Arunkumar, N., Karunamoorthy, L., Anand, S., & Ramesh Babu, T. (2006). Linear approach for solving a piecewise linear vendor selection problem of quantity discounts using lexicographic method. International Journal of Advanced Manufacturing Technology, 28(11), 1254–1260.
Abstract: The multi-objective problem pertaining to vendor selection becomes complicated with the inclusion of a discount pricing schedule due to its nature of piecewise linearity. To overcome the difficulty of solving such a piecewise linear multi-objective problem, a linear approach is described in this paper. The use of the lexicographic method enables the decision-maker to establish the limit for defective components and late deliveries as constraints in the model. Demand can be exactly met considering the defective components present in the supply. Applying this approach to a manufacturing firm has proved its practicality. Also, the proposed methodology can be effectively used in JIT/Lean supply environments by fixing the number of vendors.
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Cook, W. D., Golan, I., Kazakov, A., & Kress, M. (1988). A case study of non-compensatory approach to ranking transportation projects. Journal of the Operational Research Society, 39(10), 901–910.
Abstract: This paper examines the use of a concordance-type model for prioritizing transportation projects. In the particular case examined, multiple criteria are involved, and projects can be rated only on a qualitative basis. The model augments the well-known ELECTRA methodology with a tournament ranking procedure. The resulting procedure, known as SELECTRA, is presently being used to rank order over 200 investment projects within the Ontario Ministry of Transportation and Communications.
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Cooper, W. W., Wei, Q., & Yu, G. (1997). Using displaced cone representation in DEA models for nondominated solutions in multiobjective programming. Systems Science and Mathematical Sciences, 10(1), 41–49.
Abstract: Concepts revolving around ’displaced cones’ are used to extend the ideas of nondominated solutions in multiobjective programming. Necessary and sufficient conditions are formed around the additive models of DEA to idelltify nondominated solutions. This provdes a basis for effecting contacts with other disciplines and other parts of DEA.
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Estellita Lins, M. P., Angulo-Meza, L., & Silva, A. C. M. D. (2004). A multi-objective approach to determine alternative targets in data envelopment analysis. Journal of the Operational Research Society, 55(10), 1090–1101.
Abstract: The choice for radial projections of classic data envelopment analysis (DEA) models, resulting in a number of projections onto the Pareto-inefficient portion of the frontier, has been seen lately as a disadvantage in DEA. The search for a non-radial projection method resulted in developments such as preference structure models. These models consider a priori preference incorporation, using weights in the search for the most preferred efficient target, although presenting some implementation difficulties. In this paper, we propose a multi-objective approach that determines the bases for a posteriori preference incorporation, through individual projections of each variable (input or output) as an objective function, thus allowing one to obtain a target at every extreme-efficient point on the frontier. This multi-objective approach is shown to be equivalent to the preference structure models, yet presenting some advantages, such as the mapping of the possible weights, assigned to partial efficiencies of an observed unit, in order to reach a specific target.
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Fang, L., & Zhang, C. - Q. (2007). Resource allocation based on the DEA model. Journal of the Operational Research Society, 59(8), 1136–1141.
Abstract: The purpose of this paper is to develop an approach to a resource-allocation problem that typically appears in organizations with a centralized decision-making environment, for example, police stations, banks, and universities. The central unit is assumed to be interested in maximizing both the total efficiency and the efficiency of the individual unit by allocating available resources to them. Building upon this, we present a data envelopment analysis-based model for allocating input resources to DMUs (the decision-making units) under the framework of multiple objective programming. Numerical examples are used to illustrate the approach.
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Farahani, R. Z., Seifi, M. S., & Asgari, N. (2010). Multiple criteria facility location problems: A survey. Applied Mathematical Modelling, 34(7), 1689–1709.
Abstract: This paper provides a review on recent efforts and development in multi-criteria location problems in three categories including bi-objective, multi-objective and multi-attribute problems and their solution methods. Also, it provides an overview on various criteria used. While there are a few chapters or sections in different location books related to this topic, we have not seen any comprehensive review papers or book chapter that can cover it. We believe this paper can be used as a complementary and updated version.
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Gomes, E. G., & Lins, M. P. E. (2002). Integrating geographical information systems and multi-criteria methods: A case study. Annals of Operations Research, 116(1-4), 243–269.
Abstract: This paper presents an application of the integration between Geographical Information Systems (GIS) and Multi-Criteria Decision Analysis (MCDA) to aid spatial decisions. We present a hypothetical case study to illustrate the GIS – MCDA integration: the selection of the best municipal district of Rio de Janeiro State, Brazil, in relation to the quality of urban life. The best municipal district is the one that presents the closest characteristics to those considered ideal by the decision-maker. The approach adopted is the Multi-Objective Linear Programming (MOLP) and the chosen method is the Pareto Race.
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Jahanshahloo, G. R., & Foroughi, A. A. (2005). Efficiency analysis, generating an efficient extreme point for an MOLP, and some comparisons. Applied Mathematics and Computation, 162(2), 991–1005.
Abstract: This paper starts with analyzing efficiency of an alternative in a multi objective problem. By combination of concepts in data envelopment analysis (DEA) and multiple objective linear programming (MOLP), we search a composite alternative to compare with a given alternative and assess its efficiency in an MOLP problem. In addition to some results, this leads us to produce some procedures for generating an initial efficient extreme point to an MOLP problem. We compare our procedures with some other existing methods and exhibit some advantages of our methods. In addition, we consider some models of DEA as MOLP problems and use them to illustrate some contents of the paper, which also appears some analogies between these areas.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2004). Input estimation and identification of extra inputs in inverse DEA models. Applied Mathematics and Computation, 156(2), 427–437.
Abstract: In this paper we show that the inverse data envelopment analysis (DEA) models can be used to estimate inputs for a decision making unit (DMU) when some or all outputs and efficiency level of this DMU are increased or preserved. An approach is also introduced to identify extra inputs (maximum reduction amounts in inputs) when the outputs are estimated using the proposed models by Yan et al. [European Journal of Operational Research 136 (2002) 19] and Jahanshahloo et al. [Applied Mathematics and Computation 19 (2003)]. Numeric results are presented for an example taken from the literature.
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Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2004). The outputs estimation of a DMU according to improvement of its efficiency. Applied Mathematics and Computation, 147(2), 409–413.
Abstract: This paper develops the presented method by Yan et al. [Eur. J. Operat. Res. 136 (2002) 19]. In this paper, by using inverse data envelopment analysis model, a method to estimate output levels of a decision making unit is presented when some or all of its input entities are increased and its current efficiency level is improved.
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