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A Multi-objective Approach for Transboundary River Water Allocation

WATER RESOURCES MANAGEMENT 2014年第15期28卷 5447-5463页

作者： Roozbahani, R. Abbasi, B. Schreider, S. Ardakani, A. RMIT Univ Sch Math & Geospatial Sci Melbourne Vic 3001 Australia Xopt Ltd Melbourne Vic 3058 Australia

The allocation of water to the stakeholders of a large basin involves conflicting objectives, since increasing the allocated water to one stakeholder leads to a reduction in water allocated to other stakeholders. The consideration of conflicting objectives is inevitable when the basin is a transboundary basin, where a river crosses at least one political border, either a border within a nation or an international boundary. This paper proposes a multi-objective optimization model for sharing water among stakeholders of a transboundary river, assuming that the stakeholders cooperate. Here, the cooperation implies a balanced water allocation to stakeholders since shortage in each stakeholder have negative impacts on others. Each objective function of the multi-objective model represents the water profit of a stakeholder;which has to be maximized. To reach a cooperative solution, a new method for transforming the multi-objective formulation to a three-step single objective formulation is proposed. The solution guarantees each stakeholder's profit which is larger than a percentage of its highest possible profit obtained in the case when the percentage of profit is equal for all stakeholders. The proposed model formulation was applied to the Sefidrud River where eight provinces are the stakeholders competing for water resources of this basin.

关键词： Water Allocation mixed-integer programming Multi-objective Optimisation Transboundary Watersheds

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Mathematical programming Formulations and Algorithms for Discrete k-Median Clustering of Time-Series Data

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INFORMS JOURNAL ON COMPUTING 2014年第1期26卷 160-172页

作者： Seref, Onur Fan, Ya-Ju Chaovalitwongse, Wanpracha Art Virginia Polytech Inst & State Univ Dept Business Informat Technol Blacksburg VA 24061 USA Lawrence Livermore Natl Lab Livermore CA 94551 USA Univ Washington Dept Ind & Syst Engn Seattle WA 98195 USA Univ Washington Dept Radiol Seattle WA 98195 USA

Discrete k-median (DKM) clustering problems arise in many real-life applications that involve time-series data sets, in which nondiscrete clustering methods may not represent the problem domain adequately. In this study, we propose mathematical programming formulations and solution methods to efficiently solve the DKM clustering problem. We develop approximation algorithms from a bilinear formulation of the discrete k-median problem using an uncoupled bilinear program algorithm. This approximation algorithm, which we refer to as DKM-L, is composed of two alternating linear programs, where one can be solved in linear time and the other is a minimum cost assignment problem. We then modify this algorithm by replacing the assignment problem with an efficient sequential algorithm for a faster approximation, which we call DKM-S. We also propose a compact exact integer formulation, DKM-I, and a more efficient network design-based exact mixed-integer formulation, DKM-M. All of our methods use arbitrary pairwise distance matrices as input. We apply our methods to simulated single-variate and multivariate random walk time-series data. We report comparative clustering performances using normalized mutual information (NMI) and solution speeds among the DKM methods we propose. We also compare our methods to other clustering algorithms that can operate with distance matrices, such as hierarchical cluster trees (HCT) and partition around medoids (PAM). We present NMI scores and classification accuracies of our DKM algorithms compared to HCT and PAM using five different distance measures on simluated data, as well as public benchmark and real-life neural time-series data sets. We show that DKM-S is much faster than HCT, PAM, and all other DKM methods and produces consistently good clustering results on all data sets.

关键词： clustering optimization discrete k-median mixed-integer programming uncoupled bilinear program algorithm sequential optimization time series

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Approximate solution of mp-MILP problems using piecewise affine relaxation of bilinear terms

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COMPUTERS & CHEMICAL ENGINEERING 2014年 61卷 136-155页

作者： Wittmann-Hohlbein, Martina Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2BY England

We propose an approximate solution strategy for multi-parametric mixed integer linear programming (mp-MILP) problems with parameter dependency at multiple locations in the model. A two-stage solution strategy, consisting of an approximation stage and a multi-parametric programming stage, is introduced. At the approximation stage, surrogate mp-MILP models are derived by overestimating bilinear terms in the constraints over an ab initio partitioning of the domain. We then incorporate piecewise affine relaxation based models using a linear partitioning scheme and a logarithmic partitioning scheme, respectively. The models are tuned by the number of partitions chosen. Problem sizes of the varied models, and computational requirements for the algorithmic procedure are compared. The conservatism of the suboptimal solution of the mp-MILP problem for the piecewise affine relaxation based two-stage method is discussed. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Multi-parametric programming mixed-integer programming Bilinear programming

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The traveling therapist scheduling problem

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IIE TRANSACTIONS 2014年第7期46卷 683-706页

作者： Bard, Jonathan F. Shao, Yufen Qi, Xiangtong Jarrah, Ahmad I. Univ Texas Austin Austin TX 78712 USA Exxon Mobil Houston TX USA Hong Kong Univ Sci & Technol Dept Ind Engn & Logist Management Kowloon Hong Kong Peoples R China George Washington Univ Washington DC USA

This article presents a new model for constructing weekly schedules for therapists who treat patients with fixed appointment times at various healthcare facilities throughout a large geographic area. The objective is to satisfy the demand for service over a 5-day planning horizon at minimum cost subject to a variety of constraints related to time windows, overtime rules, and breaks. Each therapist works under an individually negotiated contract and may be full-time or part-time. Patient preferences for specific therapists and therapist preferences for assignments at specific facilities are also taken into account when they do not jeopardize feasibility. To gain an understanding of the computational issues, the complexity of various relaxations is examined and characterized. The results indicated that even simple versions of the problem are NP-hard. The model takes the form of a large-scale mixed-integer program but was not solvable with CPLEX for instances of realistic size. Subsequently, a branch-and-price-and-cut algorithm was developed and proved capable of finding near-optimal solutions within 50 minutes for small instances. High-quality solutions were ultimately found with a rolling horizon algorithm in a fraction of that time. The work was performed in conjunction with Key Rehab, a company that provides physical, occupational, and speech therapy services throughout the U.S. Midwest. The policies, practices, compensation rules, and legal restrictions under which Key operates are reflected in the model formulation.

关键词： mixed-integer programming home healthcare column generation weekly planning Therapist scheduling

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Balancing of robotic mixed-model two-sided assembly line with robot setup times

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2014年第5-8期74卷 1005-1016页

作者： Aghajani, Mojtaba Ghodsi, Reza Javadi, Babak Univ Tehran Dept Ind Engn Fac Engn Tehran Iran

In this paper, type II robotic mixed-model two-sided assembly line balancing (RMTALB-II) problem is considered. In recent years, robots have been widely used in assembly systems as called robotic assembly lines where a set of tasks have to be assigned to stations and each station needs to select one of the different robots to process the assigned tasks. Two-sided assembly lines are especially used to produce large-sized high-volume products, such as automobiles, trucks, and buses. In this type of production line, both left side and right side of the line are used in parallel. However, little attention has been paid to solve RMTALB problems. Moreover, according to our best knowledge, there is no published work in the literature on RMTALB. This paper presents a new mixed-integer programming model for RMTALB-II to minimize the cycle time for a given number of mated stations. Since RMTALB problems are in NP-hard class of combinatorial optimization problems, a simulated annealing (SA) algorithm as metaheuristic method is proposed to solve the problem. Some problems are solved by SA and performance of the SA is evaluated by comparing their results with the optimal solution. The computational results show that SA is more efficient.

关键词： Robotic mixed-model two-sided assembly line mixed-integer programming Simulated annealing

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An integer-programming-Based Approach to the Close-Enough Traveling Salesman Problem

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INFORMS JOURNAL ON COMPUTING 2014年第3期26卷 415-432页

作者： Behdani, Behnam Smith, J. Cole Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

W e address a variant of the Euclidean traveling salesman problem known as the close-enough traveling salesman problem (CETSP), where the traveler visits a node if it enters a compact neighborhood set of that node. We formulate a mixed-integer programming model based on a discretization scheme for the problem. Both lower and upper bounds on the optimal CETSP tour length can be derived from the solution of this model, and the quality of the bounds obtained depends on the granularity of the discretization scheme. Our approach first develops valid inequalities that enhance the bound and solvability of this formulation. We then provide two alternative formulations, one that yields an improved lower bound on the optimal CETSP tour length, and one that greatly improves the solvability of the original formulation by recasting it as a two-stage problem amenable to decomposition. Computational results demonstrate the effectiveness of the proposed methods.

关键词： close-enough traveling salesman problem geometric routing problems mixed-integer programming computational geometry discretization

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Model for flexibility evaluation in manufacturing network strategic planning

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2014年第15期52卷 4396-4411页

作者： Kemmoe, Sylverin Pernot, Pierre-Alban Tchernev, Nikolay Auvergne Univ CRCGM EA 38 49 Clermont Ferrand France Univ Clermont Ferrand LIMOS UMR CNRS 6138 Aubiere France Auvergne Univ LIMOS UMR CNRS 6138 Aubiere France

In response to market pressures, manufacturers have adopted different approaches to provide flexibility regarding several aspects. In this paper, we suggest a model for the evaluation of the flexibility of the manufacturing supply chain, based on graph theory techniques. This model defines maximum excess demand that may be met using flexibility. Recourse to flexibility enablers is determined based on cost minimisation. Such enablers are volume flexibility, mix flexibility and safety stocks. The proposed model is solved using a two-step Mix integer Linear Programme;the first step consists in defining maximum demand that may be met while the second step concerns minimising cost. The main benefit of our model is to deal with realistic problems in a rather short time. Therefore, it can be used in a wide 'what-if' design process. It means evaluating various contemplated flexibility configurations in multiple demand scenarios in order to choose the best option. It can be also used during operational supply chain planning in order to face to an unbalanced situation. This paper ends with a numerical example illustrating our model's efficiency.

关键词： manufacturing flexibility flexibility evaluation strategic planning mixed-integer programming graph theory

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Absolute return portfolios

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2014年 45卷 20-41页

作者： Valle, C. A. Meade, N. Beasley, J. E. Brunel Univ Uxbridge UB8 3PH Middx England Univ London Imperial Coll Sci Technol & Med Sch Business London SW7 2AZ England JB Consultants Morden SM4 4HS England

In this paper we consider the problem of selecting an absolute return portfolio. This is a portfolio of assets that is designed to deliver a good return irrespective of how the underlying market (typically as represented by a market index) performs. We present a three-stage mixed-integer zero-one program for the problem that explicitly considers transaction costs associated with trading. The first two stages relate to a regression of portfolio return against time, whilst the third stage relates to minimising transaction cost. We extend our approach to the problem of designing portfolios with differing characteristics. In particular we present models for enhanced indexation (relative return) portfolios and for portfolios that are a mix of absolute and relative return. Computational results are given for portfolios derived from universes defined by S&P international equity indices. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Absolute return portfolio Linear regression mixed-integer programming

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An MIP Formulation for Joint Market-Clearing of Energy and Reserves Based on Ramp Scheduling

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IEEE TRANSACTIONS ON POWER SYSTEMS 2014年第1期29卷 476-488页

作者： Morales-Espana, German Ramos, Andres Garcia-Gonzalez, Javier Univ Pontificia Comillas Inst Res Technol IIT Sch Engn ICAI Madrid Spain

The day-ahead unit-commitment (UC)-based market-clearing (MC) is widely acknowledged to be the most economically efficient mechanism for scheduling resources in power systems. In conventional UC problems, power schedules are used to represent the staircase energy schedule. However, the realizability of this schedule cannot be guaranteed due to the violation of ramping limits, and hence conventional UC formulations do not manage the flexibility of generating units efficiently. This paper provides a UC-based MC formulation, drawing a clear distinction between power and energy. Demand and generation are modeled as hourly piecewise-linear functions representing their instantaneous power trajectories. The schedule of generating unit output is no longer a staircase function, but a smoother function that respects all ramp constraints. The formulation represents in detail the operating reserves (online and offline), their time deployment limits (e.g., 15 min), their potential substitution, and their limits according to the actual ramp schedule. Startup and shutdown power trajectories are also modeled, and thus a more efficient energy and reserves schedule is obtained. The model is formulated as a mixed-integer programming (MIP) problem, and was tested with a 10-unit and 100-unit system in which its computational performance was compared with a traditional UC formulation.

关键词： mixed-integer programming operating reserves startup and shutdown ramps UC-based market-clearing

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Optimal evacuation planning using staging and routing

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2014年第1期65卷 124-140页

作者： Bish, D. R. Sherali, H. D. Hobeika, A. G. Virginia Tech Grado Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA Virginia Tech Via Dept Civil & Environm Engn Blacksburg VA 24061 USA

Evacuation is an important disaster management tool. Evacuating a large region by automobile (the most commonly used mode) is a difficult task, especially as high levels of traffic congestion often form. This paper studies the use of demand-based strategies, specifically, the staging and routing of evacuees. These strategies attempt to manage demand in order to reduce or eliminate congestion. A strategic mixed-integer programming planning model that accounts for evacuation dynamics and congestion is used to study these strategies. The strategies adopted incorporate different evacuee types based on destination requirements and shelter capacity restrictions. The main objective studied is to minimize the network clearance time. We examine the structure of optimal strategies, yielding insights into the use of staging and routing in evacuation management. These insights are then used to develop effective solution procedures. To demonstrate the efficacy of the proposed solution technique, we provide computational experience using a large realistic example based on Virginia Beach.

关键词： evacuation planning disaster management staging routing mixed-integer programming

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