The length of the planning horizon was a key factor determining the relative performance of Model I and Model II formulations in spatially explicit forest management planning problems. Results from the hypothetical problems suggest that Model I formulations outperform Model II formulations for four-period problems. However, Model II formulations perform significantly better than Model I formulations for problems with planning horizons of six and eight planning periods. Real forest results exhibit similar trends.

关键词： forest planning models mixed-integer programming area-based adjacency constraints area-restriction models

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A Computational Method for Estimating Travel Frequencies in Site Layout Planning

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JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT 2016年第5期142卷

作者： Hammad, Ahmed W. A. Akbarnezhad, Ali Rey, David Waller, S. Travis Univ New S Wales Sch Civil & Environm Engn Sydney NSW 2052 Australia Univ New S Wales Sch Civil & Environm Engn rCITI Sydney NSW 2052 Australia

Optimizing the layout of facilities on a construction site to minimize the material handling costs has been widely investigated in the literature. An integral part of the objective function utilized in the previously proposed optimization models is the frequency parameter, which generally provides a rough estimate of the frequency of travel between each pair of facilities at a specific stage of the project. The majority of travel frequencies deduced in prior studies have been estimated merely based on past experience and may not be an actual representation of movements within the project studied. There is currently a lack of a systematic approach for estimating travel frequencies, required in site layout planning, based on the information available at early stages of the project. Obtaining a reasonable estimate of the travel frequency matrix requires a realistic evaluation of the material transportation quantities at each construction stage. This necessitates the utilization of information on the progress of different activities and their corresponding material needs during the various stages. This paper presents a framework for obtaining travel frequencies at different construction project phases by taking advantage of the information made available by building information models and project schedules. The estimated frequencies are later embedded as parameters in an optimization model to improve site layout planning. The results of a case study are presented to highlight the capabilities of the proposed framework. (C) 2015 American Society of Civil Engineers.

关键词： Building information modeling (BIM) Construction site layout planning Facility layout optimization mixed-integer programming Travel frequency Project planning and design

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Optimization models for planning shale gas well refracture treatments

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AICHE JOURNAL 2016年第12期62卷 4297-4307页

作者： Cafaro, Diego C. Drouven, Markus G. Grossmann, Ignacio E. INTEC UNL CONICET Guemes 3450 RA-3000 Santa Fe Argentina Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

Refracturing is a promising option for addressing the characteristically steep decline curves of shale gas wells. In this work we propose two optimization models to address the refracturing planning problem. First, we present a continuous-time nonlinear programming model based on a novel forecast function that predicts pre- and post-treatment productivity declines. Next, we propose a discrete-time, multi-period mixed-integer linear programming (MILP) model that explicitly accounts for the possibility of multiple refracture treatments over the lifespan of a well. In an attempt to reduce solution times to a minimum, we compare three alternative formulations against each other (big-M formulation, disjunctive formulation using Standard and Compact Hull-Reformulations) and find that the disjunctive models yield the best computational performance. Finally, we apply the proposed MILP model to two case studies to demonstrate how refracturing can increase the expected recovery of a well and improve its profitability by several hundred thousand USD. (c) 2016 American Institute of Chemical Engineers AIChE J, 62: 4297-4307, 2016

关键词： shale gas mixed-integer programming refracturing planning

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Revealed Preference Tests of Collectively Rational Consumption Behavior: Formulations and Algorithms

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OPERATIONS RESEARCH 2016年第6期64卷 1197-1216页

作者： Nobibon, Fabrice Talla Cherchye, Laurens Crama, Yves Demuynck, Thomas De Rock, Bram Spieksma, Frits C. R. FedEx B-1000 Brussels Belgium Univ Leuven Ctr Econ Studies B-3000 Leuven Belgium Univ Liege HEC Management Sch QuantOM B-4000 Liege Belgium Maastricht Univ NL-6211 LK Maastricht Netherlands Univ Libre Bruxelles ECARES B-1050 Brussels Belgium Univ Leuven Fac Business & Econ ORSTAT B-3000 Leuven Belgium

This paper focuses on revealed preference tests of the collective model of household consumption. We start by showing that the decision problems corresponding to testing collective rationality are NP-complete. This makes the application of these tests problematic for (increasingly available) large(r)-scale data sets. We then present two approaches to overcome this negative result. First, we introduce exact algorithms based on mixed-integer programming (MIP) formulations of the collective rationality tests, which can be usefully applied to medium-sized data sets. Next, we propose simulated annealing heuristics, which allow for efficient testing of the collective model in the case of large data sets. We illustrate our methods by a number of computational experiments based on Dutch labor supply data.

关键词： revealed preference axioms rationality mixed-integer programming global optimization simulated annealing

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Design and administration of collaborative networked headquarters

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2016年第23期54卷 7074-7090页

作者： Moghaddam, Mohsen Nof, Shimon Y. Menipaz, Ehud Purdue Univ PRISM Ctr W Lafayette IN 47907 USA Purdue Univ Sch IE W Lafayette IN 47907 USA Ben Gurion Univ Negev Dept Ind Engn & Management Beer Sheva Israel

Regional headquarters (RHs) lead regionally serving subsidiaries responsible for organising geographically dispersed manufacturing and/or service operations in their respective regional subsidiaries (RSs), with certain levels of autonomy and decision-making authority. RHs have recently attracted greater attention, as a major investment of decentralised manufacturing and service operations. The goal of this work is thus to develop a comprehensive framework to enable optimal design and administration of interconnected, collaborative, and networked manufacturing and service systems. The decisions include optimal design of (1) RH networks based on multiple indicators, and (2) collaboration mechanisms between the RHs. Cyber-supported communication technologies enable the RHs to collaboratively process their electronic tasks (e-Tasks), such that the overall service level, resource utilisation and stability are improved. A bi-objective mixed integer programming model is developed for modelling the RH network design and administration problem. Data envelopment analysis is applied for combining multiple RH network design indicators into unified preference scores. Due to the computational complexity of the problem, a memetic algorithm is developed with a local search mechanism for making task sharing decisions. Several numerical experiments are conducted to illustrate, analyse and highlight the unique features and implications of the developed methodology.

关键词： best matching task sharing mixed-integer programming memetic algorithm collaborative control theory

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Area aggregation in map generalisation by mixed-integer programming

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INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE 2010年第12期24卷 1871-1897页

作者： Haunert, Jan-Henrik Wolff, Alexander Leibniz Univ Hannover Inst Kartog & Geoinformat Hannover Germany Tech Univ Eindhoven Fac Wiskunde Informat NL-5600 MB Eindhoven Netherlands

Topographic databases normally contain areas of different land cover classes, commonly defining a planar partition, that is, gaps and overlaps are not allowed. When reducing the scale of such a database, some areas become too small for representation and need to be aggregated. This unintentionally but unavoidably results in changes of classes. In this article we present an optimisation method for the aggregation problem. This method aims to minimise changes of classes and to create compact shapes, subject to hard constraints ensuring aggregates of sufficient size for the target scale. To quantify class changes we apply a semantic distance measure. We give a graph theoretical problem formulation and prove that the problem is NP-hard, meaning that we cannot hope to find an efficient algorithm. Instead, we present a solution by mixed-integer programming that can be used to optimally solve small instances with existing optimisation software. In order to process large datasets, we introduce specialised heuristics that allow certain variables to be eliminated in advance and a problem instance to be decomposed into independent sub-instances. We tested our method for a dataset of the official German topographic database ATKIS with input scale 1:50,000 and output scale 1:250,000. For small instances, we compare results of this approach with optimal solutions that were obtained without heuristics. We compare results for large instances with those of an existing iterative algorithm and an alternative optimisation approach by simulated annealing. These tests allow us to conclude that, with the defined heuristics, our optimisation method yields high-quality results for large datasets in modest time.

关键词： map generalisation aggregation combinatorial optimisation mixed-integer programming NP-hardness

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Optimal Energy-Efficient Transmit Beamforming for Multi-User MISO Downlink

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第20期63卷 5574-5588页

作者： Tervo, Oskari Le-Nam Tran Juntti, Markku Univ Oulu Dept Commun Engn FI-90014 Oulu Finland Univ Oulu Ctr Wireless Commun FI-90014 Oulu Finland Maynooth Univ Dept Elect Engn Maynooth Kildare Ireland

This paper studies beamforming techniques for energy efficiency maximization (EEmax) in multiuser multiple-input single-output (MISO) downlink system. For this challenging nonconvex problem, we first derive an optimal solution using branch-and-reduce-and-bound (BRB) approach. We also propose two low-complexity approximate designs. The first one uses the well-known zero-forcing beamforming (ZFBF) to eliminate inter-user interference so that the EEmax problem reduces to a concave-convex fractional program. Particularly, the problem is then efficiently solved by closed-form expressions in combination with the Dinkelbach's approach. In the second design, we aim at finding a stationary point using the sequential convex approximation (SCA) method. By proper transformations, we arrive at a fast converging iterative algorithm where a convex program is solved in each iteration. We further show that the problem in each iteration can also be approximated as a second-order cone program (SOCP), allowing for exploiting computationally efficient state-of-the-art SOCP solvers. Numerical experiments demonstrate that the second design converges quickly and achieves a near-optimal performance. To further increase the energy efficiency, we also consider the joint beamforming and antenna selection (JBAS) problem for which two designs are proposed. In the first approach, we capitalize on the perspective reformulation in combination with continuous relaxation to solve the JBAS problem. In the second one, sparsity-inducing regularization is introduced to approximate the JBAS problem, which is then solved by the SCA method. Numerical results show that joint beamforming and antenna selection offers significant energy efficiency improvement for large numbers of transmit antennas.

关键词： Antenna selection Dinkelbach method energy efficiency fractional programming MISO broadcast channel mixed-integer programming second-order cone programming sequential convex approximation

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Solving network design problems via iterative aggregation

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MATHEMATICAL programming COMPUTATION 2015年第2期7卷 189-217页

作者： Baermann, Andreas Liers, Frauke Martin, Alexander Merkert, Maximilian Thurner, Christoph Weninger, Dieter Univ Erlangen Nurnberg Dept Math Lehrstuhl Wirtschaftsmath Cauerstr 11 D-91058 Erlangen Germany

In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme allows existing preinstalled capacities. Starting with an initial aggregation, we solve a sequence of network design master problems over increasingly fine-grained representations of the original network. In each step, a subproblem is solved that either proves optimality of the solution or gives a directive where to refine the representation of the network in the subsequent iteration. The algorithm terminates with a globally optimal solution to the original problem. Our implementation uses a standard integer programming solver for solving the master problems as well as the subproblems. The computational results on random and realistic instances confirm the profitable use of the iterative aggregation technique. The computing time often reduces drastically when our method is compared to solving the original problem from scratch.

关键词： Aggregation Network design Combinatorial optimization mixed-integer programming Branch-and-cut

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Theoretical framework for formulating MIP scheduling models with multiple and non-uniform discrete-time grids

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COMPUTERS & CHEMICAL ENGINEERING 2015年 72卷 233-254页

作者： Velez, Sara Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA

We present a framework for the formulation of MIP scheduling models based on multiple and nonuniform discrete time grids. In a previous work we showed that it is possible to use different (possibly nonuniform) time grids for each task, unit, and material. Here, we generalize these ideas to account for general resources, and a range of processing characteristics such as limited intermediate storage and changeovers. Each resource has its own grid based on resource consumption and availability allowing resource constraints to be modeled more accurately without increasing the number of binary variables. We develop algorithms to define the unit-, task-, material-, and resource-specific grids directly from problem data. Importantly, we prove that the multi-grid formulation is able to find a schedule with the same optimal objective as the discrete-time single-grid model with an arbitrarily fine grid. The proposed framework leads to the formulation of models with reduced number of binary variables and constraints, which are able to find good solutions faster than existing models. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： mixed-integer programming Process optimization Supply chain management

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Resource-constrained project scheduling with concave processing rate functions

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2015年第5期66卷 794-806页

作者： Steeneek, Daniel W. Sarin, Subhash C. Virginia Tech Blacksburg VA 24061 USA

In this paper, we address a resource-constrained project scheduling problem involving a single resource. The resource can be applied at varying consumption rates to the activities of the project. The duration of each activity is defined by a convex, non-increasing time-resource trade-off function. In addition, activities are not preemptable (ie, the resource consumption rate of an activity cannot be altered while the activity is being processed). We explicitly consider variation of the rate at which an activity is performed with variation in resource consumption rate. We designate the number of units (amount of an activity) performed per unit time with variation in resource consumption rate as the processing rate function, and assume this function to be concave. We present a tree-search-based method in concert with the solution of a nonlinear program and the use of dominance properties to determine: (i) the sequence in which to perform the activities of the project, and (ii) the resource consumption rate to allocate to each activity so as to minimize the project duration (makespan). We also present results of an experimental investigation that reveal the efficacy of the proposed methodology Finally, we present an application of this methodology to a practical setting.

关键词： project scheduling project management mixed-integer programming non-linear programming

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