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A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

ANNALS OF OPERATIONS RESEARCH 2016年第1-2期238卷 475-496页

作者： Petridis, Konstantinos Chatzigeorgiou, Alexander Stiakakis, Emmanouil Aston Univ Aston Business Sch Birmingham B4 7ET W Midlands England Univ Macedonia Dept Appl Informat Thessaloniki 54006 Greece

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA (S-T DEA) approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a multiobjective Mixed Integer Linear programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development.

关键词： Data Envelopment Analysis Efficiency OR in software multiobjective programming Linear programming

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Multiple objective project portfolio selection based on reference points

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Journal of Business Economics 2016年第1-2期86卷 23-33页

作者： Stewart, Theodor J. Department of Statical Sciences University of Cape Town 7701 Rondebosch Cape Town South Africa Alliance Manchester Business School University of Manchester Manchester M15 6PB United Kingdom

The problem of selecting a portfolio of research and development projects from a set of proposed projects subject to resource constraints is formulated as a multiobjective optimization problem. Three categories of objectives are identified, namely quantitative, qualitative and balance/distributional. The first two are linear in the binary decision variables, but the third involves nonlinear measures of discrepancy between desired and actual distributions of activity amongst defined categories. The result is a nonlinear combinatorial multiobjective optimization problem. A form of reference point approach is motivated and developed as a solution method, and a special purpose genetic algorithm is implemented for obtaining the solution numerically. Extensions to interactive approaches for exploration of the efficient frontier are presented and discussed. © 2015, Springer-Verlag Berlin Heidelberg.

关键词： multiobjective programming Project portfolios Reference point method

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A note on strong duality theorem for a multiobjective higher order nondifferentiable symmetric dual programs

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OPSEARCH 2016年第1期53卷 151-156页

作者： Debnath, Indira P. Gupta, S. K. Ahmad, I. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

In this paper, we establish a strong duality theorem for a Mond-Weir type multiobjective higher order nondifferentiable symmetric dual programs. Our work relaxes the hypotheses used to prove the strong duality result (by omitting one of the condition (hypothesis (IV)), Theorem 2.1) in the recent paper (Yang et al. J. Ind. Manag. Optim. 9, 525-530, (2013)).

关键词： Symmetric duality Strong duality multiobjective programming Support function Properly efficient solution

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Pareto optimal solutions providing optimal routes between every two different nodes in the cost-time trade-off routing network without the objectives being prioritized

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OPSEARCH 2016年第4期53卷 778-807页

作者： Prakash, Satya Gupta, Anuj Garg, Richa Tanwar, Bhuvnesh Kaushik, Deepika Aggarwal, Sourabh Amity Sch Engn & Technol 580 Delhi Palam Vihar Rd New Delhi 110061 India Flat 6 2 Tavistock Rd Croydon CR0 2AS England

A cost-time trade-off routing network problem is considered. In the network, each arc is associated with an ordered pair whose first component is the cost and the second component is the time of direct travel between two adjacent nodes. The cost-time trade-off routing network problem has two objectives without being prioritized. The objectives are to minimize the total cost and total time of travel between every two different nodes in the network. It is required to find all the Pareto optimal routes between every two different nodes in the network. An algorithm is developed for finding the set of Pareto optimal solutions providing all the optimal routes between every two different nodes in the network. The new algorithm extends Floyd's algorithm, presently applicable only for solving the single-objective routing network problem, to solve the cost-time trade-off routing network problem, incorporating the concept of lexicographically lesser between two ordered pairs. The problem is solved in two phases. In the first phase, the cost-time trade-off routing network problem is represented by a square matrix whose rows and columns are equal to the number of nodes and whose entries are ordered pairs associated with the arcs in the network. In the second phase, the set of Pareto optimal solutions of the cost-time trade-off routing network problem is obtained through solving a sequence of prioritized bicriterion problems. The new algorithm is explained and is illustrated through solving a numerical example. Utility of the work is also indicated.

关键词： Optimization multiobjective programming Bicriterion Pareto optimal solution Floyd's algorithm

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On sufficiency and duality in multiobjective programming problem under generalized α-type I univexity

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JOURNAL OF GLOBAL OPTIMIZATION 2010年第2期46卷 207-216页

作者： Jayswal, Anurag Birla Inst Technol Dept Appl Math Ranchi 835215 Jharkhand India

In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized alpha-univex type I vector valued functions. A number of Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond-Weir type duality results are also presented.

关键词： Generalized convexity alpha-type I univexity multiobjective programming Sufficient optimality conditions Duality

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Nondifferentiable multiobjective programming under generalized d_l-invexity

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第1期202卷 32-41页

作者： Slimani, Hachem Radjef, Mohammed Said Univ Bejaia Dept Operat Res Lab Modeling & Optimizat Syst LAMOS Bejaia 06000 Algeria

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce new concepts of d(l)-invexity and generalized d(l)-invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d(l) New Fritz-John type necessary and Karush-Kuhn-Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient, efficient or properly efficient. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual under various types of generalized d(l)-invexity assumptions. (C) 2009 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Semi-directionally differentiable functions Generalized d(l)-invexity Optimality Duality (Weakly or properly) efficient point

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Planning a TV advertising campaign: A crisp multiobjective programming model from fuzzy basic data

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2010年第1-2期38卷 84-94页

作者： Perez-Gladish, B. Gonzalez, I. Bilbao-Terol, A. Arenas-Parra, M. Univ Oviedo Dept Econ Cuantitat Fac Ciencias Econ E-33006 Oviedo Asturias Spain Univ Politecn Valencia Alcoy Sch Valencia Spain

This paper proposes a crisp two-objective logarithmic programming model to help companies decide their advertising campaigns on TV networks for mature products. Both objectives are: (a) to achieve the highest audience impact and (b) to reduce advertising costs as much as possible. Information input is fuzzily elaborated from statistical data, the fuzzy variables being defuzzified to introduce them into the crisp model. This fuzzy information is elicited by TV experts (often independent consultants). Although these experts know statistical information on audience in the past, they do not fully trust its predictive ability. The approach leads to the strategic advertisement (ad) placement among different broadcasts. Users (often managers of big companies) should inform the analyst about their advertising campaign budget. From Weber and Fechner-based psychological research, the ad impact during the advertising campaign is measured depending on the logarithm of ad repetitions. The crisp two-objective problem is solved by a tradeoff method subject to TV technical constraints. A case study with real world data is developed. (C) 2009 Elsevier Ltd. All rights reserved

关键词： Ad impact Weber and Fechner's logarithmic law Audience expectation Budgeting multiobjective programming Fuzzy techniques

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Modified interactive Chebyshev algorithm (MICA) for convex multiobjective programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期204卷 557-564页

作者： Luque, Mariano Ruiz, Francisco Steuer, Ralph E. Univ Malaga E-29071 Malaga Spain Univ Georgia Terry Coll Business Athens GA 30602 USA

In this paper. we describe an interactive procedural algorithm for convex multiobjective programming based upon the Tchebycheff method, Wierzbicki's reference point approach, and the procedure of Michalowski and Szapiro. At each iteration, the decision maker (DM) has the option of expressing his or her objective-function aspirations in the form of a reference criterion vector. Also, the DM has the option of expressing minimally acceptable values for each of the objectives in the form of a reservation vector. Based upon this information, a certain region is defined for examination. In addition, a special set of weights is constructed. Then with the weights, the algorithm of this paper is able to generate a group of efficient solutions that provides for an overall view of the current iteration's certain region. By modification of the reference and reservation vectors, one can "steer" the algorithm at each iteration. From a theoretical point of view, we prove that none of the efficient solutions obtained using this scheme impair any reservation value for convex problems. The behavior of the algorithm is illustrated by means of graphical representations and an illustrative numerical example. (C) 2009 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Interactive procedures Tchebycheff method Reference point methods Aspiration criterion vectors Reservation levels

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A fuzzy-robust stochastic multiobjective programming approach for petroleum waste management planning

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APPLIED MATHEMATICAL MODELLING 2010年第10期34卷 2778-2788页

作者： Zhang, Xiaodong Huang, Guo H. Chan, Christine W. Liu, Zhenfang Lin, Qianguo Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Peking Univ Coll Urban Environm Sci Beijing 100871 Peoples R China

This paper proposes a fuzzy-robust stochastic multiobjective programming (FRSMOP) approach, which integrates fuzzy-robust linear programming and stochastic linear programming into a general multiobjective programming framework. A chosen number of noninferior solutions can be generated for reflecting the decision-makers' preferences and subjectivity. The FRSMOP method can effectively deal with the uncertainties in the parameters expressed as fuzzy membership functions and probability distribution. The robustness of the optimization processes and solutions can be significantly enhanced through dimensional enlargement of the fuzzy constraints. The developed FRSMOP was then applied to a case study of planning petroleum waste-flow-allocation options and managing the related activities in an integrated petroleum waste management system under uncertainty. Two objectives are considered: minimization of system cost and minimization of waste flows directly to landfill. Lower waste flows directly to landfill would lead to higher system costs due to high transportation and operational costs for recycling and incinerating facilities, while higher waste flows directly to landfill corresponding to lower system costs could not meet waste diversion objective environmentally. The results indicate that uncertainties and complexities can be effectively reflected, and useful information can be generated for providing decision support. (C) 2009 Elsevier Inc. All rights reserved.

关键词： multiobjective programming Stochastic Fuzzy Robust Petroleum waste management

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An application of multiobjective programming to the study of workers' satisfaction in the Spanish labour market

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期203卷 430-443页

作者： Marcenaro-Gutierrez, O. D. Luque, M. Ruiz, F. Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Univ Malaga Dept Appl Econ Stat & Econometr E-29071 Malaga Spain

In this paper, a multiobjective scheme is used to study the satisfaction levels of Spanish workers. Data obtained from the European Community Household Panel (ECHP) are used to build a multiobjective model on the basis of a previous statistical and econometric analysis of these data. Then, a Reference Point-based method is implemented to determine the profile of the most satisfied worker in Spain nowadays. Finally, a combined Goal programming - Reference Point approach is used to determine policies which can be carried out in order to increase workers' satisfaction levels. (C) 2009 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Workers' satisfaction Reference point Goal programming Econometric analysis

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